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Home > News & Events > Inactive Financial Institution Letters 




Inactive Financial Institution Letters 


[Federal Register: July 25, 1995 (Volume 60, Number 142)]
[Proposed Rules ]               
[Page 38081-38142]
From the Federal Register Online via GPO Access [wais.access.gpo.gov]


      

[[Page 38081]]

_______________________________________________________________________

Part II

Department of the Treasury



12 CFR Part 3

Federal Reserve System



12 CFR Part 208 et al.

Federal Deposit Insurance Corporation



12 CFR Part 325



_______________________________________________________________________



Market Risk-Based Capital Standards and Capital Requirements for Market 
Risk; Proposed Rules


[[Page 38082]]


DEPARTMENT OF THE TREASURY

Office of the Comptroller of the Currency

12 CFR Part 3

[Docket No. 95-19]
RIN 1557-AB14

FEDERAL RESERVE SYSTEM

12 CFR Parts 208 and 225

[Regulations H and Y; Docket No. R-0884]

FEDERAL DEPOSIT INSURANCE CORPORATION

12 CFR Part 325

RIN 3064-AB64

 
Risk-Based Capital Standards: Market Risk

AGENCIES: Office of the Comptroller of the Currency (OCC), Department 
of the Treasury; Board of Governors of the Federal Reserve System 
(Board), and the Federal Deposit Insurance Corporation (FDIC).

ACTION: Joint notice of proposed rulemaking.

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SUMMARY: The Office of the Comptroller of the Currency (OCC), the Board 
of Governors of the Federal Reserve System (Board), and the Federal 
Deposit Insurance Corporation (FDIC) (the Agencies) are proposing to 
amend their risk-based capital requirements to incorporate a measure 
for market risk in foreign exchange and commodity activities and in the 
trading of debt and equity instruments. Under the proposal, banks and 
bank holding companies (institutions) regulated by the OCC, the Board, 
and the FDIC with relatively large trading activities would calculate 
their capital charges for market risk using either their own internal 
value-at-risk model(s) or, alternatively, risk measurement techniques 
that were developed by supervisors. The effect of the proposed market 
risk measure would be that, in addition to existing capital 
requirements for credit risk, certain institutions would be required to 
hold capital based on the measure of their market risk exposure.

DATES: Comments must be received on or before September 18, 1995.

ADDRESSES: Comments should be directed to:
    OCC: Comments may be submitted to Docket Number 95-19, 
Communications Division, Third Floor, Office of the Comptroller of the 
Currency, 250 E Street, S.W., Washington, DC 20219. Comments will be 
available for inspection and photocopying at that address.
    Board: Comments directed to the Board should refer to Docket No.R-
0884 and may be mailed to William W. Wiles, Secretary, Board of 
Governors of the Federal Reserve System, 20th Street and Constitution 
Avenue, N.W., Washington, D.C. 20551. Comments may also be delivered to 
Room B-2222 of the Eccles Building between 8:45 and 5:15 p.m. weekdays, 
or to the guard station in the Eccles Building courtyard on 20th 
Street, N.W. (between Constitution Avenue and C Street) at any time. 
Comments may be inspected in Room MP-500 of the Martin Building between 
9 a.m. and 5 p.m. weekdays, except as provided in 12 CFR 261.8 of the 
Board's rules regarding availability of information.
    FDIC: Written comments should be sent to Jerry L. Langley, 
Executive Secretary, Attention: Room F-402, Federal Deposit Insurance 
Corporation, 550 17th Street N.W., Washington, D.C. 20429. Comments may 
be hand-delivered to Room, F-402, 1776 F Street N.W., Washington, D.C. 
20429, on business days between 8:30 a.m. and 5 p.m. (Fax number 
(202)898-3838; Internet address: comments@fdic.gov). Comments will be 
available for inspection and photocopying in Room 7118, 550 17th 
Street, N.W., Washington, D.C. 20429, between 9 a.m. and 4:30 p.m. on 
business days.

FOR FURTHER INFORMATION CONTACT:
    OCC: Roger Tufts, Senior Economic Advisor (202/874-5070), or 
Christina Benson, Capital Markets Specialist, (202/874-5070) Office of 
the Chief National Bank Examiner. For legal issues, Ronald Shimabukuro, 
Senior Attorney, Legislative and Regulatory Activities Division (202/
874-5090), Office of the Comptroller of the Currency, 250 E Street 
S.W., Washington, D.C. 20219.
    Board: Roger Cole, Deputy Associate Director (202/452-2618), James 
Houpt, Assistant Director (202/452-3358), Barbara Bouchard, Supervisory 
Financial Analyst (202/452-3072), Division of Banking Supervision and 
Regulation; or Stephanie Martin, Senior Attorney (202/452-3198), Legal 
Division. For the hearing impaired only, Telecommunication Device for 
the Deaf, Dorothea Thompson (202/452-3544).
    FDIC: William A. Stark, Assistant Director, (202/898-6972), Kenton 
Fox, Senior Capital Markets Specialist, (202/898-7119), Division of 
Supervision; Jamey Basham, Counsel, (202/898-7265), Legal Division, 
FDIC, 550 17th Street, N.W., Washington, D.C. 20429.

SUPPLEMENTARY INFORMATION: The Agencies are proposing amendments to 
their risk-based capital requirements to incorporate a measure for 
market risk. The proposed amendments would generally apply only to 
institutions that have (1) total assets exceeding $5 billion and either 
on-balance-sheet trading activities representing at least 3.0 percent 
of total assets or a volume of off-balance-sheet trading activities 
with notional amounts exceeding $5 billion, or (2) total assets of $5 
billion or less and a volume of trading activities representing at 
least 10.0 percent of total assets.

I. Background

    The Agencies' risk-based capital standards are based upon the 
principles contained in the agreement on International Convergence of 
Capital Measurement and Capital Standards of July, 1988 (the Accord) 
that was agreed to by the Basle Committee on Banking Supervision (the 
Committee) and endorsed by the central bank governors of the Group of 
Ten (G-10) countries.1 That Accord sets forth a framework for 
measuring capital adequacy under which weighted risk assets are 
calculated by weighting an institution's assets and off-balance-sheet 
items on the basis of their perceived credit risk using a relatively 
small number of risk categories.

    \1\ The Basle Supervisors' Committee is comprised of 
representatives of the central banks and supervisory authorities 
from the G-10 countries (Belgium, Canada, France, Germany, Italy, 
Japan, The Netherlands, Sweden, Switzerland, the United Kingdom, and 
the United States) plus Luxembourg.
---------------------------------------------------------------------------

    By focusing on credit risk, the risk that a loss will be incurred 
due to an obligor or counterparty default on a transaction, the Accord 
generally excludes coverage of risks arising from adverse movements in 
market interest rates, foreign exchange rates, or commodity or equity 
prices. The potential for loss from such movements is referred to as 
market risk. In April 1993, the Committee, recognizing the need to 
incorporate market risk into the risk-based capital standard, requested 
comments on an initial measurement framework. The Agencies' current 
proposal reflects substantial revisions to that 1993 paper and is based 
upon revisions to the Accord that were proposed by the Committee on 
April 12, 1995.2

    \2\ The Committee's document is entitled ``Proposal to Issue a 
Supplement to the Basle Capital Accord to Cover Market Risks'' and 
is available through the Board's and the OCC's Freedom of 
Information Office and the FDIC's Reading Room.
---------------------------------------------------------------------------

    The 1993 paper proposed standardized measurement procedures for 
assessing risks in traded debt, equity, 

[[Page 38083]]
and foreign exchange activities and provided only a limited role for a 
bank's internal model(s) in measuring market risk exposure for 
regulatory capital purposes. These procedures were strongly criticized 
by commenters to the consultative document, especially by institutions 
in the United States. These institutions generally believed that the 
measurement framework was unduly cumbersome and potentially inaccurate, 
especially for institutions with significant and diversified trading 
activities.
    In lieu of the standardized framework, these institutions urged the 
Committee to allow greater use of an institution's internal market risk 
models. They noted that large trading banks have materially expanded 
the sophistication and coverage of their market risk trading models. 
These models are typically described as ``value-at-risk'' (VAR) models, 
which estimate the maximum amount by which an institution's portfolio 
could decline in market value, given a certain level of statistical 
confidence and an assumed holding period. The commenters believed that 
these models would provide a more accurate risk measure and would be 
better able to incorporate new products and activities than would the 
standardized framework. They also believed that imposing a rigid 
supervisory measurement system on institutions would result in 
unnecessary costs and could encourage improper risk management 
practices if institutions sought to minimize the capital requirements 
resulting from the proposed risk measure. Many large European banks 
also urged the use of internal models for measuring market risks for 
regulatory capital purposes, but were generally less critical, in part 
because the European Union had adopted into European law a regime 
similar to the one outlined in the 1993 paper.3

    \3\ The European Union's Second Directive sets forth a capital 
regime for market risk that applies to banking and securities firms 
that operate in EU member countries. These capital requirements 
become effective at the beginning of 1996.
---------------------------------------------------------------------------

    In response to these and other comments and concerns, the Committee 
issued a new proposal on April 12, 1995. In addition to expanding the 
earlier proposal by providing measures for risks in commodities and 
options, this latest proposal would allow institutions to use their 
internal market risk models to measure the level of their market risk 
exposure against which they would be required to hold capital. This 
approach is referred to as the ``internal models approach.'' An 
institution's use of this approach would be subject to the approval of 
its appropriate supervisor and would be contingent upon conformance 
with certain qualitative and quantitative standards regarding the 
measurement and management of market risks. An institution whose 
internal model failed to meet those standards or otherwise failed to 
gain regulatory approval would be required to use standardized risk 
measurement techniques as set forth in the Committee's April 1995 
proposal. This latter approach is referred to as the ``standardized 
risk measure'' approach, as it applies standardized assumptions and 
risk factors to an institution's activities.
    The Agencies are now proposing amendments to their risk-based 
capital standards that are similar to the proposal recently issued by 
the Committee.4 The Agencies would encourage institutions that are 
affected by this proposal, and especially those with large trading 
accounts, to comply with the proposed requirements by using the 
proprietary internal models that they use to manage market risk.

     4 As set forth in the regulatory text, the Agencies 
propose to adopt the market risk requirements as new appendices to 
their capital adequacy standards. The OCC may be required to make 
additional conforming amendments to its risk-based capital 
guidelines.
---------------------------------------------------------------------------

    The Agencies believe that such models should provide a more 
accurate measure of market risk than the standardized risk measure and 
would impose fewer costs and burdens on institutions. By using internal 
models not only for operating purposes, but also as a basis for 
determining capital requirements, institutions should be further 
encouraged to continue their efforts to refine the accuracy of their 
proprietary models, especially with regard to options risk. Given their 
preference for the use of internal models for measuring market risk, 
the Agencies request comments regarding whether institutions should be 
permitted a choice between the two measurement procedures, or only be 
permitted to use internal models.

II. Scope: Activities and Institutions Covered by the Proposal

    This proposal would establish new capital requirements for general 
market risk and specific risk as they pertain to the trading activities 
of a banking organization and to the organization's other foreign 
exchange and commodities activities. As such, the proposed standard, by 
creating a risk-based capital ratio adjusted for market risk through 
the addition of a market risk-equivalent assets measure, is an 
integrated supplement to existing standards that address credit risk 
through the current weighted-risk assets measure.
    For purposes of this proposal, general market risk refers to 
changes in the market value of the covered transactions that arise from 
broad market movements, such as changing levels of market interest 
rates, broad equity indices, or currency exchange rates. Specific risk 
includes the credit risk of an issuer of a traded security, as well as 
other factors that affect the market value of specific instruments, but 
that do not materially alter broad market conditions. Consequently, 
instruments other than over-the-counter (OTC) derivatives that are 
covered by this proposal would, in effect, be removed from and no 
longer subject to the credit risk standard previously established. OTC 
derivatives would remain subject to the counterparty credit risk 
requirements set forth in the existing risk-based capital standard.
    This proposal defines trading activities as the sum of all trading 
assets and liabilities as reported in the quarterly Consolidated 
Reports of Condition and Income (call report) and would apply on a 
fully consolidated basis to all national banks, state member banks, and 
bank holding companies that meet the following criteria:
    (1) The institution has total assets exceeding $5 billion, and (a) 
the gross sum of trading assets and liabilities on a daily average 
basis for the quarter account for 3.0 percent or more of total assets, 
or (b) the sum of the notional amount of interest rate, foreign 
exchange, equity and commodity off-balance-sheet derivative contracts 
relating to trading activities exceeds $5 billion, or
    (2) The institution has total assets of $5 billion or less and 
trading assets and liabilities exceed 10 percent of total assets.
    The Agencies may also apply the standard to other institutions for 
safety and soundness purposes in limited circumstances and on a case-
by-case basis.

III. Definition of Capital and the Capital Requirement

    The Agencies are also proposing to expand the definition and types 
of qualifying capital that an institution could use to meet its market 
risk capital requirements. This modification and others require that 
the procedures for calculating an institution's overall risk-based 
capital ratio be changed.
    Definition of capital. The Accord permits institutions to meet 
regulatory capital requirements with a combination of ``core'' (Tier 1) 
and ``supplementary'' 

[[Page 38084]]
(Tier 2) capital. Tier 1 includes equity, noncumulative perpetual 
preferred stock, and minority interest in consolidated subsidiaries, 
less goodwill, while Tier 2 includes the allowance for loan and lease 
losses, other preferred stock, and subordinated debt that has an 
original weighted average maturity of at least five years.5

    \5\ Bank holding companies may include cumulative perpetual 
preferred stock in Tier 1 capital, subject to the conditions that 
are specified in the Board's capital guidelines.
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    This proposal would permit institutions to use a third tier of 
capital (Tier 3), consisting of short-term subordinated debt. However, 
this capital could be used only to meet capital requirements pertaining 
to market risk and only if that debt meets certain qualifying 
conditions: It must have an original maturity of at least two years, be 
unsecured and fully paid up, and subject to a lock-in provision that 
prevents the issuer from repaying the debt even at maturity if the 
issuer's capital ratios are, or with repayment would become, less than 
the minimum 8.0 percent risk-based capital requirement.
    The agencies are proposing to allow the use of Tier 3 capital in 
recognition that such short-term subordinated debt can help to protect 
depositors and the Bank Insurance Fund against loss. Indeed, because 
the underwriting activities of securities firms often create volatile 
capital requirements, securities regulators in many countries permit 
their institutions to treat such debt as capital, with similar 
qualifications. The Agencies, however, believe that Tier 1 instruments 
should remain a substantial proportion of an institution's total 
capital and, therefore, propose the following constraints:
    (1) Tier 3 capital may not exceed 250 percent of the amount of Tier 
1 capital allocated for market risk, and
    (2) Tier 1 capital must represent at least 50 percent of an 
institution's total eligible capital--the sum of Tier 1, qualifying 
Tier 2, and Tier 3 to the extent it is permitted in item (1), above.
    Note that any element of Tier 2 capital must continue to conform 
with the requirements of the original Accord; that is, Tier 2 may not 
exceed total Tier 1 capital, and long-term subordinated debt may not 
exceed 50 percent of Tier 1.
    Calculation of the capital ratio. An institution subject to this 
proposal would remain subject to the Agencies' risk-based capital 
standards based on credit risk, but would also be required to 
supplement its risk-based capital ratio to adjust it for market risk. 
Under the proposal, an institution would accomplish this by multiplying 
its capital requirement for market risk (as calculated by the internal 
model or standardized approach) by 12.5 (the reciprocal of the minimum 
capital ratio of 8.0 percent) and adding the resulting market risk 
equivalent figure to its weighted risk assets, as calculated by the 
credit risk standard. The institution's Tier 1 and total risk-based 
capital ratios would be calculated as the sum of the eligible capital 
as a percent of the sum of market risk-equivalent assets and weighted 
risk assets. This approach avoids the distortions that could result 
from allocating the necessary capital to either market or credit risk 
and then calculating an institution's capital ratio on the basis of the 
remaining capital. It also incorporates the risk-based capital ratio 
adjusted for market risk into the capital category definitions under 
the Agencies' prompt corrective action regulations.
    Due to the 250 percent constraint on Tier 3 capital, an institution 
that wishes to use Tier 3 capital must first calculate its minimum 
credit risk requirement to determine the amount of Tier 1 capital that 
is available to support market risk. This amount sets an upper limit on 
the amount of Tier 3 capital that the institution may have. In 
calculating its aggregate capital ratio, however, only that portion of 
Tier 3 that is actually needed to meet its market risk requirement may 
be included as eligible capital. Tier 3 capital in excess of this 
amount will not be considered as eligible capital as it is not 
permitted to meet credit risk. Eligible capital would be the sum of the 
whole of the institution's Tier 1 capital, plus all of its Tier 2 
capital under the limits imposed in the credit risk Accord, and Tier 3 
capital subject to the above restrictions. The quoted ratio will thus 
represent capital that is available to meet both credit risk and market 
risk.6

    \6\ For example, if an institution had $120 of Tier 1 capital, 
of which $100 was needed to meet its minimum 8.0 percent risk-based 
capital standard for credit risk, only $20 would be available for 
market risk. That $20, in turn, would ``support'' as much as $50 of 
Tier 3 capital ($20 X 250%) for purposes of meeting the capital 
requirement for market risk. If the market risk capital requirement 
were $50, the institution could count only $30 of Tier 3 capital as 
eligible capital in calculating its regulatory capital requirements.
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IV. Partial Models

    With supervisory approval, institutions whose internal models do 
not cover all elements of their trading activities may use components 
of the alternative standardized approach to measure market risks for 
risk-based capital purposes. Such combinations, however, should be 
limited to situations in which the institution is in the process of 
developing and implementing the internal models approach for all of its 
trading activities and would be permitted only on a temporary basis. In 
addition, the combination of approaches used should be consistent with 
the method the institution uses in managing its risks. For example, if 
an institution has a comprehensive value-at-risk model for its interest 
rate exposures in its trading portfolio but not for its equities 
exposures, the agencies would expect the institution to use the 
standardized measure for equities and the internal model for interest 
rate exposures. These conditions are designed to prevent institutions 
from selecting the lower of alternative risk measures and are also 
intended to encourage institutions to develop and improve their risk 
measurement and management practices.
    When combinations of the two risk measurement techniques are used, 
the institution should measure a complete risk category using a single 
approach and not mix techniques within a given category of risk. For 
this purpose, the risk categories are defined as interest rates, 
foreign exchange, equity prices, and commodity prices. Moreover, once 
an institution adopts a comprehensive value-at-risk model that is 
acceptable, it may not revert to the standardized risk measure, except 
in unusual circumstances and only with supervisory consent. The 
proposal provides some flexibility for de minimis positions, activities 
in remote locations, in minor currencies, or in activities that present 
negligible risk to the institution.

V. Internal Models Approach

    The Agencies believe that an institution's market risk can be most 
accurately measured using detailed information available only to the 
institution and processed by its own proprietary risk measurement 
model(s). Accordingly, the Agencies would encourage all institutions--
especially those with significant trading activities--to pursue this 
approach. To be most reliable, however, the modelling process must be 
fully integrated into the institution's broader procedures for managing 
risk and must be actively supported by senior management. It must also 
conform with other specific qualitative and quantitative standards that 
the Agencies believe are necessary in order to achieve an adequate 
level of rigor and consistency in a capital standard. Under this 
proposal, institutions that plan to use internal models in calculating 
their capital requirements for market risk 

[[Page 38085]]
would need to contact their appropriate supervisor and make 
arrangements for having their models validated for regulatory capital 
purposes.

Modelling Market Risk

    In order to measure exposures when evaluating trading risks, many 
institutions calculate the ``value-at-risk'' (VAR), representing the 
maximum amount by which the market value of their trading portfolios 
could decline during a specific period of time and with a certain 
degree of statistical confidence. For example, at the close of business 
on day one a bank might calculate its VAR to be $10 million, indicating 
that it has only some small chance of losing more than that amount on 
its existing holdings, if they were held through the end of day two. 
Most institutions use this measure as a management tool for evaluating 
their trading positions, limits, and strategies. By measuring the risk 
daily, management can quickly revise its positions, limits and 
strategies as market conditions change.
    A value-at-risk model requires a variety of inputs: (1) Accurate 
and timely information about the institution's trading positions, (2) 
information about past movements of relevant market prices and rates, 
and (3) several key measurement parameters, such as the length of the 
historical period for which market changes are observed (observation 
period), management's required level of confidence, and the assumed 
holding period for which the value of current trading positions may 
change. When evaluating their current positions and estimating future 
market volatility, institutions typically use a series of ``market risk 
factors'' that they have determined affect the value of their positions 
and the risks to which they are exposed. These factors, in turn, can be 
grouped into four categories, depending on the nature of the underlying 
risk: interest rates, exchange rates, and equity and commodity prices, 
with related options volatilities included in each risk factor 
category.
    Having determined which risk factors to use, an institution 
estimates the potential future volatility of the factors. Most often 
this calculation is based on the past movements of these factors over 
some specified time horizon, with some institutions using long 
historical time periods and others focusing on more recent market 
behavior. However derived, the estimates of potential market movements 
are combined with current position data to calculate an estimate of the 
potential loss that may arise from those positions for a specified 
holding period. Just as institutions use different historical time 
periods when computing possible changes in market risk factors, they 
also use different confidence levels to estimate potential losses. Some 
institutions use a 90 or 95 percent confidence level (one-tail), while 
others use a higher level of statistical confidence.
    Institutions also use different modelling procedures in calculating 
their market risk exposures. The most common models are based upon 
variance/covariance methodologies, historical simulations, or Monte 
Carlo simulation techniques. In the case of the variance/covariance 
approach, the change in value of the portfolio is calculated by 
combining the risk factor sensitivities of the individual positions--
derived from valuation models--with a variance/covariance matrix based 
on risk factor volatilities and correlations. An institution would 
calculate the volatilities and correlations of the risk factors on the 
basis of the holding period and the observation period. Value-at-risk 
is determined according to the desired level of statistical confidence.
    Using historical simulations, an institution would calculate the 
hypothetical change in value of the current portfolio in the light of 
actual historical movements in risk factors. This calculation is done 
for each of the defined holding periods over a given historical 
measurement horizon to arrive at a range of simulated profits and 
losses, and the confidence level, again, determines the value-at-risk.
    Monte Carlo techniques also consider historical movements, but only 
to determine the probability of particular price and rate changes. 
Using these probabilities, the institution would then construct a large 
number of theoretical movements to evaluate the range of its 
portfolio's potential market values and identify the maximum loss 
consistent with the necessary confidence level.

Proposed Modelling Constraints

    The Agencies recognize that institutions have adopted different 
assumptions and measurement techniques in their internal market risk 
models and that such differences often reflect distinct business 
strategies and approaches to risk management. In developing a framework 
for the use of internal models for regulatory capital purposes, the 
Agencies believe that some constraints should be placed on model 
parameters and assumptions. Such restrictions would help to ensure that 
prudential capital levels are maintained and that institutions with 
similar risk exposures have similar capital requirements.
    Since institutions use VAR to guide them in setting trading limits, 
rather than for evaluating capital adequacy, they set their model 
parameters to address normal conditions. Indeed, the models are 
designed to ensure that actual trading results often exceed the 
projected levels so that management is better able to evaluate the 
model's predictive accuracy and to respond to events that generate 
unexpectedly large gains or losses. During a given year, for example, a 
model based on a 90 percent confidence level (one tail) could be 
expected to underestimate actual trading losses more than 20 times.
    Moreover, knowing that a day's trading results could be expected to 
exceed the VAR ten percent, five percent, or even only one percent of 
the time, says nothing about the magnitude by which the VAR might be 
exceeded. The probabilities of VAR models cannot be extended to 
estimate the size of a highly unlikely event because most models assume 
that market movements are distributed normally. While that assumption 
may be adequate for a model's intended purpose, it permits the model to 
greatly understate the likelihood of a large loss. For example, 
assuming a normal distribution, the likelihood of experiencing a four 
standard deviation event is approximately 3 in 100,000--in trading 
terms, about once in 130 years. In practice, however, such unusual 
market movements are seen in most major markets on average almost every 
year.7

    \7\ Daily rate or price movements of a half-dozen major 
currencies and U.S. Treasury maturities and of several U.S. equity 
indices each moved by at least four standard deviations on average 
about once a year during the period 1977-1994. The drop in the value 
of the S&P 500 index on October 19, 1987 represented a 20 standard 
deviation event in terms of daily price movements.
    These conditions require that regulators impose some constraints or 
other adjustments to the VAR figure that each institution derives in 
order to provide the rigor and consistency that a capital requirement 
demands. At the same time, the Agencies want to minimize the costs and 
dislocations to an internal modelling system that external constraints 
could create and have sought to balance these conflicting objectives 
through a combination of qualitative and quantitative constraints.

Qualitative Standards

    The qualitative standards are designed to ensure that institutions 
using internal models have market risk management systems that are 
conceptually sound and implemented 

[[Page 38086]]
with integrity.8 The internal risk measurement model should be 
closely integrated in the daily risk management process and serve as a 
basis for reporting of risk exposures to senior officers. Institutions 
should have, for example, highly trained personnel who can evaluate the 
adequacy of the risk models and who are organizationally independent of 
personnel responsible for executing trades. These individuals should 
compare actual daily trading gains and losses with VAR figures 
generated by the model as part of their on-going evaluations of the 
modelling process. At least annually, internal auditors should assess 
the institution's overall process for managing and measuring trading 
risks.

    \8\ With respect to the qualitative standards, the OCC is 
planning to provide additional guidance through supplementary 
banking issuances.
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    Notwithstanding the use of VAR as a basis for a regulatory capital 
charge, institutions should also routinely evaluate their exposures to 
highly stressful events, selected to identify the circumstances to 
which their particular trading portfolios are most vulnerable. Such a 
program of stress testing supplements the capital standard and 
illustrates management's commitment to evaluating trading risks fully.
    The stress testing process, along with other relevant internal 
policies, controls, and procedures, should be well documented and 
available for examiners to review. Examiners will need this 
information, as well as comparisons of VAR measures with actual daily 
trading results, to judge the acceptability of the institution's model 
on an initial and periodic basis. Under the proposal, if key management 
procedures are missing or weak, or if the integrity of a model is 
questionable, the appropriate supervisor may either disallow the model 
for regulatory capital purposes or require capital above the minimum 
specified in the proposal. The latter may be done by increasing the 
size of the multiplier that would be applied to an institution's VAR 
(discussed below under ``Capital Requirement''). Typically, the 
Agencies would expect to see any management or modelling shortcomings 
addressed and the risk measure improved, rather than seek to resolve 
the matter by applying a larger multiplier to a marginally satisfactory 
or questionable modelling or management approach.

Quantitative Standards

    Whereas the qualitative standards focus on the integrity of the 
modelling process and incorporate standards of sound practice, the 
quantitative standards are designed to develop a prudential capital 
requirement by addressing the level of rigor in an institution's models 
and the consistency of model parameters among institutions. The 
Agencies have sought to minimize the quantitative constraints and to 
make those that were deemed necessary as compatible as practicable with 
existing procedures of institutions. The Agencies recognize, however, 
that some of these standards may require an institution to make certain 
modifications to its internal model when using it for computing 
regulatory capital requirements. The Agencies propose that an 
institution that elects to use the internal model approach be subject 
to the following standards for its internal model:
    (1) Value-at-risk should be computed each business day and should 
be based on a 99 percent (one-tailed) confidence level of estimated 
maximum loss.
    (2) The assumed holding period used for the VAR measure must be 10 
business days, although for positions that display linear price 
characteristics (not options, which display nonlinear characteristics) 
the institution may use results based on one-day periods, increased to 
ten days by multiplying by the square root of time.9

    \9\ For example, one can estimate the ten day price volatility 
of an instrument by multiplying the volatility calculated on one-day 
changes by the square root of ten.
---------------------------------------------------------------------------

    (3) The model must measure all material risks incurred by the 
institution, although no specific type of model is prescribed.
    (4) The model may utilize historical correlations within broad 
categories of risk factors (interest rates, exchange rates, and equity 
and commodity prices), but not among these categories. That is, the 
consolidated value-at-risk is the sum of the individual VARs measured 
for each broad category.
    (5) The non-linear price characteristics of options must be 
adequately addressed, both by ensuring that the model incorporates 
potential non-linear price behavior and by evaluating actual minimum 10 
day holding periods, rather than multiplying the results based on one-
day periods by the square root of time. The volatility of the rates and 
prices (vega) underlying the options must also be included among the 
risk factors.
    (6) The historical observation period used to estimate future price 
and rate changes must have a minimum length of one year. The Agencies 
request specific comment on whether they should also require 
institutions to calculate their exposures using a shorter observation 
period (e.g. less than 6 months), with the capital requirement based on 
the higher result.
    (7) Data must be updated no less frequently than once every three 
months and more frequently if market conditions warrant.
    (8) Each yield curve in a major currency must be modeled using at 
least six risk factors, selected to reflect the characteristics of the 
interest rate sensitive instruments that the institution trades. The 
model must also take account of spread risk.
    Several of these constraints warrant a discussion of their 
underlying rationale:
    Minimum holding period (and issues regarding options). Typically, 
longer holding periods lead to larger expected price changes and, 
consequently, to larger measures of risk. When estimating risk in 
trading activities for management purposes, most institutions assume 
only a one-day holding period, since trading decisions are made 
constantly, and some instruments are held for only minutes or hours. 
This approach may be fully satisfactory for day-to-day management 
purposes but seems less appropriate when designing a prudent capital 
standard.
    In periods of market turmoil, when an institution's capital is most 
needed, many financial instruments could become unexpectedly illiquid, 
as market participants become less willing to accept market risk. One 
method of increasing the rigor of the risk measure and addressing an 
unexpectedly large price change that could result from a decline in 
market liquidity would be to assume a longer holding period. The 
proposed requirement that institutions use a 10-day holding period does 
not imply that the Agencies would expect them to plan for that 
eventuality. Indeed, some positions, such as those involving spot 
foreign exchange contracts, will mature and settle within that time 
frame and could not be held for 10 days, in any event. Therefore, in 
this context, the 10-day period should be viewed simply as a way of 
producing a more stressful market shock by assuming an instantaneous 
price movement of a size that one would normally expect to witness only 
over the longer period of time.
    However, in order to minimize modelling costs and recognize the 
linear nature of price movements of many financial instruments, the 
Agencies would permit institutions to estimate a 10-day price or rate 
movement--for instruments other than options--using the risk factor 
changes calculated on the basis of one-day holding periods. This 
adjustment could be accomplished using the ``square root of time'' 
method 

[[Page 38087]]
by multiplying the one-day results by 3.16 (the square root of ten 
trading days).
    The prices of options, however, do not change proportionately with 
the price of the underlying instrument, and their potential price 
volatility cannot be so easily estimated. Therefore, institutions would 
be required to take steps to identify the non-linear behavior of option 
prices with respect to changes in underlying rates or prices. In 
addition, institutions would not, for example, be allowed to scale the 
price volatility of an option that was based on one-day sensitivities 
using the square root of ten. However, since the price or rate 
volatility of the instrument on which the option is based is considered 
to increase proportionately with the square root of time, institutions 
would be permitted to use the square root of time technique to expand 
the one-day volatility of the option's underlying instrument when 
calculating the price volatility of the option itself. Alternatively, 
institutions could estimate the changes in the value of options on the 
basis of actual movements in underlying factors measured during a full 
10-day period.
    Institutions should also evaluate the effect of changes in the 
volatility of rate or price movements of instruments underlying their 
option positions (vega) on option values. This can be done by modelling 
volatilities as additional risk factors and including them in the 
overall set of risk factors affecting the value of the institution's 
trading positions. Institutions with relatively large or complex 
options portfolios should also measure volatilities across different 
points along the maturity yield curve.

Aggregating Exposures

    When evaluating the potential change in a portfolio's market value, 
one must consider the likelihood that prices of certain instruments in 
the portfolio may move together (or in opposite directions). However, 
observed correlations among the prices of some instruments are 
themselves volatile and may be especially likely to change during 
periods of market stress. Therefore, which assumptions are prudent and 
which ones are not cannot be determined in advance. Moreover, one 
correlation assumption is not always more conservative than another, 
since the outcome depends on whether an institution's position in a 
given instrument is long or short. In practice, most models calculate 
the correlations within risk factor categories, but differ in their 
recognition of historical correlations across broad categories of risk 
factors (interest rates, foreign exchange, etc.).
    The Agencies do not want to specify correlations or to set 
standards for what levels of correlations could be recognized by a 
model. Given the importance--but also the uncertainty--of historical 
correlations, the Agencies propose to permit institutions to use 
correlations within categories of risk factors, but not among 
categories, where the interrelationships of market factors may be more 
tenuous, especially during periods of market stress.10 Thus, total 
VAR would be the simple sum of the calculated VAR for individual 
categories. The Agencies recognize that this approach is conservative 
and believe that it is appropriate for a capital charge against market 
price moves during periods of stress, when historic correlations have 
been observed to breakdown. The Agencies also note that it is 
consistent with the risk measurement practices of many large trading 
banks.

    \10\ Use of correlations is permitted provided the supervisor is 
satisfied that the calculation of correlations within a category is 
performed with integrity.
---------------------------------------------------------------------------

Minimum Observation Period

    In managing market risk, institutions draw from a broad range of 
historical periods to calculate historical volatilities and 
correlations for the purpose of estimating future price and rate 
movements. Some institutions use periods as short as 30-60 days, while 
others use periods extending as long as several years. Although the 
choice of historical periods may have little effect on a trading 
portfolio's level of expected VAR over an extended period of time, it 
can have a significant effect on the measure of exposure at any 
specific time. VARs based on short historical periods will be more 
volatile and responsive to changing market conditions than measures 
based on longer periods, producing relatively large VARs during periods 
of high market volatility and low VARs when the markets are calm. 
Conversely, VARs based on longer periods will exhibit more stability, 
reflecting a wider range of market conditions and the smaller effect of 
recent observations.
    Since VARs based on short periods may, at times, produce small 
estimates of risk and could also produce a wide range of risk measures 
among institutions having similar portfolios, the Agencies are 
proposing a minimum historical observation period of one year. That 
constraint should reduce the dispersion and help ensure that 
institutions have adequate capital requirements at all times. While the 
Agencies believe such a one-year constraint may be sufficient, they are 
also requesting comment on whether institutions should be required to 
calculate their exposures using two observation periods--one as 
constrained above and the other representing a shorter period, such as 
six months or less. Under this dual observation approach, the capital 
requirement would be based on the period that indicated the greater 
risk.

Minimum Number of Risk Factors

    The risk factors contained in an institution's market risk 
measurement system should be sufficiently comprehensive to capture all 
of the material risks inherent in the portfolio of its on- and off-
balance sheet trading positions, including interest and exchange rates, 
equity and commodity prices, and the volatilities related to option 
positions. Although institutions will have substantial flexibility in 
specifying the risk factors that are most relevant to their portfolios, 
the Agencies expect the number and composition of factors to be 
commensurate with the nature and scope of each institution's risks.
    In order to adequately measure exposures to interest rates and to 
bring about greater conformity of results among institutions, the 
Agencies are proposing a minimum of six maturity bands (each 
representing a separate risk factor) to be used for material positions 
in the major currencies and markets. All institutions would be expected 
to measure spread risk (e.g., the difference between rates on corporate 
and U.S. government instruments) adequately, with the required level of 
sophistication being a function of the nature and scope of the 
institution's activities and exposures.

Capital Requirement

    Experience has shown that financial markets can have brief periods 
of high volatility preceded or followed by extended periods of calm. 
Under some modelling procedures, the large number of small daily market 
changes can substantially offset the infrequent periods of high 
volatility. Even when constrained and calculated as proposed, there are 
several reasons why an institution's need for capital might sometimes 
exceed this figure:
    (1) The past is not always a good guide to the future;
    (2) The assumptions about statistical ``normality'' built into some 
models may not be justified because of the relatively high frequency of 
large market movements; 

[[Page 38088]]

    (3) The correlations assumed in the model may prove to be 
incorrect;
    (4) Market liquidity may become inadequate to close out positions; 
and
    (5) The institution may face multiple stressful events over short 
periods of time.
    Consequently, the Agencies believe that in order for an 
institution's VAR figure to serve as an adequate basis for a capital 
requirement, it should be multiplied by an appropriate prudential 
factor. The Agencies are proposing a minimum multiple of three, which 
could be increased if the results of ``back-testing'' are not 
sufficiently satisfactory.11

    \11\ Back-testing refers to the process of comparing calculated 
daily VARs with actual daily trading results to determine how 
effectively the risk measure identified the boundaries of gains or 
losses consistent with the predetermined level of statistical 
confidence.
---------------------------------------------------------------------------

    The Agencies also recognize that institutions may change their 
trading positions rapidly and may substantially increase their 
exposures for brief periods in order to respond to perceived 
opportunities or market conditions. At such times, an institution's 
exposure to market risk may be larger than its average VAR times three. 
In order to address such circumstances, the Agencies are proposing that 
institutions maintain capital on a daily basis to support the larger of 
either (1) the average VAR figure for the last 60 business days, 
calculated under the proposed criteria and increased by the assigned 
multiple, or (2) the previous day's VAR, similarly calculated but 
without the multiple. By considering not only an average VAR but also a 
single day's measure, the Agencies expect institutions to hold capital 
sufficient to cover peak levels of market volatility and to manage 
their activities accordingly.
    Many VAR models focus principally on measuring general market risks 
and incorporate only partial elements of specific risk. Therefore, 
institutions would remain subject to separate capital requirements to 
cover specific risk on equities and traded debt, to the extent it is 
not addressed by their VAR models. This separate charge would be added 
after the VAR figure is increased by the multiplier and would, in no 
case, be less than one-half the specific risk charge calculated using 
the standardized approach. The Agencies specifically request comments 
on which features to consider when reviewing models in order to 
evaluate their coverage of specific risk.

VI. Standardized Risk Measure

    The standardized risk measure calculates separate capital 
requirements for specific and general market risks and uses different 
techniques to measure an institution's risk exposure, depending upon 
its source: debt instruments, equities, foreign currencies, and 
commodities, including their respective options.12

    \12\ Several techniques are offered for measuring the price risk 
in options (see ``Options'', discussed below or in the proposed 
regulatory language for each agency). Under one approach, called the 
``delta-plus'' approach, an institution would include the delta-
equivalent value of the underlying instrument when evaluating the 
market risk of each category of instruments (debt, equity, etc.). 
Under the two other approaches, the underlying instrument of an 
option may be ``carved-out'', not subject to the prescribed risk 
measure for the underlying, and evaluated together with its option 
according to the procedures described for options.
---------------------------------------------------------------------------

Debt instruments held in trading portfolios

    The market risk capital requirement for debt instruments in a 
trading account consists of separate charges for general market and 
specific risks.
    a. General market risk. The general market risk capital requirement 
for debt instruments (including off-balance-sheet derivatives) that are 
part of trading activities is designed to capture the potential loss 
that may arise from movements in market interest rates. An institution 
may determine this component of its capital requirement either by using 
standardized risk weights that approximate the price sensitivity of 
various instruments or by calculating, itself, the precise duration of 
each instrument, weighted by a specified change in interest rates.
    Both methods use a maturity-ladder approach that employs a series 
of time bands and zones, designed to take into account differences in 
price sensitivities and interest rate volatilities across various 
maturities. Under either method, the institution's capital charge for 
general market risk would be the sum of a base charge that results from 
fully netting various risk-weighted positions (i.e., longs versus 
shorts) and a series of additional charges (add-ons) that effectively 
disallow part of the previous full netting in order to address basis 
and yield curve risk. The capital charges would be separately computed 
for each currency in which an institution has significant positions. No 
netting of positions or charges would be allowed across different 
currencies.
    When using the first approach, referred to as the ``maturity'' 
method, an institution would first distribute its on- and off-balance-
sheet positions in each currency among a range of time-bands based on 
the maturity or nearest interest rate reset date of the instrument. 
Long positions would be treated as positive amounts and short positions 
would be treated as negative amounts. The institution would then 
calculate its net long or short position for each time-band and would 
multiply that net position by the risk weight provided by the 
supervisor for that time-band. The resulting risk-weighted position 
represents the amount by which the market value of that debt position 
is expected to change for a specified movement in interest rates. The 
risk weights and associated interest rate changes are shown in each 
Agency's proposed regulatory language (OCC--Table 2, Board--Table I, 
and FDIC--Table 1).13 Adding the sum of all risk-weighted 
positions (long or short) across all time-bands results in a final net 
risk-weighted position. This amount would be the base capital charge 
for general market risk.14

    \13\ In the case of securities backed by fixed rate mortgages, 
an institution would slot the instruments into time bands on the 
basis of their current expected weighted average lives (reflecting 
the effect of expected prepayments at current market interest 
rates), rather than by their contractual maturities.
    \14\ Since the price sensitivity of zero coupon and low coupon 
instruments can be materially greater than that of instruments with 
higher coupons, institutions would be required to assign higher risk 
weights to low coupon instruments as shown in the proposed Tables.
---------------------------------------------------------------------------

    The base charge is calculated differently under the second, or 
alternative ``duration'' method. In this case, an institution would 
calculate the estimated price movement for a specific instrument by 
multiplying the instrument's modified duration by a specified interest 
rate shock that is based on the instrument's duration as shown in the 
proposed regulatory language.15 That product, representing the 
amount of expected price change of the instrument, is then distributed 
into the array of time-bands on the basis of the instrument's duration 
(see proposed Table 4--OCC, Table III--Board, Table 3--FDIC). For 
example, an instrument with a maturity of 4 years and 3 months might 
have a modified duration of 3.5 years. Based on its duration, it would 
be ``shocked'' by 75 basis points, resulting in an expected price 
change of 2.625 percent (3.5  x  0.75 percent). That estimated 2.625 
percent change, multiplied by the current value of the instrument, 
would be placed into the 3.3 to 4.0 year time-band for 

[[Page 38089]]
determining the charge for general market risk.

    \15\ The duration of an instrument indicates its approximate 
percentage change in price for a small parallel shift in the yield 
curve assuming that its cash flow does not change when the yield 
curve shifts.
---------------------------------------------------------------------------

    As in the maturity method, the base capital charge for general 
market risk is the sum of the estimated price changes across all time 
bands. If that sum is negative, the base charge would be its absolute 
value. Different time-bands are used for the two methods because an 
instrument's duration can be substantially different from its maturity.
    In addition to the base capital charge for general market risk, as 
reflected by the institution's net risk-weighted position, an 
institution would be subject to a series of capital ``add-ons'' that 
are designed to take into account imperfect and uncertain correlations 
among instrument types and maturities. These add-ons recognize that 
long and short positions might not, in practice, offset each other by 
the full amount that their risk-weightings would suggest, and 
therefore, some portion of the hedged or offsetting position should be 
disallowed.
    The first disallowance (referred to as the vertical disallowance) 
is intended to address the basis risk that exists between instruments 
with the same or similar maturities and also the possibly different 
price movements that may be experienced by different instruments within 
the same time-band due to the range of maturities (or repricing 
periods) that may exist within a time-band. To capture this risk, a 
vertical disallowance is applied to the smaller of the offsetting (long 
or short) positions within a time-band.16 This disallowance is 10 
percent under the maturity method, and 5 percent under the duration 
method. For example, under the maturity method, if the sum of weighted 
long positions within a time-band equals $100 million and the sum of 
weighted short positions equals $90 million, the vertical disallowance 
for the time-band would be 10 percent of $90 million, or $9 million. 
This amount would be added to the institution's base capital charge. 
The use of two different vertical disallowances recognizes that because 
the duration method takes into account an instrument's specific 
characteristics (maturity and coupon), there is less opportunity for 
measurement error.17

    \16\ If the offsetting amounts (long and short) are equal, the 
disallowance can be applied to either figure.
    \17\ In the case of cash positions and transactions conducted on 
an exchange (e.g. futures) an institution has the opportunity to 
adjust its market risk either by acquiring a new position or selling 
an existing one. However, that is not typically the case with 
interest rate swaps, for which an institution almost always adjusts 
its position by entering into a new or offsetting swap, rather than 
by selling or unwinding one that it already holds. This procedure, 
required partly because of the lack of standardization in the terms 
and credit risk characteristics of swaps, can produce large swap 
portfolios and potentially large disallowances under the 
standardized approach.
    Consequently, the Agencies' proposal would allow institutions 
with large swap books to use alternative procedures for calculating 
the amounts that would be distributed into the maturity or duration 
time bands. One approach would be to convert the payments required 
by a swap into their present values using zero coupon yields and 
then to place those amounts into their appropriate time bands using 
the procedures that apply to zero (or low) coupon bonds. The net 
amounts for each time band would then be weighted and subject to the 
disallowances of the general market risk framework as if they were 
bonds. The Agencies would also consider other procedures.
---------------------------------------------------------------------------

    The second disallowance (or horizontal disallowance) addresses the 
risk that interest rates along the yield curve are not perfectly 
correlated and that risk-weighted positions that might have been 
expected to offset will not fully offset, in practice. The horizontal 
disallowance applies to the smaller of the offsetting positions across 
different time-bands. The amount of this disallowance varies in size by 
zone (that is, a grouping of contiguous time bands), with greater 
netting allowed for positions in different time bands but within the 
same zone than is allowed for positions that are in different zones 
(Table 3--OCC, Table II--Board, Table 2--FDIC in the proposed 
regulatory language). The horizontal disallowances range from 30 
percent to 100 percent of the smaller figure in a pair of offsetting 
transactions.18

     18 Since the disallowance is applied to only one side of an 
offsetting transaction, a 100 percent disallowance effectively 
treats the hedge as being 50 percent effective.
---------------------------------------------------------------------------

    In calculating these disallowances, an institution would first 
determine its offsetting positions within a zone and the associated 
``within zone'' disallowance amounts. Once the institution has netted 
its positions within a zone, it would determine the amount of 
offsetting and associated disallowances across zones. An institution's 
general market risk requirement for debt instruments within a given 
currency would be the sum of (1) the value of its net risk-weighted 
position (base charge) and (2) all of its vertical and horizontal 
disallowances.
    b. Specific risk. Under the proposal, generally every traded 
security, whether long or short, would be assessed a capital charge for 
specific market risk. In the debt portfolio this charge is based on the 
identity of the obligor and, in the case of corporate securities, on 
the credit rating and maturity of the instrument. Consistent with the 
original Accord, debt instruments of national governments of OECD 
countries are assigned zero specific risk. Other securities are 
assigned risk weights ranging from 0.25 percent to 1.6 percent if they 
are issued by qualifying borrowers. Securities of nonqualifying issuers 
are charged a specific risk of 8.0 percent. To be considered as 
qualifying, the security must be rated as investment grade by at least 
two nationally recognized credit rating firms or, if the issuer has 
securities listed on a recognized stock exchange, it must be deemed to 
be of comparable investment quality by the reporting institution.
    This latter condition is provided to accommodate the fact that in 
some countries credit ratings and the coverage of credit rating firms 
are not as extensive as in the United States. Consequently, the 
securities of many large and well-established foreign companies may not 
be rated. In such cases, a company's listing on an organized exchange 
may be an acceptable substitute for credit ratings if such listings are 
limited to financially strong and well-established firms. In these 
cases, and in the absence of independent credit ratings, the securities 
of a listed company may qualify for a lower capital charge if the 
trading institution and its appropriate supervisor believe the 
securities are equivalent to investment grade. However, the Agencies 
are proposing that, given the presence and wide coverage in the United 
States of credit rating firms, institutions would not be allowed to 
qualify the securities of a U.S. firm on the basis of a listing on an 
organized exchange.
    During the examination process, the Agencies would also consider 
the extent to which an institution trades non-investment grade 
instruments (sometimes called high yield debt) that do not qualify for 
risk weights less than 8.0 percent because of the lack of investment 
grade ratings. If these holdings are not well diversified or if they 
otherwise represent material exposures to the institution, the Agencies 
may prevent an institution from netting the exposures arising from 
these instruments with otherwise offsetting exposures resulting from 
positions in qualifying instruments.

Equities Held in Trading Portfolios

    The standardized measure of market risk in traded equities also 
consists of separate charges for specific and general market risk. 
These charges would apply not only to direct holdings of equity 
securities, but also to equity derivatives and off-balance-sheet 
positions whose market values are directly affected by equity prices.
    a. General market risk. An institution's general market risk 
capital charge would be 8.0 percent of its net 

[[Page 38090]]
equity position--the difference between the sum of its long and the sum 
of its short positions. The net long or short position against which a 
general market risk charge would be assessed must be calculated on a 
market-by-market basis, i.e., a separate calculation must be computed 
for each national market in which the institution holds equities. 
Institutions would not, for example, be able to net a long position in 
U.S. companies traded on the New York Stock Exchange against a short 
position in Japanese companies traded on the Tokyo Stock Exchange.
    b. Specific risk. The capital charge for specific risk is based on 
the reporting institution's gross equity positions (i.e., the absolute 
sum of all long equity positions and of all short equity positions, 
with netting allowed only when the institution has long and short 
positions in exactly the same instrument). This charge would also be 
8.0 percent, unless the portfolio is both liquid and well-diversified 
or the position relates to an index comprising a diversified portfolio 
of equities.
    Examiners will verify that any portfolio designated as ``liquid and 
well-diversified'' by an institution is characterized by a limited 
sensitivity to price changes of any single equity issue or closely 
related group of equity issues held in the portfolio. In particular, 
the volatility of the value of the portfolio should not be dominated by 
the volatility of any individual equity issue or by equity issues from 
any single industry or economic sector. In general, such portfolios 
should be characterized by a large number of individual equity 
positions, with no single position representing a large portion of the 
portfolio's total market value. In addition, it would generally be the 
case that a sizeable proportion of the portfolio would be comprised of 
issues traded on organized exchanges.
    For such liquid and well-diversified portfolios, the specific risk 
charge would be 4.0 percent. A specific risk charge of 2.0 percent 
would apply to the net long or short position in a broad-based, 
diversified equity index and is viewed as necessary to provide for the 
risk that the performance of the index will differ from those of other 
market measures and also for potential difficulties that could arise in 
executing transactions at expected prices.

Foreign Exchange

    This capital requirement covers the risk of holding or taking 
positions in foreign currencies, including gold, and is based on an 
institution's net positions in individual currencies, whether or not 
those positions are booked in the trading account. Net positions, in 
turn, include an institution's net spot and forward positions; any 
guarantees that are certain to be called and likely to be 
irrecoverable; net future income and expenses that are not yet accrued, 
but that are already fully hedged; and any other items representing a 
profit or loss in foreign currencies. Forward and future positions 
would be converted into the reporting currency at spot market rates.
    Institutions may, subject to supervisory approval, exclude from 
this calculation any structural positions in foreign currencies. For 
this purpose, such structural positions are limited to transactions 
designed to hedge an institution's capital ratios against the effect of 
adverse exchange rate movements on (1) subordinated debt, equity, or 
minority interests in consolidated subsidiaries and dotation capital 
assigned to foreign branches that are denominated in foreign 
currencies, and (2) any positions related to unconsolidated 
subsidiaries and to other items that are deducted from an institution's 
capital when calculating its capital base. In any event, such 
structural foreign currency positions should reflect long-term policies 
of the institution and not relate to trading positions.
    The standardized approach assumes the same volatility for all 
currencies and requires an institution to hold capital equal to 8.0 
percent of the sum of (a) its net position in gold and (b) the sum of 
the net short positions or the sum of the net long positions in each 
foreign currency, whichever is greater. With supervisory approval, an 
institution may be exempt from this capital requirement if the sum of 
its gross long and short positions does not exceed 100 percent of its 
eligible capital and its overall net foreign exchange position does not 
exceed 2.0 percent of this capital, as defined above in Section II.

Commodities

    The capital requirement for commodities risk applies to holdings or 
positions taken in commodities, including precious metals, but 
excluding gold (which is treated as a foreign currency because of its 
market liquidity). As with foreign currencies, the coverage extends to 
all commodities positions of the institution, not only to those booked 
in trading accounts. For this purpose, a commodity is defined as a 
physical product which is or can be traded on a secondary market, e.g., 
agricultural products, minerals, and precious metals. The standardized 
approach for measuring general market risk in commodities provides only 
a rough indication of the risk exposure and is appropriate only for 
institutions with relatively small amounts of commodities activity.
    Within the standardized approach, two alternative measures are 
available, referred to as the ``simple'' and the ``maturity'' methods. 
Both measures address directional risk, which is the risk that a 
commodity's spot price will increase or decrease, as well as basis 
risk, interest rate risk, and forward gap risk, which are also 
important risks, especially for institutions that engage in forward or 
derivative contracts. These institutions can face significant losses in 
their positions as a result of adverse changes in the relationship 
between prices of similar commodities, increases in the cost of 
financing forward positions, or changes in forward prices produced by 
any number of economic or market conditions.
    Both the simple and maturity approaches require an institution to 
calculate its net position in each commodity on the basis of spot 
rates. Long and short positions in the same commodity may be netted, 
but positions in different commodities would generally not be allowed 
to offset, except where different sub-categories of commodities are 
deliverable against each other.
    Under the simple approach, an institution's capital charge for 
directional risk would equal 15 percent of its net position, long or 
short, in each commodity. A supplemental charge of 3.0 percent of the 
gross position in each commodity would be added to cover basis, 
interest rate and forward gap risk.
    The capital charge using the maturity method reflects not only the 
net and gross positions in each commodity, but also the maturity of 
each commodity contract. For each commodity, positions would first be 
distributed among seven time bands. Physical holdings of commodities 
would be allocated to the first band. The matched long position plus 
the matched short position within each time-band would then be 
multiplied by a ``spread rate,'' (proposed at a uniform 1.5 percent 
rate) to capture forward gap and interest rate risk. Net positions from 
one time-band must be used to offset opposite positions in another 
time-band and would incur a ``surcharge'' equal to 0.6 percent of the 
net position for every time-band it is carried forward in recognition 
that such offsetting may not be perfect. This process ultimately 
produces an overall net position for each commodity. A 15 percent 
capital charge would be applied to that net position. The total capital 
charge for any given commodity would be the sum of (a) the initial 1.5 
percent 

[[Page 38091]]
charge for the matched positions in each time band, (b) any surcharge, 
and (c) the charge on the overall net position.

Options

    The Agencies recognize the diversity of activities in options and 
the difficulties in measuring an option's price risk. Accordingly, the 
proposal provides three alternative risk measures for institutions that 
do not adopt the internal models approach. These alternatives are: (a) 
a ``simplified'' method, which is available to institutions that only 
purchase traded options, (b) a ``scenario analysis'' method that 
evaluates option values under a range of market scenarios, and (c) a 
``delta-plus'' method that provides specific measures of individual 
components of an option's risk. The method used should be commensurate 
with and appropriate for the nature and scope of the institution's 
options activities. Institutions that have extensive dealings in 
options must have appropriately accurate measures of risk.
    Several variables determine an option's price:
    (1) The current price of the underlying asset;
    (2) The strike price of the option, which is the price of the 
underlying security at which the option has value;
    (3) The volatility of the price of the underlying security;
    (4) The time remaining before the option expires; and
    (5) The prevailing ``risk free'' interest rate.
    The effect of these variables on an option's value are represented 
by a series of Greek letters: delta (the price sensitivity of an option 
relative to price changes in the underlying security, rate, or index--
the ``underlying''), gamma (the change in delta for a given change in 
the underlying), vega (the effect of changes in the volatility of the 
underlying), theta (the effect given the passage of time), and rho (how 
the option price changes for a given change in risk free interest 
rates). Delta is a frequently used indicator of an option's risk, but 
others--particularly gamma--should be specifically addressed by 
institutions that trade options to any material extent. Such 
institutions should not rely merely on linear approximations of price 
movements, but should undertake to capture the non-linear relation 
between changes in the option's price and changes in the underlying 
rate or price.

Simplified Approach

    The simplified approach for options may only be used by 
institutions whose options activities are confined to a small volume of 
purchased options. This approach permits an institution either to 
``carve out'' both the option and a corresponding underlying position 
from other elements of the standardized approach or to view the option 
as ``naked''--that is, without a matching cash position. In order to 
avoid potentially penalizing an institution for purchasing an option, 
institutions could avoid linking (and subsequently carving-out) a 
purchased option and a corresponding cash position if doing so would 
create an exposure within the underlying position and produce a capital 
requirement that exceeded the value of the purchased option. 
Consequently, there are two possibilities:
    (1) If a carve-out is made, the capital charge is equal to the 
specific and general market risk charge on the underlying position, 
less the amount the option is in the money, bounded at zero.
    (2) If the purchased option is viewed by itself, the charge for the 
option is the smaller of (a) its market value or (b) the sum of the 
specific and general market risk charge that would apply to its 
underlying instrument. Any existing related (but not linked) cash 
position would continue to receive the full specific and general market 
risk charge produced by other elements of the standardized approach.
    In both cases, the method is relatively conservative, creating an 
incentive for institutions to use a more accurate measure of risk. 
Institutions that want a more accurate measure of option risk or whose 
trading activities include the writing (selling) of options must use 
either the scenario or the delta-plus methods offered under the 
standardized approach, or the previously described internal models 
approach.

Scenario Analysis

    Using scenario analysis, institutions would evaluate the market 
values of their options and related hedging positions by changing the 
underlying rate or price over a specified range and by also assuming 
different levels of volatility for that rate or price. Each combination 
of assumed volatilities and rate or price changes would represent a 
scenario.
    The range of rate or price movements would be based on the nature 
of the option. For options based on debt instruments or interest rates, 
the range would be consistent with the maximum rate movement indicated 
in the proposal dealing with traded debt: 100 basis points for 
underlying instruments in zone 1, 90 basis points for those in zone 2, 
and 75 basis points for those in zone 3. Similarly, the ranges used for 
other options would be consistent with the assumed price or rate change 
applied to their underlying cash positions: 8 percent for foreign 
exchange, 12 percent for individual equities, 8 percent for equity 
indices, and 15 percent for commodities. In all cases, the range would 
cover both an increase and decrease from current values of the 
underlying security (or rate) by these percentages and would be divided 
into at least 10 equally spaced intervals centered by the current rate 
or price.
    Given the near-linear relationship between volatility and option 
values for many options, the Agencies believe it would be sufficient in 
most cases to evaluate the option portfolio assuming a 25 percent 
increase and decrease in the level of volatility from that implied by 
current market prices. If warranted, however, the Agencies may require 
a different change in volatility and the consideration of intermediate 
points.
    An institution would determine the market value of each option and 
any related hedging position or group of options and related hedging 
positions for each scenario.19 Such options and positions based on 
debt instruments in the same zone, or on the same equity, equity index, 
exchange rate, or commodity may be grouped together and evaluated on a 
portfolio basis when evaluating the effect of a given scenario. The 
market risk capital charge for a portfolio would be the largest loss 
estimated for that portfolio from among the evaluated scenarios. The 
charge for all option portfolios would be the sum of the charges on the 
individual portfolios. The Agencies recognize that this approach is 
conservative, since it assumes that the largest loss will occur within 
each segment of the option portfolio simultaneously.

    \19\ For this purpose, a single option and any related hedging 
position and a group of options and any related hedging positions 
are all referred to as an ``options portfolio.''
---------------------------------------------------------------------------

The delta-plus method

    Institutions that write options would be allowed to include delta-
weighted options positions within the standardized methodology. Such 
options should be reported as a position equal to the market value of 
the underlying instrument multiplied by the delta. However, since an 
option's delta does not sufficiently address other risks associated 
with the option's market value, institutions would also be required to 
measure the option's gamma and vega in order to calculate the total 
capital charge for the option. These sensitivities would be calculated 
by an approved exchange model or by the 

[[Page 38092]]
institution's proprietary options pricing model, subject to oversight 
by the appropriate supervisor.
    Delta-weighted positions of options based on debt securities or 
interest rates would be slotted into the debt securities time-bands, as 
set out above for debt instruments, under the following procedure. A 
two-legged approach would be used as for other derivatives, requiring 
one entry at the time the underlying contract takes effect and a second 
at the time the underlying contract matures. For instance, a bought 
call option on a June three-month interest-rate future will in April be 
considered, on the basis of its ``delta'' equivalent value, to be a 
long position with a maturity of five months and a short position with 
a maturity of two months. The written option would be similarly slotted 
as a long position with a maturity of two months and a short position 
with a maturity of five months. Floating rate instruments with caps or 
floors would be treated as a combination of floating rate securities 
and a series of European-style options. For example, the holder of a 
three-year floating rate bond indexed to six month LIBOR with a cap of 
15 percent would treat the instrument as: (1) A debt security that 
reprices in six months; and (2) a series of five written call options 
on a floating rate asset (FRA) with a basis of 15 percent, each with a 
negative sign at the time the underlying FRA takes effect and a 
positive sign at the time the underlying FRA matures.
    In addition to the above capital charges arising from delta risk, 
the proposal requires capital for gamma and vega risks. Institutions 
using this method would be required to calculate the gamma and vega for 
each option position. The results would be slotted into separate 
maturity ladders by currency. For options such as caps and floors whose 
underlying instrument is an interest rate, the delta and gamma would be 
expressed in terms of a hypothetical underlying security. Subsequently:
    (1) For gamma risk, for each time-band, net gammas which are 
negative would be multiplied by the risk weights set out in the 
proposed regulatory language (OCC--Table 5, Board--Table IV, FDIC--
Table 4) and by the square of the market value of the underlyings (net 
gammas which are positive would be disregarded);
    (2) For volatility risk, institutions would be required to 
calculate the capital charges for vegas in each time-band assuming a 
proportional shift in volatility of 25 percent;
    (3) The capital charge would be the absolute value of the sum of 
the individual capital charges for net negative gammas plus the 
absolute value of the sum of the individual capital charges for vega 
risk for each time-band.
    The capital charge for options on equities would also be based on 
the delta weighted positions of the options by incorporating those 
weighted positions into the market risk measure for equities described 
above. For purposes of this calculation individual equity issues and 
indices are to be treated as separate underlyings. In addition to the 
capital charge for delta risk, institutions would apply a further 
capital charge for gamma and vega risk:
    (1) For gamma risk, the net negative gammas for each underlying 
instrument would be multiplied by 0.72 percent when that instrument is 
an individual equity and by 0.32 percent when it is an index.20 
That product would then be multiplied by the square of the market value 
of the underlying;

     20 Using the Taylor expansion, the risk weights are 
calculated as follows: Risk weight for gamma =0.5 x  (assumed price 
change of underlying)\2\ For an individual equity, 0.5 x 0.12\2\= 
0.72%. In the case of an index as the underlying, the assumed price 
change of the underlying equals 8.0 percent.
    (2) For volatility risk, institutions would be required to 
calculate the capital charges for vegas for each underlying instrument 
assuming a proportional shift in volatility of plus or minus 25 
percent;
    (3) The capital charge would be the absolute value of the sum of 
the individual capital charges for net negative gammas plus the 
absolute value of the sum of the individual capital charges for vega 
risk.
    The capital charge for options on foreign exchange and gold 
positions would be based on the shorthand method set out earlier. For 
delta risk, the net delta (or delta-based) equivalent of the total book 
of foreign currency and gold options would be incorporated into the 
measurement of the exposure in a single currency position. The gamma 
and vega risks would be measured as follows:
    (1) For gamma risk, for each underlying exchange rate net gammas 
which are negative would be multiplied by 0.32 percent and by the 
square of the market value of the position; 21

    \21\ The assumed price change is 8.0 percent.
---------------------------------------------------------------------------

    (2) For volatility risk, institutions would be required to 
calculate the capital charges for vegas for each currency pair and gold 
assuming a proportional shift in volatility of plus or minus 25 
percent;
    (3) The capital charge would be the absolute value of the sum of 
the individual capital charges for net negative gammas plus the 
absolute value of the sum of the individual capital charges for vega 
risk.
    The capital charge for options on commodities would be based on the 
same approach set out above for commodities. The delta weighted 
positions would be incorporated into one of the two measures described 
in that section. In addition to the capital charge for delta risk, 
institutions would incur a further capital charge for gamma and vega 
risk:
    (1) For gamma risk, net negative gammas for each underlying would 
be multiplied by 1.125 percent and by the square of the market value of 
the commodity; 22

    \22\ The assumed price change is 15 percent.
---------------------------------------------------------------------------

    (2) For volatility risk, institutions would be required to 
calculate the capital charges for vegas for each commodity as defined 
above in the section dealing with commodities, assuming a proportional 
shift in volatility of plus or minus 25 percent;
    (3) The capital charge would be the absolute value of the sum of 
the individual capital charges for net negative gammas plus the 
absolute value of the sum of the individual capital charges for vega 
risk.
    A worked example of the delta-plus method for commodities is set 
out in Attachment IV of the Board's and the FDIC's proposed regulatory 
language. In the case of options based on debt securities or interest 
rates and with the approval of the appropriate supervisor, institutions 
that are significant traders in options could be allowed to net 
positive and negative gammas and vegas across time-bands to a limited 
extent. However, such netting would be permitted only if it is based on 
prudent and conservative assumptions and the institution materially 
satisfies the qualitative standards outlined under the internal models 
approach.
    In addition, instead of applying a uniform relative change in 
volatility to measure vega risk, institutions may base the calculation 
on a volatility ladder in which the implied change in volatility varies 
with the maturity of the option. When using such a volatility ladder 
the assumed proportional shift in volatility should be at least 25 
percent at the short end of the maturity spectrum. The proportional 
shift in volatility for longer maturities should be at least as 
stringent in statistical terms as the 25 percent shift at the short 
end. Use of this alternative would be subject to validation by the 
supervisor, and to the qualitative standards listed in the internal 
models section that are relevant to this aspect of the institution's 

[[Page 38093]]
business. In the long term, institutions using this alternative would 
be expected to move to fully articulated value-at-risk models, subject 
to the full qualitative and quantitative standards for models.
    Besides the options risks mentioned above, the Agencies recognize 
that there are other risks associated with options, e.g., rho and 
theta. While they are not proposing a measurement system for those 
risks at present, institutions undertaking significant options business 
would still be expected to monitor such risks closely.
VII. Questions on Which the Agencies Specifically Request Comment

General Topics

    1. The Agencies propose to apply these standards to a relatively 
small number of institutions that have material trading activities. As 
the criteria are proposed, about 25 ``large'' institutions and a few 
other smaller institutions with relatively more significant trading 
activities would meet the requirements and be subject to the new 
capital standards. Is the exemption of smaller institutions 
appropriate, given their risk profile and the implied regulatory 
burden, or does it provide them with an undue competitive advantage? On 
the other hand, would the amendment affect too many institutions, given 
the nature of their trading activities and market risk profiles?
    2. Consistent with their procedures for existing capital standards, 
the Agencies would apply the proposed standard to any national bank, 
state member bank and bank holding company that meets the criteria on a 
consolidated basis. What are the burden implications of applying the 
standard to both banks and bank holding companies?
    3. The Board currently evaluates the capital adequacy of bank 
holding companies that have Section 20 subsidiaries on a fully 
consolidated basis and also without the assets and capital of the 
Section 20 subsidiaries. Should it continue this practice regarding 
market risk, or should it focus on only the consolidated holding 
company?
    4. Should the Agencies permit institutions the choice of the 
standardized or internal model approaches, or should it permit only the 
internal model approach on the basis that the institution's trading 
activities are sufficient to warrant the more accurate measure of risk?
    5. The Agencies are interested in comments on whether the internal 
model quantitative standards, together with the scaling factor, could 
result in capital requirements that on average are significantly 
different (for example, higher) than those required under the 
standardized approach.
    6. The Agencies propose to allow institutions to use the 
standardized method for measuring some categories of risk (e.g., debt, 
equities, etc.), and internal models for other categories. Should 
institutions be given this flexibility, or should they be required to 
use one approach throughout?
    7. The Agencies propose a reduced capital charge for specific risk 
in equities if an institution's equities portfolio is ``liquid and 
well-diversified,'' a concept that is defined in qualitative terms in 
the proposal. Should this concept be described more specifically and, 
if so, what criteria should be applied?

Questions on the Standardized Method

    1. Under the proposal, institutions would be allowed to net 
offsetting positions in different commodities only if the commodities 
were deliverable against each other. To what extent, if any, should the 
Agencies allow netting on the basis of the historical correlations of 
price movements of different commodities within the standardized 
approach? If netting is allowed on the basis of past correlations, what 
specific criteria should be required?
    2. One of the alternative ways of measuring the market risk of 
options in the standardized approach is to calculate separate charges 
for an option's delta, gamma, and vega risk (see the delta-plus 
method). This approach permits an institution to measure the risk of 
its options positions while measuring the risk of its other positions 
and, thereby, to evaluate them more fully on a portfolio basis. It also 
permits an institution to avoid incurring the worst-case charge for the 
option under the scenario method. The delta-plus calculations, however, 
are complex and potentially inaccurate since they do not permit full 
use of a revaluation model. Is the method sufficiently useful to 
warrant its complexity, and does it provide a sufficiently conservative 
measure of risk for institutions that write options but do not have 
options pricing models integrated into their risk measurement systems?

Questions on the Internal Model Method

    1. The Agencies are considering whether to require institutions to 
calculate their VARs using two observation periods (one long, one 
short) and basing the capital requirement on the larger figure. What 
are the costs and burden implications of requiring such a dual 
calculation?
    2. All institutions affected by the proposal would be required to 
have capital covering both general market and specific risks. 
Institutions using the internal model approach would be required to 
apply the specific risk charge (or a portion thereof) calculated using 
the standardized approach, if their models do not adequately capture 
specific risk. What modelling techniques should the Agencies consider 
when evaluating an institution's model and determining the extent to 
which the model includes specific risk in its VAR measure?
    3. As part of an on-going process of evaluating the accuracy of an 
institution's internal model, actual daily trading profits and losses 
would be compared with the measured VAR (so-called ``back-testing''). 
The Agencies would expect this back-testing normally to rely upon the 
VARs actually used by the institution for nonregulatory purposes, which 
in most cases would reflect a confidence level less than the 99 percent 
level on which the capital requirement would be based. Would this 
approach be less burdensome to the institution than requiring a 
separate calculation for the 99 percent confidence level, and would it 
provide a more statistically reliable basis for evaluating the results? 
Please comment on these procedures and any other considerations the 
Federal Reserve should take into account in reviewing back-tests.
    4. The Agencies recognize that daily VAR is used by institutions 
for setting daily trading limits, rather than for evaluating capital 
adequacy. The regulatory use of VAR as a basis for a capital 
requirement is predicated on the specification of several constraints 
on modelling parameters, as well as the use of a multiplication factor. 
Do these constraints provide sufficient capital for the underlying 
activities?
    5. To qualify for the use of the internal models approach, an 
institution must have a rigorous stress testing program which would be 
subject to supervisory review. What stress tests for market risk should 
institutions be expected to perform as part of their internal 
management process?

VIII. Regulatory Flexibility Act Analysis

OCC Regulatory Flexibility Act Analysis

    Pursuant to section 605(b) of the Regulatory Flexibility Act, the 
Comptroller of the Currency certifies that this proposal would not have 
a significant impact on a substantial 

[[Page 38094]]
number of small business entities in accord with the spirit and 
purposes of the Regulatory Flexibility Act (5 U.S.C. 601 et seq.). 
Accordingly, a regulatory flexibility analysis is not required. The 
impact of this proposed rule on banks regardless of size is expected to 
be minimal. Further, this proposed rule generally would apply to larger 
banks with significant trading account activities and would cover only 
trading activities and foreign exchange and commodity positions 
throughout the bank.

Board Regulatory Flexibility Act Analysis

    Pursuant to section 605(b) of the Regulatory Flexibility Act, the 
Board does not believe this proposal would have a significant impact on 
a substantial number of small business entities in accord with the 
spirit and purposes of the Regulatory Flexibility Act (5 U.S.C. 601 et 
seq.). Accordingly, a regulatory flexibility analysis is not required. 
In addition, because the risk-based capital standards generally do not 
apply to bank holding companies with consolidated assets of less than 
$150 million, this proposal would not affect such companies.

FDIC Regulatory Flexibility Act Analysis

    Pursuant to section 605(b) of the Regulatory Flexibility Act (Pub. 
L. 96-354, 5 U.S.C. 601 et seq.), it is certified that the proposed 
rule would not have a significant impact on a substantial number of 
small entities.
IX. Paperwork Reduction Act and Regulatory Burden

OCC Regulatory Burden

    Section 302 of the Riegle Community Development and Regulatory 
Improvement Act of 1994, Pub. L. 103-325, 108 Stat. 2160 (September 23, 
1994), provides that the federal banking agencies must consider the 
administrative burdens and benefits of any new regulations that impose 
additional requirements on insured depository institutions. As 
discussed, this proposed rule would affect only a small number of banks 
and generally would cover only trading account activities and foreign 
exchange and commodity positions throughout the bank. Additionally, any 
burden imposed would be lessened to the extent that a bank may use its 
own qualifying internal market risk model. The OCC believes that any 
additional burden placed on a bank is outweighed by the advantages of 
greater accuracy in risk management and capital allocation, which 
contribute to increased safety and soundness in the banking system.

Board Paperwork Reduction Act and Regulatory Burden

    The Board has determined that this proposal would not increase the 
regulatory paperwork burden of banking organizations pursuant to the 
provisions of the Paperwork Reduction Act (44 U.S.C. 3501 et seq.). 
Section 302 of the Riegle Community Development and Regulatory 
Improvement Act of 1994 (Pub. L. 103-325, 108 Stat 2160) provides that 
the federal banking agencies must consider the administrative burdens 
and benefits of any new regulations that impose additional requirements 
on insured depository institutions. As noted above, the proposed market 
risk measure would affect only a small number of institutions. The 
Board believes that any additional burden placed on these institutions 
is outweighed by the advantages of greater accuracy in risk measurement 
and capital allocation, which contribute to increased safety and 
soundness in the banking system.

FDIC Paperwork Reduction Act

    The FDIC has determined that his proposed rulemaking does not 
contain any collections of information as defined by the Paperwork 
Reduction Act (44 U.S.C. 3501 et seq.).

X. OCC Executive Order 12866 Determination

    The Comptroller of the Currency has determined that this notice of 
proposed rulemaking is not a significant regulatory action under 
Executive Order 12866.

XI. OCC Unfunded Mandates Reform Act of 1995 Determination

    Section 202 of the Unfunded Mandates Reform Act of 1995 (Unfunded 
Mandates Act), Pub. L. 104-4, 109 Stat. 48 (March 22, 1995) requires 
that an agency prepare a budgetary impact statement before promulgating 
a rule that includes a Federal mandate that may result in the 
expenditure by state, local, and tribal governments, in the aggregate, 
or by the private sector, of $100 million or more in any one year. If a 
budgetary impact statement is required, section 205 of the Unfunded 
Mandates Act also requires an agency to identify and consider a 
reasonable number of regulatory alternatives before promulgating a 
rule. Because the OCC has determined that this notice of proposed 
rulemaking will not result in expenditures by state, local and tribal 
governments, or by the private sector, of more than $100 million in any 
one year, the OCC has not prepared a budgetary impact statement or 
specifically addressed the regulatory alternatives considered. As 
discussed in the preamble, this proposed rule may require additional 
capital for market risks. However, the application of this proposed 
rule would be generally limited to banks with significant trading 
account activities and would cover only foreign exchange and commodity 
positions throughout the bank. Currently, the OCC estimates that less 
than 25 national banks will be subject to the requirements of this 
proposed rule. In addition, any burden imposed on this small group of 
national banks would be lessened to the extent that a bank may use its 
own qualifying internal market risk model.

List of Subjects

12 CFR Part 3

    Administrative practice and procedure, Capital, National banks, 
Reporting and recordkeeping requirements, Risk.

12 CFR Part 208

    Accounting, Agriculture, Banks, banking, Confidential business 
information, Crime, Currency, Federal Reserve System, Mortgages, 
Reporting and recordkeeping requirements, Securities.

12 CFR Part 225

    Administrative practice and procedure, Banks, banking, Federal 
Reserve System, Holding companies, Reporting and recordkeeping 
requirements, Securities.

12 CFR Part 325

    Administrative practice and procedure, Banks, banking, Capital 
adequacy, Reporting and recordkeeping requirements, Savings 
associations, State non-member banks.

Authority and Issuance

OFFICE OF THE COMPTROLLER OF THE CURRENCY

12 CFR Chapter I

    For the reasons set out in the preamble, part 3 of title 12, 
chapter I of the Code of Federal Regulations is proposed to be amended 
as set forth below.

PART 3--MINIMUM CAPITAL RATIOS; ISSUANCE OF DIRECTIVES

    1. The authority citation for part 3 continues to read as follows:

    Authority: 12 U.S.C. 93a, 161, 1818, 1828(n), 1828 note, 1831n 
note, 1835, 3907, and 3909.


[[Page 38095]]

    2. New appendix B is added to part 3 to read as follows:

Appendix B to Part 3--Market Risk

Section 1. Purpose, Applicability, Effective Date, and Definitions

    (a) Purpose. The purpose of this appendix B is to ensure that 
banks maintain adequate capital for market risk. Market risk is 
generally the risk of loss arising from movements in market prices. 
The market risk requirements of this appendix B are limited to the 
market risk associated with the trading account of the bank and to 
the overall foreign exchange risk and the commodities risk 
throughout the bank, including related options and other derivative 
contracts. Under this appendix B a bank may measure its market risk 
exposure with either its own qualifying internal market risk model 
or the alternative standardized market risk model provided. However, 
the OCC generally expects that banks with significant trading 
activities will calculate their market risk using a qualifying 
internal market risk model.
    (b) Applicability. The market risk requirement of this appendix 
B applies to the following banks:
    (1) Any bank with total assets in excess of $5 billion and 
either total on-balance sheet trading account activities of 3 
percent or more of the total assets of the bank, or total notional 
off-balance sheet trading account activities in excess of $5 
billion; and
    (2) Any bank with total assets of $5 billion or less and total 
trading account activities in excess of 10 percent of the total 
assets of the bank; and
    (3) Any bank with a significant exposure to market risk and the 
OCC deems necessary to protect the safety and soundness of the bank.
    (c) Effective date. The market risk requirements of this 
appendix B are effective December 31, 1997.
    (d) Definitions. For the purposes of this appendix B, the 
following definitions apply:
    (1) Covered market risk assets means all trading account assets 
plus all other on- and off-balance sheet assets which have foreign 
exchange risk, equity price risk, and commodity risk throughout the 
bank including related options and other derivative contracts.
    (2) Derivative contract means generally a financial contract 
whose value is derived from the values of one or more underlying 
asset, reference rate or index of asset values. Derivative contracts 
include both standardized contracts that are traded on exchanges and 
customized, privately negotiated contracts known as over-the-counter 
(OTC) derivative contracts.
    (3) Lock-in clause means a provision in a subordinated debt 
agreement that precludes payment by the bank of either interest or 
principal (even upon maturity) of the subordinated debt if such 
payment would cause the issuing bank to fall or remain below the 
minimum risk-based capital requirement as provided in appendix A of 
this part 3 as adjusted for market risk.
    (4) Market risk means the risk of loss resulting from movements 
in market prices. Market risks consist of both general and specific 
market risks. General market risk is the change in market value of a 
particular asset that results from broad market movements such as a 
change in market interest rates, foreign exchange rates, equity 
prices, and commodity prices. Specific market risks are those risks 
that affect the market value of a specific instrument, such as the 
credit risk of the issuer of that particular instrument, but do not 
materially alter broad market conditions.
    (5) Tier 3 capital means capital that may be used by a bank to 
satisfy the market risk capital requirements under this appendix B 
as determined in accordance with section 3 of this appendix B.
    (6) Total assets means the quarter-end total assets figure 
required to be computed for and stated in a bank's most recent 
quarterly Consolidated Report of Condition and Income (Call Report).
    (7) Trading account activities means the sum of trading account 
assets and trading account liabilities.
    (8) Trading account assets means all positions in financial 
instruments acquired with the intent to resell in order to profit 
from short-term price movements. Trading account assets include, but 
are not limited to:
    (i) Assets acquired with the intent to resell to customers;
    (ii) Positions in financial instruments arising from matched 
principal brokering or market making; or
    (iii) Positions in financial instruments taken in order to hedge 
positions in other financial instruments of the trading 
account.1

    \1\ When non-trading account instruments are hedged with trading 
account instruments, whether on- or off-balance-sheet, the bank may 
include the non-trading account instruments in the measure for 
general market risk. However, such non-trading account instruments 
remain subject to the credit risk capital charges of appendix A of 
this part.
---------------------------------------------------------------------------

    (9) Value-at-risk means the statistical estimate representing 
the maximum amount by which the market value of covered market risk 
assets could decline during a specific period for a stated level of 
statistical confidence.

Section 2. Market Risk Capital Requirement

    (a) Capital requirement. All banks subject to this appendix B 
shall maintain a minimum market risk capital ratio of 8 percent. The 
market risk capital ratio is the ratio of eligible market risk 
capital to adjusted market risk assets. Eligible market risk capital 
consists of Tier 1, Tier 2, and Tier 3 capital as determined in 
accordance with section 3 of this appendix B. Adjusted market risk 
assets is the sum of the risk weighted assets as determined in 
accordance with appendix A of this part 3 (risk-based capital 
guidelines) plus the market risk equivalent assets. The market rate 
equivalent assets equal 12.5 times the market risk exposure as 
determined in accordance with section 4 of this appendix B.
    (b) Relationship to risk-based capital requirement. The amount 
of capital required for market risk is in addition to the amount of 
capital required for counterparty credit risk under the risk-based 
capital guidelines as determined in accordance with appendix A of 
this part 3.

Section 3. Eligible Market Risk Capital

    (a) Types of eligible market risk capital. A bank may use Tier 1 
and Tier 2 capital, as determined in accordance with Sec. 3.2 of 
this part 3, to satisfy the market risk requirement. A bank also may 
use Tier 3 capital to satisfy its market risk requirement as 
determined in accordance with section 3(b) and subject to the 
limitations of section 3(c) of this appendix B.
    (b) Tier 3 capital. For the purposes of this appendix B, Tier 3 
capital consists of short-term subordinated debt subject to a lock-
in clause. In addition, the subordinated debt must have an original 
maturity of at least two years, be unsecured and subordinated to the 
claims of depositors must be fully paid-in, and may not be subject 
to any covenants, terms, or restrictions inconsistent with safe and 
sound banking practices.
    (c) Limitations. Tier 3 capital only may be used to satisfy the 
market risk capital requirements under this appendix B and may not 
be used to satisfy the capital risk-based capital requirements for 
counterparty risk under appendix A of this part 3, including 
counterpart credit risk associated with derivative transactions in 
either the trading or nontrading accounts. In addition, the use of 
Tier 3 capital is subject to the following quantitative limitations:
    (1) Tier 3 capital may not exceed 250 percent of a bank's Tier 1 
capital allocated for market risk.
    (2) The total of Tier 2 capital and Tier 3 capital is limited to 
100 percent of Tier 1 capital.
    (3) Tier 2 capital may be substituted for Tier 3 capital up 
subject to the same 250 percent limitation on Tier 3 capital and all 
other limitations on Tier 2 capital under the risk-based capital 
guidelines, as determined by appendix A of this part 3.

Section 4. Market Risk Exposure

    Market risk exposure represents the total dollar amount at risk 
arising from movements in market prices. A bank may determine its 
market risk exposure either through a qualifying internal market 
risk model as provided in accordance with section 5 of this appendix 
B, or through the standardized market risk model as provided in 
accordance with section 6 of this appendix B.
    (a) Qualifying internal market risk model. For a bank permitted 
or required by the OCC to use a qualifying internal market risk 
model, the market risk exposure of covered market risk assets is 
equal to the greater of:
    (1) The aggregate value-at-risk amount for the previous day; or
    (2) The average of the daily value-at-risk amounts for each of 
the preceding 60 business days times a multiplication factor of 
three.
    (b) Standardized market risk model. For banks using the 
standardized market risk model, the market risk exposure equals the 
measured value-at-risk amount for covered market risk assets as 
determined in section 6 of this appendix B.

Section 5. Qualifying Internal Market Risk Model

    As provided in this section, a bank may use a qualifying 
internal market risk model 

[[Page 38096]]
to determine its market risk exposure. The qualifying internal market 
risk model may use any generally accepted measurement technique 
including, but not limited to, variance-covariance models, 
historical simulations, or monte carlo simulations; however, the 
qualifying internal market risk model must capture all material 
market risk.
    (a) Value-at-risk measurement. A qualifying internal market risk 
model must incorporate a value-at-risk measurement that adequately 
evaluates the market risk associated with all covered market risk 
assets.
    (b) Risk factor categories. The value-at-risk measurement must 
include risk factors sufficient to capture the market risk inherent 
in all covered market risk assets. In addition, the risk factors 
must cover the risk categories of interest rates, exchange rates, 
equity prices, commodity prices, and the volatility of related 
market factors.
    (c) Prior approval. Prior OCC approval is required before a bank 
may use an internal market risk model for the purposes of the market 
risk requirement of this appendix B. A qualifying internal market 
risk model must satisfy the following criteria:
    (1) Qualitative factors. (i) The level of sophistication and 
accuracy of the internal market risk model must be commensurate with 
the nature and volume of bank's trading account activities.
    (ii) The market risk management systems must adequately monitor 
compliance with internal procedures and controls which generally 
would include independent risk management, annual internal audits, 
back testing, and stress testing.
    (2) Quantitative factors. (i) The value-at-risk measurement must 
be calculated with sufficient frequency to allow the bank enough 
time to react to changing market conditions.
    (ii) The value-at-risk measurement must be based on a 99th 
percentile, one-tailed confidence interval 2 with an assumed 
holding period of ten trading days.

    \2\ A one-tailed confidence interval of 99 percent means that 
there is a 1 percent probability based on historical experience that 
the combination of positions in a bank's portfolio would result in a 
loss higher than the measured value-at-risk.
---------------------------------------------------------------------------

    (iii) For positions that display linear price relationships, a 
bank may use value-at-risk measurement using shorter holding periods 
which are scaled up to ten days by the square root of time.3

    \3\ This transformation entails multiplying a bank's value-at-
risk by the square root of the ratio of the required holding period 
(ten days) to the holding period embodied in the value-at-risk 
exposure. For example, the value-at-risk calculated according to a 
one-day holding period would be scaled-up by the ``square root of 
time'' by multiplying the value-at-risk by 3.16 (the square root of 
the ratio of a ten-day holding period to a one-day holding period).
---------------------------------------------------------------------------

    (iv) The value-at-risk measurement must be calculated using an 
observation period of at least one year to measure historical 
changes in rates and prices.
    (v) A bank must update its historical rates and prices at least 
once every three months and must reassess them whenever market 
conditions change materially.
    (vi) A bank may incorporate into its value-at-risk measurement 
empirical correlations within each risk category. However, empirical 
correlations across risk categories may not be incorporated. The 
value-at-risk measurement for each risk category must be added 
together on a simple sum basis to determine the aggregate value-at-
risk exposure.
    (vii) The value-at-risk measurement must capture the unique 
risks associated with options within each of the risk categories 
subject to the following criteria:
    (A) The value-at-risk measurement must capture the non-linear 
price characteristics of option positions using an options pricing 
technique.
    (B) The bank must apply a minimum ten-day holding period to 
option positions or positions that display option-like 
characteristics. Options may not be scale-up the daily value-at-risk 
exposure by the square root of time.
    (C) The value-at-risk measurement must capture the volatilities 
of the rates and prices underlying option positions.
    (viii) The accuracy of a bank's qualifying internal market risk 
model must be validated by auditors.

Section 6. Standardized Market Risk Model

    As provided in this section, a bank may use the standardized 
market risk model to determine its market risk exposure.
    (a) Debt Instruments. (1) Specific Risk. (i) The market risk 
requirement for specific risk is based on the identity of the 
obligor and, in the case of corporate securities, on the credit 
rating and maturity of the instrument. The specific risk is 
calculated by weighting the current market value of each individual 
position, whether long or short, by the appropriate specific risk 
factor and summing the weighted values. In measuring specific risk, 
the bank may offset and exclude from its calculations any matched 
positions in the identical issue (including positions in derivative 
contracts). Even if the issuer is the same, offsetting is not 
permitted between different issues. The specific risk factors are 
set forth in Table 1--Specific Risk Factors for Debt Instruments, as 
follows:

          Table 1.--Specific Risk Factors for Debt Instruments          
------------------------------------------------------------------------
                                   Remaining contractual      Factor (In
           Category                      maturity              percent) 
------------------------------------------------------------------------
Government...................  N/A.........................         0.00
Qualifying...................  6 months or less............         0.25
                               Over 6 to 12 months.........         1.00
                               Over 12 months..............         1.60
Other........................  N/A.........................         8.00
------------------------------------------------------------------------

    (ii) The government category includes all forms of debt 
instruments of central governments of the OECD-based group of 
countries including bonds, Treasury bills and other short-term 
instruments, as well as local currency instruments of non-OECD 
central governments to the extent that the bank has liabilities 
booked in that currency.
    (iii) The qualifying category includes securities of U.S. 
government-sponsored agencies, general obligation securities issued 
by states and other political subdivisions of the OECD-based group 
of countries, multilateral development banks, and debt instruments 
issued by U.S. depository institutions or OECD-banks that do not 
qualify as capital of the issuing institution. It also includes 
other securities, including revenue securities issued by states and 
other political subdivisions of the OECD-based group of countries, 
that are rated investment-grade by at least two nationally 
recognized credit rating services, or rated investment-grade by one 
nationally recognized credit rating agency and not less than 
investment-grade by any other credit rating agency, or, with the 
exception of securities issued by U.S. firms and subject to review 
by the OCC, unrated but deemed to be of comparable investment 
quality by the reporting bank and the issuer has securities listed 
on a recognized stock exchange.
    (iv) The other category includes debt securities not qualifying 
as government or qualifying securities. This would include non-OECD 
central government securities that do not meet the criteria for the 
government or qualifying categories. This category also includes 
instruments that qualify as capital issued by other banking 
organizations.
    (v) The OCC will consider the extent of a bank's position in 
non-investment grade instruments (sometimes referred to as ``high 
yield debt'') that do not have investment-grade ratings. If those 
holdings are not well-diversified or otherwise represent a material 
position to the institution, the OCC may prohibit a bank from 
offsetting positions in these instruments with other positions in 
qualifying instruments that may be offset when calculating its 
general market risk requirement. In addition, the OCC may impose a 
specific risk capital requirement as high as 16.0 percent.
    (2) General Market Risk. (i) A bank may measure its exposure to 
general market risk using, on a continuous basis, either the 
maturity method (which uses standardized risk weights that 
approximate the price sensitivity of various instruments) or the 
duration method (where the institution calculates the precise 
duration of each instrument, weighted by a specified change in 
interest rates).
    (ii) Both methods use a maturity-ladder that incorporates a 
series of ``time bands'' and ``zones'' to group together securities 
of similar maturities and that are designed to take into account 
differences in price sensitivities and interest rate volatilities 
across different maturities. Under either method, the capital 
requirement for general market risk is the sum of a base charge that 
results from fully netting various risk-weighted positions and a 
series of additional charges (add-ons), which effectively 
``disallow'' part of the previous full netting to address basis and 
yield curve risk.
    (iii) For each currency in which a bank has significant 
positions, a separate capital requirement must be calculated. No 
netting of positions is permitted across different currencies. 
Offsetting positions of the same amount in the same issues, whether 
actual or 

[[Page 38097]]
notional, may be excluded from the calculation, as well as closely 
matched swaps, forwards, futures, and forward rate agreements (FRAs) 
that meet the conditions set out in section 6(a)(3) of this appendix 
B.
    (iv) In the maturity method, the bank distributes each long or 
short position (at current market value) of a debt instrument into 
the time bands of the maturity ladder. Fixed-rate instruments are 
allocated according to the remaining term to maturity and floating-
rate instruments according to the next repricing date. A callable 
bond trading above par is slotted according to its first call date, 
while a callable bond priced below par is slotted according to 
remaining maturity. Fixed-rate mortgage-backed securities, including 
collateralized mortgage obligations (CMOs) and real estate mortgage 
investment conduits (REMICs), are slotted according to their 
expected weighted average lives.
    (v) Once all long and short positions are slotted into the 
appropriate time band, the long positions in each time-band are 
summed and the short positions in each time-band are summed. The 
summed long and/or short positions are multiplied by the appropriate 
risk-weight factor (reflecting the price sensitivity of the 
positions to changes in interest rates) to determine the risk-
weighted long and/or short position for each time-band. The risk 
weights for each time-band are set out in Table 2--Maturity Method: 
Time-Band and Weights, as follows:

            Table 2.--Maturity Method: Time-Bands and Weights           
------------------------------------------------------------------------
                                      Coupon less than 3% and     Risk  
  Zone        Coupon 3% or more          zero coupon bonds      weights 
------------------------------------------------------------------------
1.......  Up to 1 month............  Up to 1 month...........       0.00
          1 up to 3 months.........  1 up to 3 months........       0.20
          3 up to 6 months.........  3 up to 6 months........       0.40
          6 up to 12 months........  6 up to 12 months.......       0.70
2.......  1 up to 2 years..........  1 up to 1.9 years.......       1.25
          2 up to 3 years..........  1.9 up to 2.8 years.....       1.75
          3 up to 4 years..........  2.8 up to 3.6 years.....       2.25
3.......  4 up to 5 years..........  3.6 up to 4.3 years.....       2.75
          5 up to 7 years..........  4.3 up to 5.7 years.....       3.25
          7 up to 10 years.........  5.7 up to 7.3 years.....       3.75
          10 up to 15 years........  7.3 up to 9.3 years.....       4.50
          15 up to 20 years........  9.3 up to 10.6 years....       5.25
          Over 20 years............  10.6 up to 12 years.....       6.00
                                     12 up to 20 years.......       8.00
                                     Over 20 years...........      12.50
------------------------------------------------------------------------

    (vi) Within each time-band for which there are risk-weighted 
long and short positions, the risk-weighted long and short positions 
are then netted, resulting in a single net risk-weighted long or 
short position for each time-band. Because different instruments and 
different maturities may be included and netted within each time-
band, a capital requirement, referred to as the vertical 
disallowance, is assessed for basis risk. The vertical disallowance 
capital requirement is 10.0 percent of the position eliminated by 
the intra-time-band netting, that is, 10.0 percent of the smaller of 
the net risk-weighted long or net risk-weighted short position, or 
if the positions are equal, 10.0 percent of either position.4 
The vertical disallowances for each time-band are absolute values, 
that is, neither long nor short. The vertical disallowances for all 
time-bands in the maturity ladder are summed and included as an 
element of the general market risk capital requirement.

    \4\ For example, if the sum of the weighted longs in a time-band 
is $100 million and the sum of the weighted shorts is $90 million, 
the vertical disallowance for the time-band is 10.0 percent of $90 
million, or $9 million.
---------------------------------------------------------------------------

    (vii) Within each zone for which there are risk-weighted long 
and short positions in different time-bands, the weighted long and 
short positions in all of the time-bands within the zone are then 
netted, resulting in a single net long or short position for each 
zone. Because different instruments and different maturities may be 
included and netted within each zone, a capital requirement, 
referred to as the horizontal disallowance, is assessed to allow for 
the imperfect correlation of interest rates along the yield curve. 
The horizontal disallowance capital requirement is calculated as a 
percentage of the position eliminated by the intra-zone netting, 
that is, a percentage of the smaller of the net risk-weighted long 
or net risk-weighted short position, or if the positions are equal, 
a percentage of either position.5 The percent disallowance 
factors for intra-zone netting are set out in Table 3--Horizontal 
Disallowances in section 6(a)(2)(H). The horizontal disallowances, 
like the vertical disallowances, are absolute values that are summed 
and included as an element of the general market risk capital 
requirement.

    \5\ For example, if the sum of the weighted longs in the 1- to 
3-month time-band in Zone 1 is $8 million and the sum of the 
weighted shorts in the 3- to 6-month time-band is $10 million, the 
horizontal disallowance for the zone is 40 percent of $8 million, or 
$3.2 million.
    (viii) Risk-weighted long and short positions in different zones 
are then netted between the zones. Zone 1 and zone 2 are netted if 
possible, reducing or eliminating the net long or short position in 
zone 1 or zone 2 as appropriate. Zone 2 and zone 3 are then netted 
if possible, reducing or eliminating the net long or short position 
in zone 2 or zone 3 as appropriate. Zone 3 and zone 1 are then 
netted if possible, reducing or eliminating the long or short 
position in zone 3 and zone 1 as appropriate. A horizontal 
disallowance capital requirement is then assessed, calculated as a 
percentage of the position eliminated by the inter-zone netting. The 
horizontal disallowance capital requirements for each zone are then 
summed as absolute values and included in the general market risk 
capital charge. The percent disallowance factors for inter-zone 
netting are set out in Table 3--Horizontal Disallowances, as 
follows:

                   Table 3.--Horizontal Disallowances                   
------------------------------------------------------------------------
                                                  Between               
                                    Within the    adjacent     Between  
  Zone           Time-band             zone        zones     zones 1 and
                                    (percent)    (percent)   3 (percent)
------------------------------------------------------------------------
1.......  0 up to 1 month........           40           40          100
          1 up to 3 months.......                                       
          3 up to 6 months ......                                       

[[Page 38098]]
                                                                        
          6 up to 12 months......                                       
2.......  1 up to 2 years........           30           40          100
          2 up to 3 years                                               
          3 up to 4 years                                               
3.......  1 up to 5 years........           30           40          100
          5 up to 7 years                                               
          7 up to 10 years                                              
          10 up to 15 years                                             
          15 up to 20 years                                             
          Over 20 years                                                 
------------------------------------------------------------------------



    (ix) Finally, the net risk-weighted long or net risk-weighted 
short positions remaining in the zones are summed to reach a single 
net risk-weighted long or net risk-weighted short position for the 
bank's portfolio. The sum of the absolute value of this position and 
the vertical and horizontal disallowances is the capital requirement 
for general market risk.
    (x) In the duration method, the bank, after calculating each 
instrument's modified duration,6 multiplies that modified 
duration by the interest rate shock specified for an instrument of 
that duration in Table 4--Duration Method: Time-Band and Assumed 
Changes in Yield in section 6(a)(2)(K). The resulting product 
(representing the expected percentage change in the price of the 
instrument for the given interest rate shock) is then multiplied by 
the current market value of the instrument. The resulting amount is 
then slotted as a long or short position into a time-band in the 
maturity ladder in Table 4--Duration Method: Time-Band and Assumed 
Changes in Yield on the basis of the instrument's modified 
duration.7

    \6\ The duration of an instrument is its approximate percentage 
change in price for a 100 basis point parallel shift in the yield 
curve assuming that its cash flows do not change when the yield 
curve shifts. Modified duration is duration divided by a factor of 1 
plus the interest rate.
    \7\ Example, an instrument held by a bank with a maturity of 4 
years and 3 months and a current market value of $1,000 might have a 
modified duration of 3.5 years. Based on its modified duration, it 
would be subjected to the 75-basis point interest rate shock, 
resulting in an expected price change of 2.625 percent (3.5  x  
0.75). The corresponding expected change in price of $26.25, 
calculated as 2.625 percent of $1,000, would be slotted as a long 
position in the 3.3 to 4.0 year time-band of the maturity ladder.
---------------------------------------------------------------------------

    (xi) Once all of the bank's traded debt instruments have been 
slotted into the maturity ladder, the bank conducts the same rounds 
of netting and disallowances described in sections 6(a)(2)(F) 
through (H) of the maturity method in this appendix B, with the 
exception that the vertical disallowance requirement for the 
duration method is 5.0 percent (horizontal disallowances continue to 
be those set out in Table 3--Horizontal Disallowances). As with the 
maturity method, the sum of the absolute value of the final net 
position and the vertical and horizontal disallowances is the 
general market risk capital requirement.
    (xii) The duration method maturity ladder is set out in Table 
4--Duration Method: Time Bands and Assumed Changes in Yield, as 
follows:

   Table 4.--Duration Method: Time-Bands and Assumed Changes in Yield   
------------------------------------------------------------------------
                                                               Assumed  
  Zone                        Time-band                       change in 
                                                                yield   
------------------------------------------------------------------------
1.......  Up to 1 month....................................         1.00
          1 up to 3 months.................................         1.00
          3 up to 6 months.................................         1.00
          6 up to 12 months................................         1.00
2.......  1.0 up to 1.8 years..............................         0.90
          1.8 up to 2.6 years..............................         0.80
          2.6 up to 3.3 years..............................         0.75
3.......  3.3 up to 4.0 years..............................         0.75
          4.0 up to 5.2 years..............................         0.70
          5.2 up to 6.8 years..............................         0.65
          6.8 up to 8.6 years..............................         0.60
          8.6 up to 9.9 years..............................         0.60
          9.9 up to 11.3 years.............................         0.60
          11.3 up to 16.6 years............................         0.60
          Over 16.6 years..................................         0.60
------------------------------------------------------------------------

    (3) Interest rate derivative contracts. (i) Derivative contracts 
and other off-balance sheet positions that are affected by changes 
in interest rates are included in the measurement system under 
section 6(a) of this appendix B (except for options and the 
associated underlyings, which are included in the measurement system 
under the treatment discussed in section 6(e) of this appendix B).
    (ii) Derivatives are converted into positions in the relevant 
underlying instrument and are included in the calculation of 
specific and general market risk capital charges as described above. 
The amount to be included is the market value of the principal 
amount of the underlying or of the notional underlying.
    (iii) Futures and forward contracts (including FRAs) are broken 
down into a combination of a long position and short position in the 
notional security. The maturity of a future or a FRA is the period 
until delivery or exercise of the contract, plus the life of the 
underlying instrument.8 Where a range of instruments may be 
delivered to fulfill the contract, the bank may chose which 
deliverable instrument goes into the maturity or duration ladder as 
the notional underlying. In the case of a future on a corporate bond 
index, positions are included at the market value of the notional 
underlying portfolio of securities.

    \8\ For example, a long position in a June three-month interest 
rate future (taken in April) is reported as a long position in a 
government security with a maturity of five months and a short 
position in a government security with a maturity of two months.
---------------------------------------------------------------------------

    (iv) Swaps are treated as two notional positions in the relevant 
instruments with appropriate maturities. The receiving side is 
treated as the long position and the paying side is treated as the 
short position.9 The separate sides of cross-currency swaps or 
forward foreign exchange transactions are slotted in the relevant 
maturity ladders for the currencies concerned. For swaps that pay or 
receive a fixed or floating interest rate against some other 
reference price, for example, an equity index, the interest rate 
component is slotted into the appropriate repricing maturity 
category, with the long or short position attributable to the equity 
component being included in the equity framework set out in section 
6(b) of this appendix B.10

    \9\ For example, an interest rate swap in which a bank is 
receiving floating-rate interest and paying fixed is treated as a 
long position in a floating rate instrument with a maturity 
equivalent to the period until the next interest rate reset date and 
a short position in a fixed-rate instrument with a maturity 
equivalent to the remaining life of the swap.
    \10\ A bank with a large swap book may, with prior approval of 
the OCC, use alternative formulae to calculate the positions to be 
included in the maturity or duration ladder. For example, a bank 
could first convert the payments required by the swap into present 
values. For that purpose, each payment would be discounted using 
zero coupon yields, and the payment's present value entered into the 
appropriate time-band using procedures that apply to zero (or low) 
coupon bonds. The net amounts would then be treated as bonds, and 
slotted into the general market risk framework. Such alternative 
treatments will, however, only be allowed if: (i) the OCC is 
satisfied with the accuracy of the system being used, (ii) the 
calculated positions fully reflect the sensitivity of the cash flows 
to interest rate changes; and (iii) the positions are denominated in 
the same currency. 

[[Page 38099]]

---------------------------------------------------------------------------

    (v) A bank may offset long and short positions (both actual and 
notional) in identical derivative instruments with exactly the same 
issuer, coupon, currency, and maturity before slotting these 
positions into time-bands. A matched position in a future and its 
corresponding underlying may also be fully offset and, thus, 
excluded from the calculation, except when the future comprises a 
range of deliverable instruments. However, in cases where, among the 
range of deliverable instruments, there is a readily identifiable 
underlying instrument that is most profitable for the trader with a 
short position to deliver, positions in the futures contract and the 
instrument may be offset. No offsetting is allowed between positions 
in different currencies.
    (vi) Offsetting positions in the same category of instruments 
can in certain circumstances be regarded as matched and treated by 
the bank as a single net position which should be entered into the 
appropriate time-band. To qualify for this treatment the positions 
must be based on the same underlying instrument, be of the same 
nominal value, and be denominated in the same currency. The separate 
sides of different swaps may also be ``matched'' subject to the same 
conditions. In addition:
    (A) For futures, offsetting positions in the notional or 
underlying instruments to which the futures contract relates must be 
for identical instruments and the instruments must mature within 
seven days of each other;
    (B) For swaps and FRAs, the reference rate (for floating rate 
positions) must be identical and the coupon closely matched; and
    (C) For swaps, FRAs and forwards, the next interest reset date, 
or for fixed coupon positions or forwards the remaining maturity, 
must correspond within the following limits: If the reset (remaining 
maturity) dates occur within one month, then the reset (remaining 
maturity) dates must be on the same day; if the reset (remaining 
maturity) dates occur between one month and one year later, then the 
reset (remaining maturity) dates must occur within seven days of 
each other, or if the reset (remaining maturity) dates occur over 
one year later, then the reset (remaining maturity) dates must occur 
within thirty days of each other.
    (vii) Interest rate and currency swaps, FRAs, forward foreign 
exchange contracts and interest rate futures are not subject to a 
specific risk charge. This exemption also applies to futures on a 
short-term (e.g., LIBOR) interest rate index. However, in the case 
of futures contracts where the underlying is a debt security, or an 
index representing a basket of debt securities, a specific risk 
charge will apply according to the category of the issuer as set out 
in section 6(a)(2) of this appendix B.
    (b) Equities. (1) Specific risk. The measure of specific risk is 
calculated on the basis of the bank's gross equity positions, that 
is, the absolute sum of the current market value of all long equity 
positions and of all short equity positions.11 The specific 
risk capital requirement is 8.0 percent of that sum, unless the 
portfolio is both liquid and well-diversified, in which case the 
specific risk capital requirement is 4.0 percent of the gross equity 
position. A specific risk charge of 2.0 percent applies to the net 
long or short position in a broad, diversified equity index.

    \11\ Matched positions in each identical equity in each national 
market may be treated as offsetting and excluded from the capital 
calculation, with any remaining position included in the 
calculations for specific and general market risk. For example, a 
future in a given equity may be offset against an opposite cash 
position in the same equity.
---------------------------------------------------------------------------

    (2) General market risk. The measure of general market risk is 
based on the difference between the sum of the long positions and 
the sum of the short positions (i.e., the overall net position in an 
equity market) at current market value. An overall net position must 
be separately calculated for each national market in which the bank 
holds equities. The capital requirement for general market risk is 
8.0 percent of the net position in each equity market.
    (3) Equity derivatives. (i) Equity derivatives and other off-
balance-sheet positions that are affected by changes in equity 
prices are included in the measurement system under section 6(b) of 
this appendix B (except for equity options, equity index options, 
and the associated underlying, which are included in the measurement 
system under the treatment discussed in section 6(e) of this 
appendix B).12 This includes futures and swaps on both 
individual equities and on equity indices. Equity derivatives should 
be converted into notional equity positions in the relevant 
underlying.

    \12\ Where equities are part of a forward contract (both 
equities to be received or to be delivered), any interest rate or 
foreign currency exposure from the other side of the contract should 
be appropriately included in sections 6(a) and (c) of this appendix 
B.
---------------------------------------------------------------------------

    (ii) Futures and forward contracts relating to individual 
equities should be reported as current market prices of the 
underlying. Futures relating to equity indices should be reported as 
the marked-to-market value of the notional underlying equity 
portfolio. Equity swaps are treated as two notional positions, with 
the receiving side as the long position and the paying side as the 
short position.13 If one of the legs involves receiving/paying 
a fixed or floating interest rate, the exposure should be slotted 
into the appropriate repricing maturity band for debt securities. 
The stock index is covered by the equity treatment.

    \13\ For example, an equity swap in which a bank is receiving an 
amount based on the change in value of one particular equity or 
equity index and paying a different index will be treated as a long 
position in the former and a short position in the latter.
---------------------------------------------------------------------------

    (iii) In the case of futures-related arbitrage strategies, the 
2.0 percent specific risk charge applicable to broad diversified 
equity indices may be applied to only one index. The opposite 
position is exempt from a specific risk charge. The strategies 
qualifying for this treatment are:
    (A) When the bank takes an opposite position in exactly the same 
index at different dates; and
    (B) When the bank has an opposite position in different but 
similar indices at the same date, subject to supervisory oversight.
    (iv) If a bank engages in a deliberate arbitrage strategy, in 
which a futures contract on a broad diversified equity index matches 
a basket of securities, it may exclude both positions from the 
standardized approach on the condition that the trade has been 
deliberately entered into and separately controlled and the 
composition of the basket of stocks represents at least 90 percent 
of the market value of the index. In such a case, the minimum 
capital requirement is 4.0 percent (that is, 2.0 percent of the 
gross value of the positions on each side). This applies even if all 
of the securities comprising the index are held in identical 
proportions. Any excess value of the securities comprising the 
basket over the value of the futures contract or excess value of the 
futures contract over the value of the basket is treated as an open 
long or short position.
    (v) If a bank takes a position in depository receipts 14
against an opposite position in the underlying equity, it may offset 
the position.

    \14\ Depository receipts are instruments issued by a trust 
company or other depository institution evidencing the deposit of 
foreign securities and facilitating trading in such instruments on 
U.S. stock exchanges.
---------------------------------------------------------------------------

    (c) Foreign Exchange Risk. (1) The capital requirement for 
foreign exchange risk covers the risk of holding or taking positions 
in foreign currencies, including gold, and is based on a bank's net 
open long positions or net open short positions in each currency, 
whether or not those positions are in the trading portfolio, plus 
the net open position in gold, regardless of sign.15

    \15\ Where a bank has future and forward contracts to deliver 
and receive gold, a maturity ladder should be constructed in 
accordance with section 6(a) of this appendix B treating gold as a 
zero coupon instrument.
    (2) A bank's net open position in each currency (and gold) is 
calculated by summing:
    (i) The net spot position (i.e., all asset items less all 
liability items, including accrued interest earned but not yet 
received and accrued expenses, denominated in the currency in 
question);
    (ii) All foreign exchange derivative instruments and other off-
balance-sheet positions that are affected by changes in exchange 
rates are included in the measurement system under section 6(c) of 
this appendix B (except for options and their associated 
underlyings, which are included in the measurement system under the 
treatment discussed in section 6(e) of this appendix B). Forward 
currency positions should be valued at current spot market exchange 
rates. For a bank in which the basis of its normal management 
accounting is to use net present values, forward positions may be 
discounted to net present values as an acceptable way of measuring 
currency positions for regulatory capital purposes;
    (iii) Guarantees (and similar instruments) that are certain to 
be called and are likely to be irrevocable;
    (iv) Net future income/expenses not yet accrued but already 
fully hedged (at the discretion of the bank). A bank that includes 
future income and expenses must do so on a consistent basis without 
selecting expected future flows in order to reduce the bank's 
position; and
    (v) Any other item representing a profit or loss in foreign 
currencies. 

[[Page 38100]]

    (3) For measuring a bank's open positions, positions in 
composite currencies, such as the ECU, may be either treated as a 
currency in their own right or split into their component parts on a 
consistent basis. Positions in gold are measured in the same manner 
as described in section 6(d) of this appendix B.16

    \16\ Where gold is part of a forward contract (quantity of gold 
to be received or to be delivered), any interest rate or foreign 
currency exposure from the other side of the contract should be 
reported as set out in section 6(a) and (c) of this appendix B.
---------------------------------------------------------------------------

    (4) The capital requirement is determined by converting the 
nominal amount (or net present value) of the net open position in 
each foreign currency (and gold) at spot rates into the reporting 
currency. The capital requirement is 8.0 percent of the sum of:
    (i) The greater of the sum of the net short open positions or, 
the sum of the net long open positions; and
    (ii) The net open position in gold, regardless of sign.17

    \17\ For example, a bank has the following net currency 
positions: Yen = +50, DM = +100, GB = +150, FFR = -20, US$= -180, 
and gold = -35. The bank would sum its long positions (total = +300) 
and sum its short positions (total = -200). The bank's capital 
requirement for foreign exchange market risk would be: (300 (the 
larger of the summed long and short positions) + 35 (gold))  x  8.0% 
= $26.80.
---------------------------------------------------------------------------

    (5) A bank doing negligible business in foreign currency and 
that does not take foreign exchange positions for its own account 
may be exempted from the capital requirement for foreign exchange 
risk provided that:
    (i) Its foreign currency business, defined as the greater of the 
sum of its gross long positions and the sum of its gross short 
positions in all foreign currencies, does not exceed 100 percent of 
eligible capital as defined in section 3 of this appendix B; and
    (ii) Its overall net open foreign exchange position as 
determined in section 6(c)(2) does not exceed 2.0 percent of its 
eligible capital.
    (6) Where a bank is assessing its foreign exchange risk on a 
consolidated basis, it may be impractical in the case of some 
marginal operations to include the currency positions of a foreign 
branch or subsidiary of the bank. In such cases, the internal limit 
in each currency may be used as a proxy for the positions, provided 
there is adequate ex post monitoring of actual positions complying 
with such limits. In these circumstances, the limits should be 
added, regardless of sign, to the net open position in each 
currency.
    (d) Commodities risk. (1) Measurement methods. This section 
provides a minimum capital requirement to cover the risk of holding 
or taking positions in commodities. There are two methods under the 
standardized approach for measuring commodity market risk--the 
simplified method and the maturity method. These methods are only 
appropriate for banks that conduct a limited amount of commodities 
business. All other banks must adopt an internal measurement system 
conforming to the criteria in section 5 of this appendix B.
    (2) Base capital requirement. Under both the simplified and 
maturity methods, each long and short commodity position (spot and 
forward) is expressed in terms of the standard unit of measurement 
(such as barrels, kilos, or grams). The open positions in each 
category of commodities are then converted at current spot rates 
into U.S. currency, with long and short positions offset to arrive 
at the net open position in each commodity. Positions in different 
categories of commodities may not, generally, be offset.18 
Under either method, the base capital requirement is 15.0 percent of 
the net open position, long or short, in each commodity.19

    \18\ However, netting is permitted between different sub-
categories of the same commodity in cases where the sub-categories 
are deliverable against each other.
    \19\ When the funding of a commodity position opens a bank to 
interest rate or foreign exchange exposure the relevant positions 
should be included in the measures of interest rate and foreign 
exchange risk described in sections 6(a) and (c) of this appendix B. 
When a commodity is part of a forward contract, any interest or 
foreign currency exposure from the other side of the contract should 
be appropriately included in sections 6(a) and 6(c) of this appendix 
B.
---------------------------------------------------------------------------

    (3) Simplified method. To protect a bank against basis risk, 
interest rate risk, and forward gap risk, each category of commodity 
is also subject to a 3.0 percent capital requirement on the bank's 
gross positions, long plus short, in the particular commodity. In 
valuing gross positions in commodity derivatives for this purpose, a 
bank should use the current spot price. The total capital 
requirement for commodities risk is the sum of the 15.0 percent base 
charges for each net commodity position and the 3.0 percent 
requirements on the gross commodity positions.
    (4) Maturity method. (i) Under this method, a bank must slot 
each long and short commodity position (converted into U.S. currency 
at current spot rates) into a maturity ladder. The time-bands for 
the maturity ladder are; from zero to one month, one up to three 
months, three up to six months, six up to twelve months, one up to 
two years, two up to three years, and over three years. A separate 
maturity ladder is used for each category of commodity. Physical 
commodities are allocated to the first time-band.
    (ii) In order to capture forward gap and interest rate risk 
within a time-band (together sometimes referred to as curvature/
spread risk), offsetting long and short positions in each time-band 
are subject to an additional capital requirement. Beginning with the 
shortest-term time-band and continuing with subsequent time-bands, 
the amount of the matched short positions plus the amount of the 
matched long position is multiplied by a spread rate of 1.5 percent.
    (iii) The unmatched net position from a shorter-term time-band 
must be carried forward to offset exposures in longer-term time-
bands. A capital requirement of 0.6 percent of the net position 
carried forward is added for each time-band that the net position is 
carried forward.20 The total capital requirement for 
commodities risk is the sum of the 15.0 percent base capital 
requirement for each net commodity position and the additional 
requirements for matched positions and for unmatched positions 
carried forward.

    \20\ For example, if $200 short is carried forward from the 3-6 
month time-band to the 1-2 year time-band, the capital charge would 
be $200  x  .006  x  2 = $2.40.
---------------------------------------------------------------------------

    (5) Commodity derivatives and other off-balance-sheet positions 
that are affected by changes in commodity prices are included in the 
measurement system under section 6(d) of this appendix B (except for 
options and the associated underlying, which are included in the 
measurement system under the treatment discussed in section 6(e) of 
this appendix B). Commodity derivatives are converted into notional 
commodity positions. Under the maturity method, the positions are 
slotted into maturity time-bands as follows:
    (i) Futures and forward contracts relating to individual 
commodities are incorporated in the measurement system as notional 
amounts (of, for example, barrels or kilos) that are converted to 
U.S. dollars at current spot rates and are assigned a maturity 
according to expiration date;
    (ii) Commodity swaps where one side of the contract is a fixed 
price and the other side is the current market price are 
incorporated as a series of positions equal to the notional amount 
of the contract at current spot rates, with one position 
corresponding to each payment on the swap and slotted in the 
maturity ladder accordingly. The positions are long positions if the 
bank is paying a fixed price and receiving a floating price, and 
short positions if the bank is receiving a fixed price and paying a 
floating price; 21 and

    \21\ If one of the sides of the transaction involves receiving/
paying a fixed or floating interest rate, that exposure should be 
slotted into the appropriate repricing maturity band in section 6(a) 
of this appendix B.
---------------------------------------------------------------------------

    (iii) Commodity swaps where the sides of the transaction are in 
different commodities are included in the relevant reporting ladder. 
No offsetting is allowed unless the commodities are in the same sub-
category.
    (e) Options. (1) Several alternatives are available for a bank 
to use in measuring its market risk for options activities. A bank 
that only has purchased options may use the simplified method set 
forth in section 6(e)(2) of this appendix B. A bank that also writes 
options may use the scenario method described in section 6(e)(3) of 
this appendix B, or the delta-plus method set forth in section 
6(e)(4) of this appendix B.22 These methods may only be used by 
banks which, in relative terms, have limited options activities. 
Banks with more significant options business are expected to adopt 
an internal measurement system conforming to the criteria in section 
5 of this appendix B. Regardless of the method used, specific risk 
related to the issuer of an instrument still applies to options 
positions for equities, equity indices and corporate debt securities 
as set forth in sections 6(a) and (b) of this appendix B. There 
remains a separate capital 

[[Page 38101]]
requirement for counterparty credit risk as set forth in appendix A to 
this part 3.

    \22\ Unless all their written option positions are hedged by 
perfectly matched long positions in exactly the same options, in 
which case there is no capital requirement for market risk.
---------------------------------------------------------------------------

    (2) Under the simplified and scenario methods, the positions for 
the options and the associated underlying, cash or forward, are not 
included in the measurement framework for debt securities, equities, 
foreign exchange or commodities risk as set forth in sections 6(a) 
through (d) of this appendix B. Rather, they are subject to capital 
requirements as calculated in this section. The capital requirements 
calculated under this section should then be added to the capital 
requirements for debt securities, equities, foreign exchange and 
commodities risk as appropriate. Under the delta-plus method, the 
delta equivalent position 23 for each option is included in the 
measurement frameworks set forth in sections 6(a) through (d) of 
this appendix B.

     23 The delta equivalent of an option is the option's delta 
value multiplied by its principal or notional value. The delta value 
of an option represents the expected change in the option's price as 
a proportion of a small change in the price of the underlying 
instrument. For example, an option whose price changes $1 for every 
$2 dollar change in the price of the underlying instrument has a 
delta of 0.50.
---------------------------------------------------------------------------

    (3) A bank that has only a limited amount and range of purchased 
options may use the following simplified approach to measure its 
market risk exposure: 24

     24 For example, if a holder of 100 shares currently valued at 
$10 each has an equivalent put option with a strike price of $11, 
the capital charge would be: $1,000  x  16.0 percent (e.g., 8.0 
percent specific plus 8.0 percent general market risk) = $160, less 
the amount the option is in the money ($11-$10)  x  100 = $100, 
i.e., the capital charge would be $60. A similar methodology applies 
for options whose underlying is a foreign currency, a debt security 
or a commodity.
---------------------------------------------------------------------------

    (i) For a bank with a long cash position and a long put or with 
a short cash position and a long call, the capital requirement is 
the market value of the underlying instrument multiplied by the sum 
of the specific and general market risk requirements for the 
underlying (that is, the specific and general market risk 
requirements that would have applied to the underlying directly 
under sections 6(a) through (d) of this appendix B), less the amount 
the option is in the money (if any) bounded at zero.25

    \25\ Some options (e.g., where the underlying is an interest 
rate, a currency, or a commodity) bear no specific risk but specific 
risk will be present in the case of options on corporate debt 
securities and for options on equities and equity indices.
---------------------------------------------------------------------------

    (ii) For a bank with a long call or a long put, the capital 
charge is the lesser of:
    (A) The market value of the underlying security multiplied by 
the sum of specific and general market risk requirements for the 
underlying (that is, the specific and general market risk 
requirements that would have applied to the underlying directly 
under sections 6(a) through (d) of this appendix B); or
    (B) The market value of the option.
    (iii) Under this measure, the capital requirement for currency 
options is 8.0 percent of the market value of the underlying and for 
commodity options is 15.0 percent of the market value of the 
underlying.
    (4) Under the scenario approach, a bank revalues its options and 
related hedging positions by changing the underlying rate or price 
over a specified range and by assuming different levels of 
volatility for that rate or price.
    (i) For each of its option portfolios, a bank constructs a grid 
based on a fixed range of changes in the portfolio's risk factors 
and calculates changes in the value of the option portfolio at each 
point within the grid. For this purpose, an option portfolio 
consists of an option and any related hedging positions or multiple 
options and related hedging positions that are grouped together 
according to their remaining maturity or the type of underlying.
    (ii) Options based on interest rates and debt instruments are 
grouped into portfolios according to the maturity zones that are set 
forth in section 6(a) of this appendix B. (Zone 1 instruments have a 
remaining maturity of up to 1 year, zone 2 instruments have a 
remaining maturity from 1 year up to 4 years, and zone 3 instruments 
have a remaining maturity of 4 years or more.)
    (iii) These options and the associated hedging positions should 
be evaluated under the assumption that the relevant interest rates 
move simultaneously. For options based on equities, separate grids 
are constructed for each individual equity issue and index. For 
options based on exchange rates, separate grids are constructed for 
individual exchange rates. For options based on commodities, 
separate grids are constructed for each category of commodity (as 
defined in sections 6(a) and (d) of this appendix B).
    (iv) For option portfolios with options based on equities, 
exchange rates, and commodities, the first dimension of the grid 
consists of rate or price changes within a specified range above and 
below the current market value of the underlying; for equities, the 
range is +/- 12.0 percent (or in the case of an index +/- 8.0 
percent), for exchange rates the range is +/- 8.0 percent, and for 
commodities the range is +/- 15.0 percent. For option portfolios 
with options based on interest rates, the range for the first 
dimension of the grid depends on the remaining maturity zone. The 
range for zone 1 is +/- 100 basis points, the range for zone 2 is +/
- 90 basis points, and the range for zone 3 is +/- 75 basis points. 
For all option portfolios, the range is divided into at least ten 
equally spaced intervals. The second dimension of each grid is a 
shift in the volatility of the underlying rate or price equal to +/- 
25.0 percent of the current volatility.26

     26 For example, if the underlying in an equity instrument with 
a current market value of $100 and a volatility of 20 percent, the 
first dimension of the grid would range from $88 to $112, divided 
into ten intervals of $2.40 and the second dimension would assume 
volatilities of 15 percent, 20 percent, and 25 percent.
---------------------------------------------------------------------------

    (v) For each assumed volatility and rate or price change (a 
scenario), the bank revalues each option portfolio. The market risk 
capital requirement for the portfolio is the largest loss in value 
from among the scenario revaluations. The total market risk capital 
requirement for all option portfolios is the sum of the individual 
option portfolio capital requirements.
    (vi) The OCC will review the application of the scenario 
approach, particularly regarding the precise way the analysis is 
constructed. A bank using the scenario approach should meet the 
appropriate qualitative criteria set forth in section 5 of this 
appendix B.
    (5) Under the delta-plus method, a bank that writes options may 
include delta-weighted options positions within each measurement 
framework as set forth in sections 6(a) through 6(d) of this 
appendix B.
    (i) Options positions should be measured as a position equal to 
the market value of the underlying instrument multiplied by the 
delta. In addition, a bank must measure the sensitivities of the 
option's gamma (the change of the delta for a given change in the 
price of the underlying) and vega (the sensitivity of the option 
price with respect to a change in volatility) to calculate the total 
capital requirement. These sensitivities may be calculated according 
to an exchange model approved by the OCC or to the bank's own 
options pricing model, subject to oversight by the OCC.
    (ii) For options with debt instruments or interest rates as the 
underlying instrument, delta-weighted options positions should be 
slotted into the debt instrument time-bands in section 6(a) of this 
appendix B using a two-legged approach (as is used for other 
derivatives), requiring one entry at the time the underlying 
contract takes effect and one at the time the underlying contract 
matures.27 Floating rate instruments with caps or floors should 
be treated as a combination of floating rate securities and a series 
of European-style options.28 A bank must also calculate the 
gamma and vega for each such option position (including hedge 
positions). The results should be slotted into separate maturity 
ladders by currency. For options such as caps and floors whose 
underlying instrument is an interest rate, the delta and gamma 
should be expressed in terms of a hypothetical underlying security. 
Subsequently:

    \27\ For example, in April a purchased call option on a June 
three-month interest-rate future would be considered on the basis of 
its delta-equivalent value to be a long position with a maturity of 
five months and a short position with a maturity of two months. The 
written option would be slotted as a long position with a maturity 
of two months and a short position with a maturity of five months.
    \28\ For example, the holder of a three-year floating rate bond 
indexed to six-month LIBOR with a cap of 15 percent would treat the 
bond as a debt security that reprices in six months, and a series of 
five written call options on a FRA with a strike rate of 15 percent, 
each slotted as a short position at the expiration date of the 
option and as a long position at the time the FRA matures.
---------------------------------------------------------------------------

    (A) For gamma risk, for each time-band, net gammas that are 
negative are multiplied by the risk weights set out in Table 5 and 
by the square of the market value of the underlying instrument (net 
positive gammas may be disregarded);
    (B) For volatility risk, a bank calculates the capital 
requirements for vega in each time-band assuming a proportional 
shift in volatility of 25.0 percent;
    (C) The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the sum of the 

[[Page 38102]]
individual capital requirements for vega risk for each time-band; and
    (D) The delta plus method risk weights are:

                Table 5.--Delta Plus Method Risk Weights                
------------------------------------------------------------------------
                                     Modified                           
                                     duration     Assumed    Risk-weight
            Time-band                (average     interest       for    
                                   assumed for  rate change    gamma\1\ 
                                    time-band)      (%)                 
------------------------------------------------------------------------
Under 1 month....................         0.00         1.00      0.00000
1 up to 3 months.................         0.20         1.00      0.00020
3 up to 6 months.................         0.40         1.00      0.00080
6 up to 12 months................         0.70         1.00      0.00245
1 up to 2 years..................         1.40         0.90      0.00794
2 up to 3 years..................         2.20         0.80      0.01549
3 up to 4 years..................         3.00         0.75      0.02531
4 up to 5 years..................         3.65         0.75      0.03747
5 up to 7 years..................         4.65         0.70      0.05298
7 up to 10 years.................         5.80         0.65      0.07106
10 up to 15 years................         7.50         0.60      0.10125
15 up to 20 years................         8.75         0.60      0.13781
Over 20 years....................        10.00         0.60      0.18000
------------------------------------------------------------------------
\1\ According to the Taylor expansion, the risk weights are calculated  
  as \1/2\ (modified duration x assumed interest rate change) \2\/100.  

    (iii) For options with equities as the underlying, delta-
weighted option positions should be incorporated in the measure of 
market risk set forth in section 6(b) of this appendix B. Individual 
equity issues and indices should be treated as separate underlyings. 
In addition to the capital requirement for delta risk, a bank should 
apply a further capital charge for gamma and vega risk:
    (A) For gamma risk, the net gammas that are negative for each 
underlying are multiplied by 0.72 percent (in the case of an 
individual equity) or 0.32 percent (in the case of an index as the 
underlying) and by the square of the market value of the underlying;
    (B) For volatility risk, a bank calculates the capital 
requirement for vega for each underlying, assuming a proportional 
shift in volatility of 25.0 percent; and
    (C) The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the individual capital requirements for vega risk.
    (iv) For options on foreign exchange and gold, the net delta (or 
delta-based) equivalent of the total book of foreign currency and 
gold options is incorporated into the measurement of the exposure in 
a single currency position as set forth in section 6(c) of this 
appendix B. The gamma and vega risks should be measured as follows:
    (A) For gamma risk, for each underlying exchange rate, net 
gammas that are negative are multiplied by 0.32 percent and by the 
square of the market value of the positions;
    (B) For volatility risk, a bank calculates the capital 
requirements for vega for each currency pair and gold assuming a 
proportional shift in volatility of 25.0 percent; and
    (C) The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the sum of the individual capital requirements for 
vega risk.
    (v) For options on commodities, the delta-weighted positions are 
incorporated in one of the measures described in section 6(d) of 
this appendix B. In addition, a bank must apply a capital 
requirement for gamma and vega risk:
    (A) For gamma risk, net gammas that are negative for each 
underlying are multiplied by 1.125 percent and by the square of the 
market value of the commodity;
    (B) For volatility risk, a bank calculates the capital 
requirements for vega for each commodity assuming a proportional 
shift in volatility of 25.0 percent; and
    (C) The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the sum of the individual capital requirements for 
vega risk.
    (vi) Under certain conditions and to a limited extent, the OCC 
may permit banks that are significant traders in options with debt 
securities or interest rates as the underlying to net positive and 
negative gammas and vegas across time-bands. Such netting must be 
based on prudent and conservative assumptions and the bank must 
materially meet the qualitative standards set forth in section 5 of 
this appendix B.
    (vii) A bank may base the calculation of vega risk on a 
volatility ladder in which the implied change in volatility varies 
with the maturity of the option. The assumed proportional shift in 
volatility must be at least 25.0 percent at the short 
end of the maturity spectrum. The proportional shift for longer 
maturities must be at least as stringent in statistical terms as the 
25.0 percent shift at the short end.
    (viii) A bank should also monitor the risks of rho (the rate of 
change of the value of the option with respect to the interest rate) 
and theta (the rate of change of the value of the option with 
respect to time).
Section 7. Reservation of authority

    (a) Partial models. The OCC reserves the authority to require a 
bank subject to the market risk requirements of this appendix B to 
develop or use an internal market risk model, the supervisory market 
risk model, or any combination thereof, for the purposes of 
compliance with the capital requirements of this appendix B.29

    \29\ The OCC generally expect banks with significant trading 
positions to use internal market risk models for the purposes of 
this appendix B.
---------------------------------------------------------------------------

    (b) De minimis exposures. The OCC also may permit a bank with 
negligible exposures to certain types of market risk (activities in 
remote locations and minor currencies) to adopt alternative 
measurements for those exposures if the alternative measurements are 
able to adequately measure the risk.
    (c) Multiplication factor for qualifying internal market risk 
model. The OCC may increase or decrease the multiplication factor 
applicable to the capital requirement under a qualifying internal 
market risk model based on an assessment of the quality and historic 
accuracy of the bank's risk management system.

    Office of the Comptroller of the Currency.

    Dated: July 10, 1995.
Eugene A. Ludwig,
Comptroller of the Currency.

FEDERAL RESERVE BOARD

12 CFR Chapter II

    For the reasons set out in the preamble, parts 208 and 225 of title 
12 of the Code of Federal Regulations are proposed to be amended as set 
forth below.

PART 208--MEMBERSHIP OF STATE BANKING INSTITUTIONS IN THE FEDERAL 
RESERVE SYSTEM (REGULATION H)

    1. The authority citation for part 208 is revised to read as 
follows:

    Authority: 12 U.S.C. 36, 248(a), 248(c), 321-338a, 371d, 461, 
481-486, 601, 611, 1814, 1823(j), 1828(o), 1831o, 1831p-1, 3105, 
3310, 3331-3351, and 3905-3909; 15 U.S.C. 

[[Page 38103]]
78b, 78l(b), 78l(g), 78l(i), 78o-4(c)(5), 78q, 78q-1 and 78w; 31 U.S.C. 
5318; 42 U.S.C. 4012a, 4104a, 4104b, 4106, and 4128.

    2. In Part 208, Sec. 208.13 is revised to read as follows:


Sec. 208.13  Capital adequacy.

    The standards and guidelines by which the capital adequacy of state 
member banks will be evaluated by the Board are set forth in appendix A 
and appendix E to part 208 for risk-based capital purposes, and, with 
respect to the ratios relating capital to total assets, in appendix B 
to part 208 and in appendix B to the Board's Regulation Y, 12 CFR part 
225.
    3. In Part 208, Sec. 208.31 is amended by revising paragraphs (e), 
(h), and (j) to read as follows:


Sec. 208.31  Definitions.

* * * * *
    (e) Risk-weighted assets means total weighted risk assets, as 
calculated in accordance with the Board's Capital Adequacy Guidelines 
for State Member Banks: Risk-Based Measure (appendix A to this part 
208) and adjusted for market risk in accordance with the Board's 
Capital Adequacy Guidelines for State Member banks: Market Risk Measure 
(appendix E to this part 208).
* * * * *
    (h) Tier 1 risk-based capital ratio means the ratio of Tier 1 
capital to weighted risk assets, as calculated in accordance with the 
Board's Capital Adequacy Guidelines for State Member Banks: Risk-Based 
Measure (appendix A to this part 208) and adjusted for market risk in 
accordance with the Board's Capital Adequacy Guidelines for State 
Member Banks: Market Risk Measure (appendix E to this part 208).
* * * * *
    (j) Total risk-based capital ratio means the ratio of qualifying 
total capital to weighted risk assets, as calculated in accordance with 
the Board's Capital Adequacy Guidelines for State Member Banks: Risk-
Based Measure (appendix A to this part 208) and adjusted for market 
risk in accordance with the Board's Capital Adequacy Guidelines for 
State Member Banks: Market Risk Measure (appendix E to this part 208).
    4. In part 208, Appendix A is amended by revising the first and 
second paragraphs of section I. to read as follows:

Appendix A to Part 208--Capital Adequacy Guidelines for State Member 
Banks: Risk-Based Measure

I. Overview

    The Board of Governors of the Federal Reserve System has adopted 
a risk-based capital measure to assist in the assessment of the 
capital adequacy of state member banks.1 The principal 
objectives of this measure are to (i) make regulatory capital 
requirements more sensitive to differences in risk profiles among 
banks; (ii) factor off-balance-sheet exposures into the assessment 
of capital adequacy; (iii) minimize disincentives to holding liquid, 
low-risk assets; and (iv) achieve greater consistency in the 
evaluation of the capital adequacy of major banks throughout the 
world.

    \1\ Some banks are also subject to capital requirements for 
market risk as set forth in appendix E of this part. Banks that are 
subject to the market risk measure are required to follow the 
guidelines set forth in appendix E of this part for determining 
qualifying and eligible capital, calculating market risk-equivalent 
assets and adding them into weighted-risk assets, and calculating 
risk-based capital ratios adjusted for market risk. Supervisory 
ratios that relate capital to total assets for state member banks 
are outlined in appendix B of this part and in appendix B to part 
225 of the Board's Regulation Y, 12 CFR part 225.
---------------------------------------------------------------------------

    The risk-based capital guidelines include both a definition of 
capital and a framework for calculating weighted risk assets by 
assigning assets and off-balance-sheet items to broad risk 
categories.2 A bank's risk-based capital ratio is calculated by 
dividing its qualifying capital (the numerator of the ratio) by its 
weighted risk assets (the denominator).3 The definition of 
qualifying capital is outlined below in section II. of this appendix 
A, and the procedures for calculating weighted risk assets are 
discussed in section III. of this appendix A. Attachment I to this 
appendix A illustrates a sample calculation of weighted risk assets 
and the risk-based capital ratio.

    \2\ The risk-based capital measure is based upon a framework 
developed jointly by supervisory authorities from the countries 
represented on the Basle Committee on Banking Regulations and 
Supervisory Practices (Basle Supervisors' Committee) and endorsed by 
the Group of Ten Central Bank Governors. The framework is described 
in a paper prepared by the Basle Supervisors' Committee entitled 
``International Convergence of Capital Measurement,'' July 1988.
    \3\ Banks generally are expected to utilize period-end amounts 
in calculating their risk-based capital ratios. When necessary and 
appropriate, ratios based on average balances may also be calculated 
on a case-by-case basis. Moreover, to the extent banks have data on 
average balances that can be used to calculate risk-based ratios, 
the Federal Reserve will take such data into account.
---------------------------------------------------------------------------

* * * * *
    5. In Part 208, a new Appendix E is added to read as follows:

Appendix E to Part 208--Capital Adequacy Guidelines for State Member 
Banks: Market Risk Measure

I. Introduction

A. Overview

    1. The Board of Governors of the Federal Reserve System has 
adopted a framework for determining capital requirements for the 
market risk exposure of state member banks.1 For this purpose, 
market risk is defined as the risk of losses in a bank's on- and 
off-balance-sheet positions arising from movements in market prices. 
The market risks subject to these capital requirements are those 
associated with debt and equity instruments held in the bank's 
trading account, as well as foreign exchange risk and commodities 
risk throughout the bank, including options and other derivative 
contracts in each risk category.

    \1\ The market risk measure is based on a framework developed 
jointly by supervisory authorities from the countries represented on 
the Basle Committee on Banking Supervision (Basle Supervisors 
Committee) and endorsed by the Group of Ten Central Bank Governors. 
The framework is described in a paper prepared by the Basle 
Supervisors Committee entitled ``[Proposal to issue a] Supplement to 
the Basle Capital Accord to Cover Market Risks.'' [April] 1995.
---------------------------------------------------------------------------

    2. Effective December 31, 1997, the market risk measure will be 
applied to all state member banks that, on a consolidated basis:
    a. Have total assets in excess of $5 billion; and either have a 
total volume of trading activities (measured as the sum of the 
bank's trading assets and liabilities 2 on a daily average 
basis for the quarter) that is 3.0 percent or more of the total 
assets of the bank, or have interest rate, foreign exchange, equity, 
and commodity off-balance-sheet derivative contracts relating to 
trading activities whose total notional amounts exceed $5 billion; 
or

    \2\ As reflected in the bank's quarterly Consolidated Reports of 
Condition and Income (call report).
---------------------------------------------------------------------------

    b. Have total assets of $5 billion or less; and have trading 
activities exceeding 10.0 percent of the total assets of the bank.
    3. Such banks are still subject to the risk-based capital 
measure set forth in appendix A of this part, subject to the 
exclusion of certain assets specified in this appendix E. However, 
these banks must calculate their market risk-equivalent assets and 
determine risk-based capital ratios adjusted for market risk in 
accordance with this appendix E.3

    \3\ The Federal Reserve may apply all or portions of this 
Appendix E to other banks when deemed necessary for safety and 
soundness purposes.
---------------------------------------------------------------------------

    4. The market risk measure provides two ways for a bank to 
determine its exposure to market risk. A bank may use its internal 
risk measurement model, subject to the conditions and criteria set 
forth in section III. of this appendix E (referred to as the 
internal models approach), or when appropriate, a bank may use all 
or portions of the alternative measurement system described in 
section IV. of this appendix E (referred to as the standardized 
approach).
    a. With prior approval from the Federal Reserve, for regulatory 
capital purposes, a bank may use its internal risk measurement model 
to measure its value-at-risk 4 for each of the following risk 
factor categories; interest rates, exchange rates, equity prices, 
and commodity prices. The value-at-risk amount for each risk factor 
category should include volatilities of related options. The value-
at-risk amount for each risk factor category is 

[[Page 38104]]
summed to determine the aggregate value-at-risk for the bank.

    \4\ A bank evaluates its current positions and estimates future 
market volatility through a value-at-risk measure, which is an 
estimate representing, with a certain degree of statistical 
confidence, the maximum amount by which the market value of trading 
positions could decline during a specific period of time. The value-
at-risk is generated through an internal model that employs a series 
of market risk factors (for example, market rates and prices that 
affect the value of trading positions).
---------------------------------------------------------------------------

    b. The standardized approach uses a set of standardized 
calculations and assumptions to measure market risk exposure 
depending on its source; debt instruments, equities, foreign 
currencies, and commodities, including volatilities of related 
options.
    5. The Board generally expects any bank that is subject to the 
market risk measure, especially those with large trading accounts, 
to comply with the measure by using internal risk-measurement 
models. A bank may not change its measurement approach for the 
purpose of minimizing capital requirements. In limited instances, on 
a case-by-case basis, the Federal Reserve may permit a bank that has 
internal models to incorporate risk measures of negligible 
exposures, for example, de minimis positions, activities in remote 
locations, minor exposures in a currency, or activities that present 
negligible risk to the bank, in an alternative manner, so long as it 
adequately captures the risk.
    6. The risk-based capital ratios adjusted for market risk 
determined in accordance with this appendix E are minimum 
supervisory ratios. Banks generally are expected to operate with 
capital positions well above the minimum ratios. In all cases, banks 
should hold capital commensurate with the level and nature of the 
risks to which they are exposed.
    7. The Federal Reserve will monitor the implementation and 
effect of these guidelines in relation to domestic and international 
developments in the banking industry. When necessary and 
appropriate, the Board will consider the need to modify this 
appendix E in light of any significant changes in the economy, 
financial markets, banking practices, or other relevant factors.

B. Market Risks Subject to a Capital Requirement

    1. General Market Risk and Specific Risk. A bank must hold 
capital against exposure to general market risk and specific risk 
arising from its trading and other foreign exchange and commodity 
activities. For this purpose, general market risk refers to changes 
in the market value of covered transactions resulting from market 
movements, such as changing levels of market interest rates, broad 
equity indices, or currency exchange rates. Specific risk refers to 
credit risk, that is, the risk that the issuer of a debt or equity 
instrument might default, as well as to other factors that affect 
the market value of specific instruments but that do not materially 
alter market conditions.5

    \5\ This appendix E does not impose specific risk capital 
requirements for foreign exchange risk and commodities positions 
because they do not have the type of issuer-specific risk associated 
with debt and equity instruments in the trading account.
---------------------------------------------------------------------------

    2. Trading Activities. a. The general market risk and specific 
risk capital requirements for trading activities are based on on- 
and off-balance-sheet positions in a bank's trading account. For 
this purpose, trading account means positions in financial 
instruments acquired with the intent to resell in order to profit 
from short-term price movements (or other price or interest-rate 
variations), including, but not limited to:
    i. Assets acquired with the intent to resell to customers;
    ii. Positions in financial instruments arising from matched 
principal brokering and market making; or
    iii. Positions taken in order to hedge other elements of the 
trading account (that is, reduce risk by offsetting other positions 
that have exposure to changes in market rates or prices).6 
Trading activities may include positions in debt instruments, 
equities, foreign currencies, and commodity instruments, or related 
derivative 7 or other off-balance-sheet contracts.

    \6\ At a bank's option, when non-trading account instruments are 
hedged with instruments in the trading account, on- or off-balance-
sheet, the non-trading account instruments may be included in the 
measure for general market risk. Such non-trading account 
instruments remain subject to the credit risk capital requirements 
of appendix A of this part.
    \7\ In general terms, a derivative is a financial contract whose 
value is derived from the values of one or more underlying assets or 
reference rates or indexes of asset values (referred to as ``the 
underlying''). Derivatives include standardized contracts that are 
traded on exchanges and customized, privately negotiated contracts 
known as over-the-counter (OTC) derivatives.
---------------------------------------------------------------------------

    b. Debt instruments in the trading account are all fixed-rate 
and floating-rate debt securities and instruments that behave like 
debt, including non-convertible preferred stock. Convertible bonds, 
i.e., preferred stock or debt issues that are convertible, at a 
stated price, into common shares of the issuer, should be treated as 
debt instruments if they trade like debt instruments and as equities 
if they trade like equities. Also included are derivative contracts 
of debt instruments and other off-balance-sheet instruments in the 
trading account that react to changes in interest rates. A security 
that has been sold subject to a repurchase agreement or lent subject 
to a securities lending agreement is treated as if it were still 
owned by the lender of the security. Such transactions remain 
subject to capital requirements for credit risk for the off-balance-
sheet portion of the transaction as set forth in section III.D. of 
appendix A of this part.
    c. Equities in the trading account are equity instruments that 
behave like equities. The instruments covered include common stocks 
(whether voting or non-voting), convertible securities that behave 
like equities, and commitments to buy or sell equity securities. 
Also included are derivative contracts of equity instruments and 
other off-balance-sheet instruments in the trading account that are 
affected by changes in equity prices. However, non-convertible 
preferred stock is included in debt instruments.
    3. Foreign Exchange and Commodities Risk. Foreign exchange or 
commodities positions, whether or not included in a bank's trading 
account, are subject to a capital requirement for the market risk of 
those positions.
    a. The capital requirement for foreign exchange risk applies to 
a bank's total currency and gold positions. This includes spot 
positions (that is, asset items and liability items, including 
accrued interest and expenses, denominated in each currency); 
forward positions (that is, forward foreign exchange transactions, 
including currency futures and the principal on currency swaps not 
included in the spot position); and certain guarantees. It includes 
future income and expenses from foreign currency transactions not 
yet accrued but already fully hedged (at the discretion of the 
reporting bank), foreign exchange derivative and other off-balance-
sheet positions that are affected by changes in exchange rates, and 
any other item representing a profit or loss in foreign currencies.
    b. A bank may, subject to approval by the Federal Reserve, 
exclude from its foreign exchange positions any structural positions 
in foreign currencies. For this purpose, such structural positions 
are limited to transactions designed to hedge a bank's capital 
ratios against the effect of adverse exchange rate movements on 
subordinated debt, equity, or minority interests in consolidated 
subsidiaries and dotation capital assigned to foreign branches that 
are denominated in foreign currencies. Also included are any 
positions related to unconsolidated subsidiaries and to other items 
that are deducted from a bank's capital when calculating its capital 
base. In any event, such structural foreign currency positions must 
reflect long-term policies of the institution and not relate to 
trading positions.
    c. A bank doing negligible business in foreign currency and that 
does not take foreign exchange positions for its own account may be 
exempted from the capital requirement for foreign exchange risk 
provided that:
    i. Its foreign currency business, defined as the greater of the 
sum of its gross long positions and the sum of its gross short 
positions in all foreign currencies, does not exceed 100 percent of 
eligible capital as defined in section II. of this appendix E; and
    ii. Its overall net open foreign exchange position as determined 
in section IV.C.2. of this appendix E does not exceed 2.0 percent of 
its eligible capital.
    d. The capital requirement for commodities risk applies to a 
bank's total commodities positions, including commodity futures, 
commodity swaps, and all other commodity derivatives or other off-
balance-sheet positions that are affected by changes in commodity 
prices. A commodity is defined as a physical product that is or can 
be traded on a secondary market (such as agricultural products, 
minerals (including oil), and precious metals), but excluding gold 
(which is treated as foreign exchange).

C. Capital Requirements
    1. Capital Requirements. The minimum capital requirement for a 
state member bank subject to the market risk measure is the sum of:
    a. The capital requirement for credit risk as determined in 
accordance with appendix A of this part, excluding debt and equity 
instruments in the trading book and positions in commodities, but 
including the counterparty credit risk requirements on all over-the-
counter derivative activities whether in the bank's trading account 
or not; and
    b. The capital requirement for market risk as determined by the 
internal models approach, the standardized approach, or a 

[[Page 38105]]
combination of the two approaches deemed to be appropriate by the 
Federal Reserve.
    2. Internal Models. a. For a bank approved to use the internal 
models approach, the capital requirement for market risk is the 
higher of:
    i. The bank's previous day's aggregate value-at-risk amount 
calculated subject to certain supervisory requirements set forth in 
section III. of this appendix E; or
    ii. An average of the daily aggregate value-at-risk amounts, 
calculated subject to the same restrictions, measured on each of the 
preceding sixty (60) business days, multiplied by a minimum 
``multiplication factor'' of three (3).8

    \8\ The Federal Reserve may adjust the multiplication factor for 
a bank to increase its capital requirement based on an assessment of 
the quality and historic accuracy of the bank's risk management 
system.
---------------------------------------------------------------------------

    b. A bank approved to use the internal models approach may also 
be subject to a separate capital requirement for specific market 
risk of traded debt and equity instruments to the extent that the 
specific market risk associated with these instruments is not 
captured by the bank's models. However, for all banks using internal 
models, the total specific risk charge should in no case be less 
than one-half the specific risk charges calculated according to the 
standardized approach.
    3. Standardized approach. A bank whose model has not been 
approved by the Federal Reserve must use the standardized approach 
for measuring its market risk. For a bank using this approach, the 
capital requirement for market risk is the sum of the market risk 
capital requirement for debt and equity instruments in the trading 
account, foreign exchange and commodities risk throughout the bank, 
and options and other derivative positions in each risk category as 
set forth in sections IV.A. to IV.E. of this appendix E.9

    \9\ Section IV.E. of this appendix E provides several 
alternatives for measuring the market risk of options. Under two of 
the alternatives, the simplified and scenario methods, the 
underlying position of an option is ``carved-out,'' and is not 
included in the prescribed risk measure for the underlying. Instead 
it is evaluated together with the related option according to the 
procedures described for options to determine the capital 
requirement. Under the third alternative, the ``delta-plus'' 
approach, the delta-equivalent value of each position is included in 
the measurement framework for the appropriate risk category (that 
is, debt or equity instruments in the trading account, foreign 
exchange or commodities risk).
---------------------------------------------------------------------------

    4. Partial models. a. With approval from the Federal Reserve, a 
bank whose internal model does not cover all risk factor categories 
may use the standardized approach to measure market risk exposure 
arising from the risk factor categories that are not covered. The 
Federal Reserve will approve combining the two approaches only on a 
temporary basis in situations where the bank is developing, but has 
not fully implemented, a comprehensive value-at-risk measurement 
system. When a bank uses both approaches, each risk factor category 
(that is, interest rates, exchange rates, equity prices, and 
commodity prices) must be measured using one or the other approach. 
The methods may not be combined within a risk factor category. Once 
a bank adopts an acceptable value-at-risk model for a particular 
risk factor category, it may not revert to the standardized approach 
except in unusual circumstances and with prior approval of the 
Federal Reserve.
    b. For a bank using a combination of approaches, the capital 
requirement for market risk is the sum of (i) the appropriate value-
at-risk amount (as determined under section I.C.2.a. of this 
appendix E), and (ii) the capital requirement for each risk category 
that is calculated using the standardized approach.
    5. Application. The capital requirements for market risk apply 
to state member banks on a worldwide consolidated basis. The Federal 
Reserve may, however, evaluate market risk on an unconsolidated 
basis when necessary. For example, when there are obstacles to the 
repatriation of profits from a foreign subsidiary or where 
management structure does not allow timely management of risk on a 
consolidated basis.
    6. Other considerations. All transactions, including forward 
sales and purchases, should be included in the calculation of market 
risk capital requirements from the date on which they were entered 
into. The Federal Reserve expects a bank to meet its capital 
requirements for market risk on a continuous basis (that is, at a 
minimum, at the close of each business day).

II. Qualifying Capital and the Market Risk-Adjusted Capital Ratio

A. Qualifying and Eligible Capital

    1. The principal forms of qualifying capital for market risk are 
Tier 1 capital and Tier 2 capital as defined in section II. of 
appendix A of this part and subject to the conditions and 
limitations of appendix A of this part. A bank may use Tier 3 
capital for the sole purpose of meeting a portion of the capital 
requirements for market risk.10

    \10\ A bank may not use Tier 3 capital to satisfy any capital 
requirements for counterparty credit risk under appendix A of this 
part, including counterparty credit risk associated with derivative 
transactions in either trading or non-trading accounts.
---------------------------------------------------------------------------

    2. Tier 3 capital consists of short-term subordinated debt that 
is subject to a lock-in clause providing that neither interest nor 
principal payment is due (even at maturity) if such payment would 
cause the issuing bank to fall or remain below the minimum 8.0 
percent risk-based capital requirement as set forth in appendix A 
and adjusted for market risk.
    3. In order to qualify as Tier 3 capital, the short-term debt 
must be unsecured, subordinated, and fully paid up; it must have an 
original maturity of at least two years; and it may not be redeemed 
before maturity without prior approval by the Federal Reserve. In 
addition, it may not contain or be covered by any covenants, terms, 
or restrictions that are inconsistent with safe and sound banking 
practices.
    4. Eligible Tier 3 capital may not exceed 250 percent of a 
bank's Tier 1 capital allocated for market risk and the maximum 
eligible amount of Tier 2 and Tier 3 capital together is limited to 
100 percent of Tier 1 capital. (Examples of how to calculate these 
limits are set forth in Attachment I to this appendix E.) Tier 2 
elements may be substituted for Tier 3 up to the same limit of 250 
percent, so long as the overall limits for Tier 2 capital set forth 
in appendix A of this part are not exceeded, that is, Tier 2 capital 
may not exceed total Tier 1 capital, and long-term subordinated debt 
may not exceed 50 percent of Tier 1 capital.

B. Calculation of Eligible Capital and the Capital Ratio

    1. In order to calculate eligible capital, a bank must first 
calculate its minimum capital requirement for credit risk in 
accordance with appendix A of this part and then its capital 
requirement for market risk. Eligible capital is the sum of the 
bank's qualifying Tier 1 capital, its qualifying Tier 2 capital 
subject to the limits stated above, and its eligible Tier 3 capital 
subject to the conditions set out under section II. of this appendix 
E.
    2. A bank that is subject to the market risk measure must 
calculate its risk-based capital ratios as follows:
    a. Determine total weighted-risk assets using the procedures and 
criteria set forth in appendix A of this part, excluding debt and 
equity instruments in the trading book and positions in commodities, 
but including all over-the-counter derivative activities whether in 
the bank's trading account or not.
    b. Calculate the measure for market risk using the internal 
models approach, the standardized approach, or an approved 
combination of these two approaches.
    c. Multiply the measure for market risk by 12.5 (i.e., the 
reciprocal of the 8.0 percent minimum risk-based capital ratio). The 
resulting product is referred to as ``market risk-equivalent 
assets.''
    d. Add market risk-equivalent assets to the weighted-risk assets 
compiled for credit risk purposes (section II.B.2.a. of this 
appendix E). The sum of these two amounts is the denominator of 
risk-based capital ratios adjusted for market risk. The numerator of 
the total risk-based capital ratio is eligible capital and the 
numerator of the Tier 1 risk-based capital ratio is Tier 1 capital.
III. The Internal Models Approach

A. Use of Models

    1. With prior approval of the Federal Reserve, a bank may use 
its internal risk measurement model(s) for purposes of measuring 
value-at-risk and determining the associated regulatory capital 
requirements for market risk exposure.
    a. Requests for approval under section III.A.1. of this appendix 
E should include, at a minimum, a complete description of the bank's 
internal modeling and risk management systems and how these systems 
conform to the criteria set forth in this section III., an 
explanation of the policies and procedures established by the bank 
to ensure continued compliance with such criteria, a discussion of 
internal and external validation procedures, and a description of 
other relevant policies and procedures consistent with sound 
practices.
    b. The Federal Reserve will approve an internal model for 
regulatory capital 

[[Page 38106]]
purposes only after determining that the bank's internal model and risk 
management systems meet the criteria in section III. of this 
appendix E. Such a determination may require on-site examinations of 
the systems. The Federal Reserve may require modification to an 
internal model as deemed necessary to ensure compliance, on a 
continuing basis, with the provisions of this appendix E. A bank's 
internal model will be subject to continuing review, both on- and 
off-site, by the Federal Reserve.11

    \11\ Banks that need to modify their existing modeling 
procedures to accommodate the requirements of this appendix E 
should, nonetheless, continue to use the internal models they 
consider most appropriate in evaluating risks for other purposes.
---------------------------------------------------------------------------

    2. A bank should ensure that the level of sophistication of its 
internal model is commensurate with the nature and volume of the 
bank's trading activity in the risk factor categories covered by 
this appendix E and measures market risk as accurately as possible. 
In addition, the model should be adjusted to reflect changing 
portfolio composition and changing market conditions.

B. Qualitative Criteria

    1. A bank using the internal models approach should have market 
risk management systems that are conceptually sound and implemented 
with integrity. Internal risk measurement models must be closely 
integrated into the day-to-day risk management process of the bank. 
For example, the risk measurement model must be used in conjunction 
with internal trading and exposure limits.
    2. A bank must meet the following minimum qualitative criteria 
before using its internal model to measure its exposure to market 
risk.12

    \12\ If the Federal Reserve is not satisfied with the extent to 
which a bank meets these criteria, the Federal Reserve may adjust 
the multiplication factor used to calculate market risk capital 
requirements or otherwise increase capital requirements.
---------------------------------------------------------------------------

    a. A bank must have a risk control unit that is independent from 
business trading units and reports directly to senior management of 
the bank. The unit must be responsible for designing and 
implementing the bank's risk management system and analyzing daily 
reports on the output of the bank's risk measurement model in the 
context of trading limits. The unit must conduct regular back-
testing.13

    \13\ Back-testing includes ex post comparisons of the risk 
measures generated by the model against the actual daily changes in 
portfolio value.
---------------------------------------------------------------------------

    b. Senior management must be actively involved in the risk 
control process. The daily reports produced by the risk management 
unit must be reviewed by a level of management with sufficient 
authority to enforce both reductions in positions taken by 
individual traders, as well as in the bank's overall risk exposure.
    c. The bank must have a routine and rigorous program of stress-
testing 14 to identify the effect of low-probability events on 
the bank's trading portfolio. Senior management must routinely 
review the results of stress-testing in the context of the potential 
effect of the events on bank capital and the appropriate procedures 
the bank should take to minimize losses. The policies of the bank 
set by management and the board of directors should identify 
appropriate stress-tests and the procedures to follow in response to 
the test results.

     14 Bank stress-testing should cover a range of factors 
that can create extraordinary losses or gains in trading portfolios 
or make the control of risk in those portfolios difficult. These 
factors include low-probability events of all types, including the 
various components of market, credit, and operational risks.
---------------------------------------------------------------------------

    d. The bank must have established procedures for ensuring 
compliance with a documented set of internal policies and controls, 
as well as for monitoring the overall operation of the risk 
measurement system.
    e. Not less than once a year, the bank must conduct, as part of 
its regular internal audit process, an independent review of the 
risk measurement system. This review must include both the 
activities of the business trading units and of the independent risk 
control unit of the bank.
    f. Not less than once a year, the bank must conduct a review of 
its overall risk management process. The review must consider:
    i. The adequacy of the documentation of the risk management 
system and process and the organization of the risk control unit;
    ii. The integration of market risk measures into daily risk 
management and the integrity of the management information system;
    iii. The process the bank employs for approving risk pricing 
models and valuation systems that are used by front- and back-office 
personnel;
    iv. The scope of market risks captured by the risk measurement 
model and the validation of any significant changes in the risk 
measurement process;
    v. The accuracy and completeness of position data, the accuracy 
and appropriateness of volatility and correlation assumptions, and 
the accuracy of valuation and risk sensitivity calculations;
    vi. The verification process the bank employs to evaluate the 
consistency, timeliness, and reliability of data sources used to run 
internal models, including the independence of such data sources; 
and
    vii. The verification process the bank uses to evaluate back-
testing that is conducted to assess the model's accuracy.

C. Market Risk Factors

    1. Overview. For regulatory capital purposes, a bank's internal 
risk measurement system(s) must use sufficient risk factors to 
capture the risks inherent in the bank's portfolio of on- and off-
balance-sheet trading positions and must, subject to the following 
guidelines, cover interest rates, equity prices, exchange rates, 
commodity prices, and volatilities related to options positions in 
each risk factor category. The level of sophistication of the bank's 
risk factors must be commensurate with the nature and scope of the 
risks taken by the bank.
    2. Interest Rates. a. A bank must use a set of market risk 
factors corresponding to interest rates in each currency in which it 
has material interest rate-sensitive on- or off-balance- sheet 
positions. The risk measurement system must model the yield curve 
15 using one of a number of generally accepted approaches, for 
example, by estimating forward rates of zero coupon yields. The 
yield curve must be divided into various maturity segments in order 
to capture variation in the volatility of rates along the yield 
curve; there will typically be one risk factor corresponding to each 
maturity segment.

     15 Generally, a yield curve is a graph showing the term 
structure of interest rates by plotting the yields of all 
instruments of the same quality by maturities ranging from the 
shortest to the longest available. The resulting curve shows whether 
short-term interest rates are higher or lower than long-term 
interest rates.
---------------------------------------------------------------------------

    b. For material exposures to interest rate movements in the 
major currencies and markets, a bank must model the yield curve 
using a minimum of six risk factors. However, the number of risk 
factors used should ultimately be driven by the nature of the bank's 
trading strategies.16 The risk measurement system must 
incorporate separate risk factors to capture spread risk.17

     16 For example, a bank that has a portfolio of various types of 
securities across many points of the yield curve and that engages in 
complex arbitrage strategies would require a greater number of risk 
factors to capture interest rate risk accurately.
     17 Spread risk refers to the potential changes in value of 
an instrument or portfolio arising from differences in the behavior 
of baseline yield curves, such as those for U.S. Treasury 
securities, and yield curves reflecting sector, quality, or 
instrument specific factors. A variety of approaches may be used to 
capture the spread risk arising from less than perfectly correlated 
movements between government and other interest rates, such as 
specifying a completely separate yield curve for non-government 
instruments (for example, swaps or municipal securities) or 
estimating the spread over government rates at various points along 
the yield curve.
---------------------------------------------------------------------------

    3. Exchange rates. A bank must use market risk factors 
corresponding to the exchange rate between the domestic currency and 
each foreign currency in which the bank has a significant exposure. 
The risk measurement system must incorporate market risk factors 
corresponding to the individual foreign currencies in which the 
bank's positions are denominated.
    4. Equity prices. A bank must use market risk factors 
corresponding to each of the equity markets in which it holds 
significant positions. The sophistication and nature of the modeling 
technique for a given market must correspond to the bank's exposure 
to the overall market as well as to the bank's concentration in 
individual equity issues in that market. At a minimum, there must be 
a risk factor designed to capture market-wide movements in equity 
prices (such as a market index), but additional risk factors could 
track various sectors or individual issues.
    5. Commodity prices. A bank must use market risk factors 
corresponding to each of the commodity markets in which it holds 
significant positions. The internal model must encompass directional 
risk, forward gap and interest rate risk, and basis risk.18 The 


[[Page 38107]]
model should also take into account the market characteristics, for 
example, delivery dates and the scope provided to traders to close 
out positions.

     18 Directional risk is the risk that a spot price will 
increase or decrease. Forward gap risk refers to the effects of 
owning a physical commodity versus owning a forward position in a 
commodity. Interest rate risk is the risk of a change in the cost of 
carrying forward positions and options. Basis risk is the risk that 
the relationship between the prices of similar commodities changes 
over time.
---------------------------------------------------------------------------

D. Quantitative Standards

    1. A bank may use one of a number of generally accepted 
measurement techniques including, for example, an internal model 
based on variance-covariance matrices, historical simulations, or 
Monte Carlo simulations so long as the model employed captures all 
the material market risks.19 The following minimum standards 
apply for purposes of using an internal model for calculating market 
risk capital requirements:

     19 In a variance/covariance approach, the change in value 
of the portfolio is calculated by combining the risk factor 
sensitivities of the individual positions--derived from valuation 
models--with a variance/covariance matrix based on risk factor 
volatilities and correlations. A bank using this approach would 
calculate the volatilities and correlations of the risk factors on 
the basis of the holding period and the observation period. A bank 
using a historical simulation would calculate the hypothetical 
change in value of the current portfolio in the light of historical 
movements in risk factors. This calculation would be done for each 
of the defined holding periods over a given historical measurement 
horizon to arrive at a range of simulated profits and losses. A bank 
using a Monte Carlo technique would consider historical movements to 
determine the probability of particular price and rate changes.
---------------------------------------------------------------------------

    a. Value-at-risk must be calculated on a daily basis using a 
99th percentile, one- tailed confidence interval 20 and the 
holding period must be ten trading days. For positions that display 
linear price characteristics, a bank may use value-at-risk numbers 
calculated according to shorter holding periods scaled up to ten 
days by the square root of time.21

     20 A one-tailed confidence interval of 99 percent means that 
there is a 1 percent probability based on historical experience that 
the combination of positions in a bank's portfolio would result in a 
loss higher than the measured value-at-risk.
     21 This transformation entails multiplying a bank's value-
at-risk by the square root of the ratio of the required holding 
period (ten days) to the holding period embodied in the value-at-
risk figure. For example, the value-at-risk calculated according to 
a one-day holding period would be scaled-up by the ``square root of 
time'' by multiplying the value-at-risk by 3.16 (the square root of 
the ratio of a ten-day holding period to a one-day holding period).
---------------------------------------------------------------------------

    b. Value-at-risk must be calculated using an observation period 
of at least one year to measure historical changes in rates and 
prices.
    c. A bank must update its historical rates and prices at least 
once every three months and must reassess them whenever market 
conditions change materially.
    2. A bank may use discretion in recognizing empirical 
correlations within each market risk factor category.22 
However, empirical correlations among risk categories are not 
recognized. The value-at-risk measure for each risk category must be 
added together on a simple sum basis to determine the aggregate 
value-at-risk amount.

     22 While a bank has flexibility to use correlations, the 
Federal Reserve must be satisfied that there is integrity in the 
bank's process for calculating correlations.
---------------------------------------------------------------------------

    3. A bank's models must accurately capture the unique risks 
associated with options within each of the market risk factor 
categories. The following minimum criteria apply to the measurement 
of options risk:
    a. A bank's internal model must capture the non-linear price 
characteristics of option positions using an options pricing 
technique. The bank must apply a minimum ten-day holding period to 
option positions or positions that display option-like 
characteristics. Banks may not scale-up the daily value-at-risk 
numbers by the square root of time.
    b. A bank's internal model must capture the volatilities of the 
rates and prices (that is, the vega) underlying option positions and 
a bank should measure the volatilities of the underlying instruments 
broken down by different option maturities.
    4. The accuracy of a bank's internal model will be reviewed 
periodically by the Federal Reserve. Such review, during which, when 
appropriate, the Federal Reserve may take into consideration reports 
and opinions generated by external auditors or qualified 
consultants, will include, at a minimum:
    a. Verification that the internal validation processes described 
in section III.B.2. of this Appendix E are operating in a 
satisfactory manner;
    b. Affirmation that the formulae used in the calculation process 
and for the pricing of options and other complex instruments, are 
validated by a qualified unit of the bank, which in all cases must 
be independent from the trading areas;
    c. Confirmation that the structure of the internal model is 
adequate with respect to the bank's activities and geographical 
coverage;
    d. Confirmation that the results of the bank's back-testing of 
its internal measurement system (that is, comparing value-at-risk 
estimates with actual profits and losses) are being used effectively 
to monitor reliability of the model's estimates over time; and
    e. Affirmation that, for regulatory capital purposes, the model 
processes all relevant data and that the modeling procedures conform 
with the parameters and specifications set forth in this appendix E.

IV. The Standardized Approach

A. Debt Instruments

    1. Specific Risk. a. The capital requirement for specific risk 
is based on the identity of the obligor and, in the case of 
corporate securities, on the credit rating and maturity of the 
instrument. The specific risk capital requirement is calculated by 
weighting the current market value of each individual position, 
whether long or short, by the appropriate category factor as set 
forth below and summing the weighted values. In measuring specific 
risk, the bank may offset and exclude from its calculations any 
matched positions in the identical issue (including positions in 
derivatives). Even if the issuer is the same, no offsetting is 
permitted between different issues since differences in coupon 
rates, liquidity, call features, etc., mean that prices may diverge 
in the short run. The categories and factors are:

------------------------------------------------------------------------
                                                                 Factor 
                Category                   Remaining maturity      (In  
                                              (contractual)     percent)
------------------------------------------------------------------------
Government..............................  N/A.................      0.00
Qualifying..............................  6 months or less....      0.25
                                          6 to 12 months......      1.00
                                          Over 12 months......      1.60
Other...................................  N/A.................      8.00
------------------------------------------------------------------------

    b. The government category includes all forms of debt 
instruments of central governments of the OECD-based group of 
countries 23 including bonds, Treasury bills and other short-
term instruments, as well as local currency instruments of non-OECD 
central governments to the extent that the bank has liabilities 
booked in that currency.

    \23\ The OECD-based group of countries is defined in section 
III.B.1. of appendix A of this part.
---------------------------------------------------------------------------

    c. The qualifying category includes securities of U.S. 
government-sponsored agencies, general obligation securities issued 
by states and other political subdivisions of the OECD-based group 
of countries, multilateral development banks, and debt instruments 
issued by U.S. depository institutions or OECD-banks that do not 
qualify as capital of the issuing institution.24 It also 
includes other securities, including revenue securities issued by 
states and other political subdivisions of the OECD-based group of 
countries, that are rated investment- grade by at least two 
nationally recognized credit rating services, or rated investment-
grade by one nationally recognized credit rating agency and not less 
than investment-grade by any other credit rating agency, or, with 
the exception of securities issued by U.S. firms and subject to 
review by the Federal Reserve, unrated but deemed to be of 
comparable investment quality by the reporting bank and the issuer 
has securities listed on a recognized stock exchange.

    \24\ U.S. government-sponsored agencies, multilateral 
development banks, and OECD banks are defined in section III.C.2. of 
appendix A of this part.
---------------------------------------------------------------------------

    d. The other category includes debt securities not qualifying as 
government or qualifying securities. This would include non-OECD 
central government securities that do not meet the criteria for the 
government or qualifying categories. This category also includes 
instruments that qualify as capital issued by other banking 
organizations.
    e. The Federal Reserve will consider the extent of a bank's 
position in non-investment grade instruments (sometimes referred to 
as high yield debt). If those holdings are not well-diversified or 
otherwise represent a material position to the institution, the 
Federal Reserve may prevent a bank from offsetting positions in 
these instruments with other positions in qualifying instruments 
that may be offset when calculating its general market risk 
requirement. In addition, the Board may impose a specific risk 
capital requirement as high as 16.0 percent.
    2. General Market Risk. a. A bank may measure its exposure to 
general market risk using, on a continuous basis, either the 

[[Page 38108]]
maturity method (which uses standardized risk weights that approximate 
the price sensitivity of various instruments) or the duration method 
(where the institution calculates the precise duration of each 
instrument, weighted by a specified change in interest rates).
    b. Both methods use a maturity-ladder that incorporates a series 
of ``time-bands'' and ``zones'' to group together securities of 
similar maturities and that are designed to take into account 
differences in price sensitivities and interest rate volatilities 
across different maturities. Under either method, the capital 
requirement for general market risk is the sum of a base charge that 
results from fully netting various risk-weighted positions and a 
series of additional charges (add-ons), which effectively 
``disallow'' part of the previous full netting to address basis and 
yield curve risk.
    c. For each currency in which a bank has significant positions, 
a separate capital requirement must be calculated. No netting of 
positions is permitted across different currencies. Offsetting 
positions of the same amount in the same issues, whether actual or 
notional, may be excluded from the calculation, as well as closely 
matched swaps, forwards, futures, and forward rate agreements (FRAs) 
that meet the conditions set out in section IV.A.3. of this Appendix 
E.
    d. In the maturity method, the bank distributes each long or 
short position (at current market value) of a debt instrument into 
the time-bands of the maturity ladder. Fixed-rate instruments are 
allocated according to the remaining term to maturity and floating-
rate instruments according to the next repricing date. A callable 
bond trading above par is slotted according to its first call date, 
while a callable bond priced below par is slotted according to 
remaining maturity. Fixed-rate mortgage-backed securities, including 
collateralized mortgage obligations (CMOs) and real estate mortgage 
investment conduits (REMICs), are slotted according to their 
expected weighted average lives.
    e. Once all long and short positions are slotted into the 
appropriate time-band, the long positions in each time-band are 
summed and the short positions in each time-band are summed. The 
summed long and/or short positions are multiplied by the appropriate 
risk-weight factor (reflecting the price sensitivity of the 
positions to changes in interest rates) to determine the risk-
weighted long and/or short position for each time-band. The risk 
weights for each time-band are set out in Table I below:

            Table I.--Maturity Method: Time-Bands and Weights           
------------------------------------------------------------------------
                                                                 Risk   
  Zone        Coupon 3% or more     Coupon less than 3% and    weights  
                                       zero coupon bonds      [percent] 
------------------------------------------------------------------------
1.......  up to 1 month...........  up to 1 month..........         0.00
          1 up to 3 months........  1 up to 3 months.......         0.20
          3 up to 6 months........  3 up to 6 months.......         0.40
          6 up to 12 months.......  6 up to 12 months......         0.70
2.......  1 up to 2 years.........  1 up to 1.9 years......         1.25
          2 up to 3 years.........  1.9 up to 2.8 yrs......         1.75
          3 up to 4 years.........  2.8 up to 3.6 yrs......         2.25
3.......  4 up to 5 years.........  3.6 up to 4.3 yrs......         2.75
          5 up to 7 years.........  4.3 up to 5.7 yrs......         3.25
          7 up to 10 years........  5.7 up to 7.3 yrs......         3.75
          10 up to 15 years.......  7.3 up to 9.3 yrs......         4.50
          15 up to 20 years.......  9.3 up to 10.6 yrs.....         5.25
          Over 20 years...........  10.6 up to 12 yrs......         6.00
                                    12 up to 20 yrs........         8.00
                                    Over 20 years..........        12.50
------------------------------------------------------------------------

    f. Within each time-band for which there are risk-weighted long 
and short positions, the risk-weighted long and short positions are 
then netted, resulting in a single net risk-weighted long or short 
position for each time-band. Since different instruments and 
different maturities may be included and netted within each time-
band, a capital requirement, referred to as the vertical 
disallowance, is assessed to allow for basis risk. The vertical 
disallowance capital requirement is 10.0 percent of the position 
eliminated by the intra-time-band netting, that is, 10.0 percent of 
the smaller of the net risk-weighted long or net risk-weighted short 
position, or if the positions are equal, 10.0 percent of either 
position.25 The vertical disallowances for each time-band are 
absolute values, that is, neither long nor short. The vertical 
disallowances for all time- bands in the maturity ladder are summed 
and included as an element of the general market risk capital 
requirement.

     25 For example, if the sum of the weighted longs in a 
time-band is $100 million and the sum of the weighted shorts is $90 
million, the vertical disallowance for the time-band is 10.0 percent 
of $90 million, or $9 million.
---------------------------------------------------------------------------

    g. Within each zone for which there are risk-weighted long and 
short positions in different time-bands, the weighted long and short 
positions in all of the time-bands within the zone are then netted, 
resulting in a single net long or short position for each zone. 
Since different instruments and different maturities may be included 
and netted within each zone, a capital requirement, referred to as 
the horizontal disallowance, is assessed to allow for the imperfect 
correlation of interest rates along the yield curve. The horizontal 
disallowance capital requirement is calculated as a percentage of 
the position eliminated by the intra-zone netting, that is, a 
percentage of the smaller of the net risk-weighted long or net risk-
weighted short position, or if the positions are equal, a percentage 
of either position.26 The percent disallowance factors for 
intra-zone netting are set out in Table II in section IV.A.2.h. of 
this Appendix E. The horizontal disallowances, like the vertical 
disallowances, are absolute values that are summed and included as 
an element of the general market risk capital requirement.

    \26\ For example, if the sum of the weighted longs in the 1-3 
month time-band in Zone 1 is $8 million and the sum of the weighted 
shorts in the 3-6 month time-band is $10 million, the horizontal 
disallowance for the zone if forty percent of $8 million, or $3.2 
million.
---------------------------------------------------------------------------

    h. Risk-weighted long and short positions in different zones are 
then netted between the zones. Zone 1 and zone 2 are netted if 
possible, reducing or eliminating the net long or short position in 
zone 1 or zone 2 as appropriate. Zone 2 and zone 3 are then netted 
if possible, reducing or eliminating the net long or short position 
in zone 2 or zone 3 as appropriate. Zone 3 and zone 1 are then 
netted if possible, reducing or eliminating the long or short 
position in zone 3 and zone 1 as appropriate. A horizontal 
disallowance capital requirement is then assessed, calculated as a 
percentage of the position eliminated by the inter-zone netting. The 
horizontal disallowance capital requirements for each zone are then 
summed as absolute values and included in the general market risk 
capital charge. The percent disallowance factors for inter-zone 
netting are set out in Table II below:

                                                                        

[[Page 38109]]
                   Table II.--Horizontal Disallowances                  
------------------------------------------------------------------------
                                                  Between               
                                    Within the    adjacent     Between  
  Zone           Time-band             zone        zones      zones 1-3 
                                    (percent)    (percent)    (percent) 
------------------------------------------------------------------------
1.......  0-1 month..............           40           40          100
          1-3 months                                                    
          3-6 months                                                    
          6-12 months                                                   
2.......  1-2 years..............           30           40          100
          2-3 years                                                     
          3-4 years                                                     
3.......  1-5 years..............           30           40          100
          5-7 years                                                     
          7-10 years                                                    
          0-15 years                                                    
          5-20 years                                                    
          over 20 years                                                 
------------------------------------------------------------------------



    i. Finally, the net risk-weighted long or net risk-weighted 
short positions remaining in the zones are summed to reach a single 
net risk-weighted long or net risk-weighted short position for the 
bank's portfolio. The sum of the absolute value of this position and 
the vertical and horizontal disallowances is the capital requirement 
for general market risk. An example of the calculation of general 
market risk under the maturity method is in Attachment II to this 
appendix E.
    j. In the duration method, the bank, after calculating each 
instrument's modified duration 27 using a formula that is 
subject to supervisory review, multiplies that modified duration by 
the interest rate shock specified for an instrument of that duration 
in Table III in section IV.A.2.k. of this appendix E. The resulting 
product (representing the expected percentage change in the price of 
the instrument for the given interest rate shock) is then multiplied 
by the current market value of the instrument. The resulting amount 
is then slotted as a long or short position into a time-band in the 
maturity ladder in Table III on the basis of the instrument's 
modified duration.28

    \27\ The duration of an instrument is its approximate percentage 
change in price for a 100 basis point parallel shift in the yield 
curve assuming that its cash flow does not change the yield curve 
shifts. Modified duration is duration divided by a factor of 1 plus 
the interest rate.
    \28\ For example, an instrument held by a bank with a maturity 
of 4 years and 3 months and a current market value of $1,000 might 
have a modified duration of 3.5 years. Based on its modified 
duration, it would be subjected to the 75-basis point interest rate 
shock, resulting in an expected price change of 2.625 percent (3.5 
x  0.75). The corresponding expected change in price of $26.25, 
calculated as 2.625 percent of $1,000, would be slotted as a long 
position in the 3.3 to 4.0 year time-band of the maturity ladder.
---------------------------------------------------------------------------

    k. Once all of the bank's traded debt instruments have been 
slotted into the maturity ladder, the bank conducts the same rounds 
of netting and disallowances described in sections IV.A.2.f. through 
IV.A.2.h. of this appendix E for the maturity method, with the 
exception that the vertical disallowance requirement for the 
duration method is 5.0 percent (horizontal disallowances continue to 
be those set out in Table II).29 As with the maturity method, 
the sum of the absolute value of the final net position and the 
vertical and horizontal disallowances is the general market risk 
capital requirement:

    \29\ Two different vertical disallowances are used since the 
duration method takes into account an instrument's specific 
characteristics (maturity and coupon) and there is less opportunity 
for measurement error.

  Table III.--Duration Method: Time-Bands and Assumed Changes in Yield  
------------------------------------------------------------------------
                                                               Assumed  
  Zone                        Time-band                       change in 
                                                                yield   
------------------------------------------------------------------------
1.......  Up to 1 month....................................         1.00
          1 up to 3 months.................................         1.00
          3 up to 6 months.................................         1.00
          6 up to 12 months................................         1.00
2.......  1.0 up to 1.8 years..............................         0.90
          1.8 up to 2.6 years..............................         0.80
          2.6 up to 3.3 years..............................         0.75
3.......  3.3 up to 4.0 years..............................         0.75
          4.0 up to 5.2 years..............................         0.70
          5.2 up to 6.8 years..............................         0.65
          6.8 up to 8.6 years..............................         0.60
          8.6 up to 9.9 years..............................         0.60
          9.9 up to 11.3 years.............................         0.60
          11.3 up to 16.6 years............................         0.60
          Over 16.6 years..................................         0.60
------------------------------------------------------------------------

    3. Interest rate derivatives. a. Debt derivatives and other off-
balance-sheet positions that are affected by changes in interest 
rates are included in the measurement system under section IV.A. of 
this Appendix E (except for options and the associated underlyings, 
which are included in the measurement system under the treatment 
discussed in section IV.E. of this Appendix E). A summary of the 
treatment for debt derivatives is set out in Attachment III to this 
Appendix E.
    b. Derivatives are converted into positions in the relevant 
underlying instrument and are included in the calculation of 
specific and general market risk capital charges as described above. 
The amount to be included is the market value of the principal 
amount of the underlying or of the notional underlying. For 
instruments where the apparent notional amount differs from the 
effective notional amount, a bank must use the effective notional 
amount.
    c. Futures and forward contracts (including FRAs) are broken 
down into a combination of a long position and short position in the 
notional security. The maturity of a future or a FRA is the period 
until delivery or exercise of the contract, plus the life of the 
underlying instrument.30 Where a range of instruments may be 
delivered to fulfill the contract, the bank may chose which 
deliverable instrument goes into the maturity or duration ladder as 
the notional underlying. In the case of a future on a corporate bond 
index, positions are included at the market value of the notional 
underlying portfolio of securities.

    \30\ For example, a long position in a June three-month interest 
rate future (taken in April) is reported as a long position in a 
government security with a maturity of five months an a short 
position in a government security with a maturity to two months.
---------------------------------------------------------------------------

    d. Swaps are treated as two notional positions in the relevant 
instruments with appropriate maturities. The receiving side is 
treated as the long position and the paying side is treated as the 
short position.31 The separate sides of cross-currency swaps or 
forward foreign exchange transactions are slotted in the relevant 
maturity ladders for the currencies concerned. For swaps that pay or 
receive a fixed or floating interest rate against some other 
reference price, for example, an equity index, the interest rate 
component is slotted into the appropriate repricing maturity 
category, with the long or short position attributable to the equity 
component being included in the equity framework set out in section 
IV.B. of this Appendix E.32

    \31\ For example, an interest rate swap under which a bank is 
receiving floating-rate interest and paying fixed is treated as a 
long position in a floating rate instrument with a maturity 
equivalent to the period until the next interest reset date and a 
short position in a fixed-rate instrument with a maturity equivalent 
to the remaining life of the swap.
    \32\ A bank with a large swap book may, with prior approval of 
the Federal Reserve, use alternative formulae to calculate the 
positions to be included in the maturity or duration ladder. For 
example, a bank could first convert the payments required by the 
swap into present values. For that purpose, each payment would be 
discounted using zero coupon yields, and the payment's present value 
entered into the  appropriate time-band using procedures that apply 
to zero (or low) coupon bonds. The net amounts would then be treated 
as bonds, and slotted into the general market risk framework. Such 
alternative treatments will, however, only be allowed if: (i) the 
Federal Reserve is fully satisfied with the accuracy of the system 
being used, (ii) the positions calculated fully reflect the 
sensitivity of the cash flows to interest rate changes; and (iii) 
the positions are denominated in the same currency.

[[Page 38110]]

---------------------------------------------------------------------------

    e. A bank may offset long and short positions (both actual and 
notional) in identical derivative instruments with exactly the same 
issuer, coupon, currency, and maturity before slotting these 
positions into time-bands. A matched position in a future and its 
corresponding underlying may also be fully offset and, thus, 
excluded from the calculation, except when the future comprises a 
range of deliverable instruments. However, in cases where, among the 
range of deliverable instruments, there is a readily identifiable 
underlying instrument that is most profitable for the trader with a 
short position to deliver, positions in the futures contract and the 
instrument may be offset. No offsetting is allowed between positions 
in different currencies.
    f. Offsetting positions in the same category of instruments can 
in certain circumstances be regarded as matched and treated by the 
bank as a single net position which should be entered into the 
appropriate time-band. To qualify for this treatment the positions 
must be based on the same underlying instrument, be of the same 
nominal value, and be denominated in the same currency. The separate 
sides of different swaps may also be ``matched'' subject to the same 
conditions. In addition:
    i. For futures, offsetting positions in the notional or 
underlying instruments to which the futures contract relates must be 
for identical instruments and the instruments must mature within 
seven days of each other;
    ii. For swaps and FRAs, the reference rate (for floating rate 
positions) must be identical and the coupon closely matched (i.e., 
within 15 basis points); and
    iii. For swaps, FRAs and forwards, the next interest reset date, 
or for fixed coupon positions or forwards the remaining maturity, 
must correspond within the following limits: If the reset (remaining 
maturity) dates occur within one month, then the reset dates must be 
on the same day; if the reset dates occur between one month and one 
year later, then the reset dates must occur within seven days of 
each other, or if the reset dates occur over one year later, then 
the reset dates must occur within thirty days of each other.
    g. Interest rate and currency swaps, FRAs, forward foreign 
exchange contracts and interest rate futures are not subject to a 
specific risk charge. This exemption also applies to futures on a 
short-term (e.g., LIBOR) interest rate index. However, in the case 
of futures contracts where the underlying is a debt security, or an 
index representing a basket of debt securities, a specific risk 
charge will apply according to the category of the issuer as set out 
in section IV.A.1. of this Appendix E.

B. Equities

    1. Specific risk. The measure of specific risk is calculated on 
the basis of the bank's gross equity positions, that is, the 
absolute sum of all long equity positions and of all short equity 
positions at current market value.33 The specific risk capital 
requirement is 8.0 percent of that sum, unless the portfolio is both 
liquid and well-diversified, in which case the specific risk capital 
requirement is 4.0 percent of the gross equity position. A specific 
risk charge of 2.0 percent applies to the net long or short position 
in a broad, diversified equity index and is viewed as necessary to 
provide for risks associated with contract execution.34

    \33\ Matched positions in each additional equity in each 
national market may be treated as offsetting and excluded from the 
capital calculation, with any remaining position included in the 
calculations for specific and general market risk. For example, a 
future in a given equity may be offset against an opposite cash 
position in the same equity.
    \34\ A portfolio that is liquid and well-diversified is 
characterized by a limited sensitivity to price changes of any 
single equity issue or closely related group of equity issues held 
in the portfolio. The volatility of the portfolio's value should not 
be dominated by the volatility of any individual equity issue or by 
equity issues from any single industry or economic sector. In 
general, such portfolios should be characterized by a large number 
of individual equity positions, with no single position representing 
a large portion of the portfolio's total market value. In addition, 
it would generally be the case that a sizeable proportion of the 
portfolio would be comprised of issues traded on organized exchanges 
or in well-established over-the-counter markets.
---------------------------------------------------------------------------

    2. General Market risk. The measure of general market risk is 
based on the difference between the sum of the long positions and 
the sum of the short positions (i.e., the overall net position in an 
equity market) at current market value. An overall net position must 
be separately calculated for each national market in which the bank 
holds equities. The capital requirement for general market risk is 
8.0 percent of the net position in each equity market.
    3. Equity derivatives. a. Equity derivatives and other off-
balance-sheet positions that are affected by changes in equity 
prices are included in the measurement system under section IV.B. of 
this Appendix E (except for equity options, equity index options, 
and the associated underlying, which are included in the measurement 
system under the treatment discussed in section IV.E. of this 
Appendix E).35 This includes futures and swaps on both 
individual equities and on equity indices. Equity derivatives should 
be converted into notional equity positions in the relevant 
underlying. A summary of the rules for equity derivatives is set out 
in Attachment III to this Appendix E.

    \35\ Where equities are part of a forward contract (both 
equities to be received or to be delivered), any interest rate or 
foreign currency exposure from the other side of the contract should 
be appropriately included in the measurement systems in sections 
IV.A. and IV.C. of this Appendix E.
---------------------------------------------------------------------------

    b. Futures and forward contracts relating to individual equities 
should be reported at current market prices of the underlying. 
Futures relating to equity indices should be reported as the marked-
to-market value of the notional underlying equity portfolio. Equity 
swaps are treated as two notional positions, with the receiving side 
as the long position and the paying side as the short 
position.36 If one of the legs involves receiving/paying a 
fixed or floating interest rate, the exposure should be slotted into 
the appropriate repricing maturity band for debt securities. The 
stock index is covered by the equity treatment.

    \36\ For example, an equity swap in which a bank is receiving an 
amount based on the change in value of one particular equity or 
equity index and paying a different index will be tracted as a long 
position in the former and a short position in the latter.
---------------------------------------------------------------------------

    c. In the case of futures-related arbitrage strategies, the 2.0 
percent specific risk charge applicable to broad diversified equity 
indices may be applied to only one index. The opposite position is 
exempt from a specific risk charge. The strategies qualifying for 
this treatment are:
    i. When the bank takes an opposite position in exactly the same 
index at different dates; and
    ii. When the bank has an opposite position in different but 
similar indices at the same date, subject to supervisory oversight.
    d. If a bank engages in a deliberate arbitrage strategy, in 
which a futures contract on a broad diversified equity index matches 
a basket of securities, it may exclude both positions from the 
standardized approach on condition that the trade has been 
deliberately entered into and separately controlled and the 
composition of the basket of stocks represents at least 90 percent 
of the market value of the index. In such a case, the minimum 
capital requirement is 4.0 percent (that is, 2.0 percent of the 
gross value of the positions on each side) to reflect risk 
associated with executing the transaction. This applies even if all 
of the securities comprising the index are held in identical 
proportions. Any excess value of the securities comprising the 
basket over the value of the futures contract or excess value of the 
futures contract over the value of the basket is treated as an open 
long or short position.
    e. If a bank takes a position in depository receipts \37\ 
against an opposite position in the underlying equity, it may offset 
the position.

    \37\ Depository receipts are instruments issued by a trust 
company or other depository institution evidencing the deposit of 
foreign securities and facilitating trading in such instruments on 
U.S. stock exchanges.
---------------------------------------------------------------------------

C. Foreign Exchange Risk

    1. The capital requirement for foreign exchange risk covers the 
risk of holding or taking positions in foreign currencies, including 
gold, and is based on a bank's net open long positions or net open 
short positions in each currency, whether or not those positions are 
in the trading portfolio, plus the net open position in gold, 
regardless of sign.\38\

    \38\ Gold is treated as a foreign exchange position rather than 
a commodity because its volatility is more in line with foreign 
currencies and banks manage it in a manner similar to foreign 
currencies.

[[Page 38111]]

---------------------------------------------------------------------------

    2. A bank's net open position in each currency (and gold) is 
calculated by summing:
    a. The net spot position (i.e., all asset items less all 
liability items, including accrued interest earned but not yet 
received and accrued expenses, denominated in the currency in 
question);
    b. All foreign exchange derivative instruments and other off-
balance-sheet positions that are affected by changes in exchange 
rates are included in the measurement system under section IV.C. of 
this Appendix E (except for options and their associated 
underlyings, which are included in the measurement system under the 
treatment discussed in section IV.E. of this Appendix E). Forward 
currency positions should be valued at current spot market exchange 
rates. For a bank in which the basis of its normal management 
accounting is to use net present values, forward positions may be 
discounted to net present values as an acceptable way of measuring 
currency positions for regulatory capital purposes;
    c. Guarantees (and similar instruments) that are certain to be 
called and are likely to be irrevocable;
    d. Net future income/expenses not yet accrued but already fully 
hedged (at the discretion of the bank). A bank that includes future 
income and expenses must do so on a consistent basis without 
selecting expected future flows in order to reduce the bank's 
position; and
    e. Any other item representing a profit or loss in foreign 
currencies.
    3. For measuring a bank's open positions, positions in composite 
currencies, such as the ECU, may be either treated as a currency in 
their own right or split into their component parts on a consistent 
basis. Positions in gold are measured in the same manner as 
described in section IV.D. of this Appendix E.\39\

    \39\ Where gold is part of a forward contract (quantity of gold 
to be received or to be delivered), any interest rate or foreign 
currency exposure from the other side of the contract should be 
included in measurement system in section IV.A. (as a zero coupon 
instrument) and IV.C. of this Appendix E.
---------------------------------------------------------------------------

    4. The capital requirement is determined by converting the 
nominal amount (or net present value) of the net open position in 
each foreign currency (and gold) at spot rates into the reporting 
currency. The capital requirement is 8.0 percent of the sum of:
    a. The greater of the sum of the net short open positions or the 
sum of the net long open positions (absolute values); and
    b. The net open position in gold, regardless of sign.\40\

    \40\ For example, a bank has the following net currency 
positions: Yen=+50, DM=+100, GB=+150, FFR=-20, US$=-180, and 
gold=-35. The bank would sum its long positions (total=+300) and sum 
its short positions (total=-200). The bank's capital requirement for 
foreign exchange market risk would be: (300 (the larger of the 
summed long and short positions) +35 (gold))  x 8.0%=$26.80.
---------------------------------------------------------------------------

    5. Where a bank is assessing its foreign exchange risk on a 
consolidated basis, it may be technically impractical in the case of 
some marginal operations to include the currency positions of a 
foreign branch or subsidiary of the bank. In such cases, the 
internal limit in each currency may be used as a proxy for the 
positions, provided there is adequate ex post monitoring of actual 
positions complying with such limits. In these circumstances, the 
limits should be added, regardless of sign, to the net open position 
in each currency.

D. Commodities Risk

    1. Measurement methods. This section provides a minimum capital 
requirement to cover the risk of holding or taking positions in 
commodities. There are two methods under the standardized approach 
for measuring commodity market risk--the simplified method and the 
maturity method. These methods are only appropriate for banks that 
conduct a limited amount of commodities business. All other banks 
must adopt an internal measurement system conforming to the criteria 
in section III. of this Appendix E.
    2. Base capital requirement. Under both the simplified and 
maturity methods, each long and short commodity position (spot and 
forward) is expressed in terms of the standard unit of measurement 
(such as barrels, kilos, or grams). The open positions in each 
category of commodities are then converted at current spot rates 
into U.S. currency, with long and short positions offset to arrive 
at the net open position in each commodity. Positions in different 
categories of commodities may not, generally, be offset.\41\ Under 
either method, the base capital requirement is 15.0 percent of the 
net open position, long or short, in each commodity.\42\

    \41\ However, offsetting is permitted between different sub-
categories of the same commodity in cases where the sub-categories 
are deliverable against each other.
    \42\ When the funding of a commodity position opens a bank to 
interest rate or foreign exchange exposure the relevant positions 
should be included in the measures of interest rate and foreign 
exchange risk described in sections IV.A. and IV.C. of this Appendix 
E. When a commodity is part of a forward contract, any interest or 
foreign currency exposure from the other side of the contract should 
be appropriately included in the measurement systems in sections 
IV.A. and IV.C. of this Appendix E.
---------------------------------------------------------------------------

    3. Simplified method. To protect a bank against basis risk, 
interest rate risk, and forward gap risk, each category of commodity 
is also subject to a 3.0 percent capital requirement on the bank's 
gross positions, long plus short, in the particular commodity. In 
valuing gross positions in commodity derivatives for this purpose, a 
bank should use the current spot price. The total capital 
requirement for commodities risk is the sum of the 15.0 percent base 
charges for each net commodity position and the 3.0 percent 
requirements on the gross commodity positions.
    4. Maturity method. a. Under this method, a bank must slot each 
long and short commodity position (converted into U.S. currency at 
current spot rates) into a maturity ladder. The time-bands for the 
maturity ladder are; from zero to one month, one up to three months, 
three up to six months, six up to twelve months, one up to two 
years, two up to three years, and over three years. A separate 
maturity ladder is used for each category of commodity. Physical 
commodities are allocated to the first time-band.
    b. In order to capture forward gap and interest rate risk within 
a time-band (together sometimes referred to as curvature/spread 
risk), offsetting long and short positions in each time-band are 
subject to an additional capital requirement. Beginning with the 
shortest-term time-band and continuing with subsequent time-bands, 
the amount of the matched short position plus the amount of the 
matched long position is multiplied by a spread rate of 1.5 percent.
    c. The unmatched net position from shorter-term time-bands must 
be carried forward to offset exposures in longer-term time-bands. A 
capital requirement of 0.6 percent of the net position carried 
forward is added for each time-band that the net position is carried 
forward.\43\ The total capital requirement for commodities risk is 
the sum of the 15.0 percent base capital requirement for each net 
commodity position and the additional requirements for matched 
positions and for unmatched positions carried forward. An example of 
this calculation is in Attachment IV to this Appendix E.

    \43\ For example, if $200 short is carried forward from the 3-6 
month time-band to the 1-2 year time-band, the capital charge would 
be $200 x .006 x 2=$2.40.
---------------------------------------------------------------------------

    5. Commodity derivatives. Commodity derivatives and other off-
balance-sheet positions that are affected by changes in commodity 
prices are included in the measurement system under section IV.D. of 
this Appendix E (except for options and the associated underlying, 
which are included in the measurement system under the treatment 
discussed in section IV.E. of this Appendix E). Commodity 
derivatives are converted into notional commodity positions. Under 
the maturity method, the positions are slotted into maturity time-
bands as follows:
    a. Futures and forward contracts relating to individual 
commodities are incorporated in the measurement system as notional 
amounts (of, for example, barrels or kilos) that are converted to 
U.S. dollars at current spot rates and are assigned a maturity 
according to expiration date;
    b. Commodity swaps where one side of the contract is a fixed 
price and the other side is the current market price are 
incorporated as a series of positions equal to the notional amount 
of the contract at current spot rates, with one position 
corresponding to each payment on the swap and slotted in the 
maturity ladder accordingly. The positions are long positions if the 
bank is paying a fixed price and receiving a floating price, and 
short positions if the bank is receiving a fixed price and paying a 
floating price; \44\ and

    \44\ If one of the sides of the transaction involves receiving/
paying a fixed or floating interest rate, that exposure should be 
slotted into the appropriate repricing maturity band in section 
IV.A. of this Appendix E.
---------------------------------------------------------------------------

    c. Commodity swaps where the sides of the transaction are in 
different commodities are included in the relevant reporting ladder. 
No offsetting is allowed unless the commodities are in the same sub-
category. 

[[Page 38112]]


E. Options

    1. Three alternatives are available for a bank to use in 
measuring its market risk for options activities. A bank that only 
has purchased options may use the simplified method set forth in 
section IV.E.2. of this Appendix E. A bank that also writes options 
may use the scenario method described in section IV.E.3. of this 
Appendix E or the delta-plus method set forth in section IV.E.4. of 
this Appendix E.\45\ These methods may only be used by banks which, 
in relative terms, have limited options activities. Banks with more 
significant options business are expected to adopt an internal 
measurement system conforming to the criteria in section III. of 
this Appendix E. Regardless of the method used, specific risk 
related to the issuer of an instrument still applies to options 
positions for equities, equity indices and corporate debt securities 
as set forth in sections IV.A. and IV.B. of this Appendix E. There 
remains a separate capital requirement for counterparty credit risk 
as set forth in appendix A to this part.

    \45\ Unless all their written option positions are hedged by 
perfectly matched long positions in exactly the same options, in 
which case there is no capital requirement for market risk.
---------------------------------------------------------------------------

    2. Under the simplified and scenario methods, the positions for 
the options and the associated underlying, cash or forward, are not 
included in the measurement framework for debt securities, equities, 
foreign exchange or commodities risk as set forth in sections IV.A. 
through IV.D. of this Appendix E. Rather, they are subject to 
capital requirements as calculated in this section IV.E. The capital 
requirements calculated under this section IV.E. should then be 
added to the capital requirements for debt securities, equities, 
foreign exchange, and commodities risk as appropriate. Under the 
delta-plus method, the delta equivalent position \46\ for each 
option is included in the measurement frameworks set forth in 
sections IV.A. through IV.D. of this Appendix E.

    \46\ The delta equivalent of an option is the option's delta 
value multiplied by its principal or notional value. The delta value 
of an option represents the expected change in the option's price as 
a proportion of a small change in the price of the underlying 
instrument. For example, an option whose price changes $1 for every 
$2 dollar change in the price of the underlying instrument has a 
delta of 0.50.
---------------------------------------------------------------------------

    3. A bank that has only a limited amount and range of purchased 
options may use the following simplified approach to measure its 
market risk exposure.
    a. For a bank with a long cash position and a long put or with a 
short cash position and a long call, the capital requirement is the 
market value of the underlying instrument multiplied by the sum of 
the specific and general market risk requirements for the underlying 
(that is, the specific and general market risk requirements that 
would have applied to the underlying directly under sections IV.A. 
through IV.D. of this Appendix E \47\), less the amount the option 
is in the money (if any) bounded at zero.\48\

    \47\ Some options (e.g., where the underlying is an interest 
rate, a currency, or a commodity) bear no specific risk but specific 
risk will be present in the case of options on corporate debt 
securities and for options on equities and equity indices.
    \48\ For example, if a holder of 100 shares currently valued at 
$10 each has an equivalent put option with a strike price of $11, 
the capital charge would be: $1,000  x 16.0 percent (e.g., 8.0 
percent specific plus 8.0 percent general market risk)=$160, less 
the amount the option is in the money ($11-$10)  x 100=$100, i.e., 
the capital charge would be $60. A similar methodology applies for 
options whose underlying is a foreign currency, a debt security or a 
commodity.
---------------------------------------------------------------------------

    b. For a bank with a long call or a long put, the capital charge 
is the lesser of:
    i. The market value of the underlying security multiplied by the 
sum of specific and general market risk requirements for the 
underlying (that is, the specific and general market risk 
requirements that would have applied to the underlying directly 
under sections IV.A. through IV.D. of this Appendix E \49\); or

    \49\ See footnote 47 in section IV.E.3.a. of this appendix E.
---------------------------------------------------------------------------

    ii. The market value of the option.
    c. Under this measure, the capital requirement for currency 
options is 8.0 percent of the market value of the underlying and for 
commodity options is 15.0 percent of the market value of the 
underlying.
    4. Under the scenario approach, a bank revalues its options and 
related hedging positions by changing the underlying rate or price 
over a specified range and by assuming different levels of 
volatility for that rate or price.
    a. For each of its option portfolios, a bank constructs a grid 
based on a fixed range of changes in the portfolio's risk factors 
and calculates changes in the value of the option portfolio at each 
point within the grid. For this purpose, an option portfolio 
consists of an option and any related hedging positions or multiple 
options and related hedging positions that are grouped together 
according to their remaining maturity or the type of underlying.
    b. Options based on interest rates and debt instruments are 
grouped into portfolios according to the maturity zones that are set 
forth in section IV.A. of this Appendix E. (Zone 1 instruments have 
a remaining maturity of up to 1 year, zone 2 instruments have a 
remaining maturity from 1 year up to 4 years, and zone 3 instruments 
have a remaining maturity of 4 years or more.) These options and the 
associated hedging positions should be evaluated under the 
assumption that the relevant interest rates move simultaneously. For 
options based on equities, separate grids are constructed for each 
individual equity issue and index. For options based on exchange 
rates, separate grids are constructed for individual exchange rates. 
For options based on commodities, separate grids are constructed for 
each category of commodity (as defined in sections I.B.3. and IV.D. 
of this Appendix E).
    c. For option portfolios with options based on equities, 
exchange rates, and commodities, the first dimension of the grid 
consists of rate or price changes within a specified range above and 
below the current market value of the underlying; for equities, the 
range is 12.0 percent (or in the case of an index 
8.0 percent), for exchange rates the range is 
8.0 percent, and for commodities the range is 
15.0 percent. For option portfolios with options based 
on interest rates, the range for the first dimension of the grid 
depends on the remaining maturity zone. The range for zone 1 is 
100 basis points, the range for zone 2 is 90 
basis points, and the range for zone 3 is 75 basis 
points. For all option portfolios, the range is divided into at 
least ten equally spaced intervals. The second dimension of each 
grid is a shift in the volatility of the underlying rate or price 
equal to 25.0 percent of the current volatility.\50\

    \50\ For example, if the underlying of an equity instrument has 
a current market value of $100 and a volatility of 20 percent, the 
first dimension of the grid would range from $88 to $112, divided 
into ten intervals of $2.40 and the second dimension would assume 
volatilities of 15 percent, 20 percent, and 25 percent.
---------------------------------------------------------------------------

    d. For each assumed volatility and rate or price change (a 
scenario), the bank revalues each option portfolio. The market risk 
capital requirement for the portfolio is the largest loss in value 
from among the scenario revaluations. The total market risk capital 
requirement for all option portfolios is the sum of the individual 
option portfolio capital requirements.
    e. The Federal Reserve will review the application of the 
scenario approach, particularly regarding the precise way the 
analysis is constructed. A bank using the scenario approach should 
meet the appropriate qualitative criteria set forth in section 
III.B. of this Appendix E.
    5. Under the delta-plus method, a bank that writes options may 
include delta-weighted options positions within each measurement 
framework as set forth in sections IV.A. through IV.D. of this 
Appendix E.
    a. Options positions should be measured as a position equal to 
the market value of the underlying instrument multiplied by the 
delta. In addition, a bank must measure the sensitivities of the 
option's gamma (the change of the delta for a given change in the 
price of the underlying) and vega (the sensitivity of the option 
price with respect to a change in volatility) to calculate the total 
capital requirement. These sensitivities may be calculated according 
to an exchange model approved by the Federal Reserve or to the 
bank's own options pricing model, subject to review by the Federal 
Reserve.
    b. For options with debt instruments or interest rates as the 
underlying instrument, delta-weighted options positions should be 
slotted into the debt instrument time-bands in section IV.A. of this 
Appendix E using a two-legged approach (as is used for other 
derivatives), requiring one entry at the time the underlying 
contract takes effect and one at the time the underlying contract 
matures.\51\ Floating rate instruments with 

[[Page 38113]]
caps or floors should be treated as a combination of floating rate 
securities and a series of European-style options.\52\ A bank must 
also calculate the gamma and vega for each such option position 
(including hedge positions). The results should be slotted into 
separate maturity ladders by currency. For options such as caps and 
floors whose underlying instrument is an interest rate, the delta 
and gamma should be expressed in terms of a hypothetical underlying 
security. Subsequently:

    \51\ For example, in April, a purchased call option on a June 
three-month interest-rate future would be considered on the basis of 
its delta-equivalent value to be a long position with a maturity of 
five months and a short position with a maturity of two months. The 
written option would be slotted as a long position with a maturity 
of two months and short position with a maturity of five months.
    \52\ For example, the holder of a three-year floating rate bond 
indexed to six-month LIBOR with a cap of 15 percent would treat the 
bond as a debt security that reprices in six months, and a series of 
five written call options a FRA with a strike rate of 15 percent, 
each slotted as a short position at the expiration date of the 
option and as a long position at the time the FRA matures.
    i. For gamma risk, for each time-band, net gammas that are 
negative are multiplied by the risk weights set out in Table IV in 
section IV.E.5.b.iv. of this Appendix E and by the square of the 
market value of the underlying instrument (net positive gammas may 
be disregarded);
    ii. For volatility risk, a bank calculates the capital 
requirements for vega in each time-band assuming a proportional 
shift in volatility of 25.0 percent;
    iii. The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the sum of the individual capital requirements for 
vega risk for each time-band; and
    iv. The delta plus method risk weights are:

                                    Table IV.--Delta Plus Method Risk Weights                                   
----------------------------------------------------------------------------------------------------------------
                                                       Modified duration                                        
                      Time-band                         (average assumed     Assumed interest    Risk-weight for
                                                         for time band)      rate change (%)        gamma\1\    
----------------------------------------------------------------------------------------------------------------
Under 1 month.......................................                 0.00                 1.00           0.00000
1 up to 3 months....................................                 0.20                 1.00           0.00020
3 up to 6 months....................................                 0.40                 1.00           0.00080
6 up to 12 months...................................                 0.70                 1.00           0.00245
1 up to 2 years.....................................                 1.40                 0.90           0.00794
2 up to 3 years.....................................                 2.20                 0.80           0.01549
3 up to 4 years.....................................                 3.00                 0.75           0.02531
4 up to 5 years.....................................                 3.65                 0.75           0.03747
5 up to 7 years.....................................                 4.65                 0.70           0.05298
7 up to 10 years....................................                 5.80                 0.65           0.07106
10 up to 15 years...................................                 7.50                 0.60           0.10125
15 up to 20 years...................................                 8.75                 0.60           0.13781
Over 20 years.......................................                10.00                 0.60           0.18000
----------------------------------------------------------------------------------------------------------------
\1\ According to the Taylor expansion, the risk weights are calculated as \1/2\ (modified duration x assumed    
  interest rate change) \2\/100.                                                                                

    c. For options with equities as the underlying, delta-weighted 
option positions should be incorporated in the measure of market 
risk set forth in section IV.B. of this Appendix E. Individual 
equity issues and indices should be treated as separate underlyings. 
In addition to the capital requirement for delta risk, a bank must 
apply a further capital charge for gamma and vega risk:
    i. For gamma risk, the net gammas that are negative for each 
underlying are multiplied by 0.72 percent (in the case of an 
individual equity) or 0.32 percent (in the case of an index as the 
underlying) and by the square of the market value of the underlying;
    ii. For volatility risk, a bank calculates the capital 
requirement for vega for each underlying, assuming a proportional 
shift in volatility of 25.0 percent; and
    iii. The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the individual capital requirements for vega risk.
    d. For options of foreign exchange and gold positions, the net 
delta (or delta-based) equivalent of the total book of foreign 
currency and gold options is incorporated into the measurement of 
the exposure in a single currency position as set forth in section 
IV.C. of this Appendix E. The gamma and vega risks are measured as 
follows:
    i. For gamma risk, for each underlying exchange rate, net gammas 
that are negative are multiplied by 0.32 percent and by the square 
of the market value of the positions;
    ii. For volatility risk, a bank calculates the capital 
requirements for vega for each currency pair and gold assuming a 
proportional shift in volatility of 25.0 percent; and
    iii. The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the sum of the individual capital requirements for 
vega risk.
    e. For options on commodities, the delta-weighted positions are 
incorporated in one of the measures described in section IV.D. of 
this Appendix E. In addition, a bank must apply a capital 
requirement for gamma and vega risk:
    i. For gamma risk, net gammas that are negative for each 
underlying are multiplied by 1.125 percent and by the square of the 
market value of the commodity;
    ii. For volatility risk, a bank calculates the capital 
requirements for vega for each commodity assuming a proportional 
shift in volatility of 25.0 percent; and
    iii. The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the sum of the individual capital requirements for 
vega risk.
    f. Under certain conditions and to a limited extent, the Federal 
Reserve may permit banks that are significant traders in options 
with debt securities or interest rates as the underlying to net 
positive and negative gammas and vegas across time-bands. Such 
netting must be based on prudent and conservative assumptions and 
the bank must materially meet the qualitative standards set forth in 
section III.B. of this Appendix E.
    g. A bank may base the calculation of vega risk on a volatility 
ladder in which the implied change in volatility varies with the 
maturity of the option. The assumed proportional shift in volatility 
must be at least 25.0 percent at the short end of the 
maturity spectrum. The proportional shift for longer maturities must 
be at least as stringent in statistical terms as the 25.0 percent 
shift at the short end.
    h. A bank should also monitor the risks of rho (the rate of 
change of the value of the option with respect to the interest rate) 
and theta (the rate of change of the value of the option with 
respect to time).

Attachments to Appendix E
Attachment I--Sample Calculation of Eligible Tier 1, Tier 2, and Tier 3 
Capital for the Risk-Based Capital Ratio Adjusted for Market Risk

    a. In each example the weighted-risk assets are $8000 and the 
market risk-adjusted assets are $625 (capital requirement for market 
risk=$50 $50 x 12.5=$625):

    Example 1: A bank has the following qualifying capital:

Tier 1=$600  Tier 2=$100  Tier 3=$1000


[[Page 38114]]

    (1) The minimum capital requirement for credit risk is $640 
($8000 x 8.0%). This requirement could be satisfied with $540 of 
Tier 1 capital and $100 of Tier 2 capital.
    (2) The remaining capital available for market risk would be:

Tier 1=$60, Tier 2=0, and Tier 3=$1000. The minimum capital 
requirement for market risk is $50 ($625 x 8.0%). Eligible Tier 3 
capital would be limited to $125 ($50 x 2.5).

    (3) The Tier 1 capital required to support market risk could be 
satisfied by allocating $14 ($50 x .285), with eligible Tier 3 
capital used for market risk being $36 ($50-$14).
    (4) Total qualifying and eligible capital would be:

$540 (Tier 1)+$100 (Tier 2)+$60 (Tier 1, comprising $14 allocated 
for market risk and $46 unallocated)+$36 (Tier 3)=$736. The bank's 
ratio of qualifying and eligible capital to weighted-risk assets 
adjusted for market risk would be: $736/$8,625)=8.5%.

    Example 2: A bank has the following qualifying capital:

Tier 1=$500  Tier 2=$140  Tier 3=$600

    (1) The minimum capital requirement for credit risk is $640 
($8000 x 8.0%). This requirement could be satisfied with $500 of 
Tier 1 capital and $140 of Tier 2 capital.
    (2) The remaining capital available for market risk would be: 
Tier 1=0, Tier 2=$0, and Tier 3=$600. Eligible Tier 3 capital would 
be limited to $0 ( 0 x 2.5). Because there is no Tier 1 capital 
required to support market risk, no eligible Tier 3 capital may be 
used for market risk.
    (3) Total qualifying and eligible capital would be: $500 (Tier 
1)+$140 (Tier 2)=$640. The bank's ratio of qualifying and eligible 
capital to weighted-risk assets adjusted for market risk would be: 
$640/$8,625)=7.4%.
    b. In both of the examples described in paragraph a. of this 
attachment the total of Tier 2 and Tier 3 capital for credit and 
market risk is not greater than 100 percent of Tier 1 capital for 
credit and market risk and the total of Tier 2 capital for credit 
risk is not greater than 100 percent of Tier 1 capital for credit 
risk.
Attachment II--Sample Calculation of General Market Risk for Debt 
Instruments Using the Maturity Method

    a. A bank with the following positions would slot them into a 
maturity ladder as shown below:
    i. Qualifying bond, $13.33mn market value, remaining maturity 8 
years, coupon 8%;
    ii. Government bond, $75mn market value, remaining maturity 2 
months, coupon 7%;
    iii. Interest rate swap, $150 mn, bank receives floating rate 
interest and pays fixed, next interest reset after 12 months, 
remaining life of swap is 8 years (assumes the current interest rate 
is identical to the one the swap is based on); and
    iv. Long position in interest rate future, $50mn, delivery date 
after 6 months, life of underlying government security is 3.5 years 
(assumes the current interest rate is identical to the one the swap 
is based on).

--------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                             Risk wght      Risk-weighted         Net time-band                         
      Zone                          Time-band and position                      [%]           position              positions        Net zone positions 
--------------------------------------------------------------------------------------------------------------------------------------------------------
1...............  0-1 mth..................................................       0.00                                                                  
                  1-3 mth Long 75 Gov. bond................................       0.20  Long 0.15...........  Long 0.15...........  Long 1.00.          
                  3-6 mth..................................................       0.40  Short 0.20..........  Short 0.20..........                      
                  Short 50 Future                                                                                                                       
                  6-12 mths................................................       0.70  Long 1.05...........  Long 1.05...........                      
                  Long 150 Swap                                                                                                                         
2...............  1-2 yrs..................................................       1.25                                                                  
                  2-3 yrs..................................................       1.75                                                                  
                  3-4 yrs..................................................       2.25  Long 1.125..........  Long 1.125..........  Long 1.125          
                  Long 50 Future                                                                                                                        
3...............  4-5 yrs..................................................       2.75                                                                  
                  5-7 yrs..................................................       3.25                                                                  
                  7-10 yrs.................................................       3.75  Short 5.625.........  Short 5.125.........  Short 5.125         
                  Short 150 Swap                                                                                                                        
                  Long 13.33 Qual Bond                                                  Long 0.50                                                       
                  10-15 yrs................................................       4.50                                                                  
                  15-20 yrs................................................       5.25                                                                  
                  Over 2 yrs...............................................       6.00                                                                  
--------------------------------------------------------------------------------------------------------------------------------------------------------

    b. A vertical disallowance would be calculated for time-band 7-
10 years. It would be 10 percent of the matched positions in the 
time-band--10.0 x 0.5=0.05 ($50,000).
    c. A horizontal disallowance would be calculated for zone 1. It 
would be 40 percent of the matched positions in the zone--
40.0 x 0.20=0.80 ($80,000). The remaining net position in Zone 1 
would be +1.00.
    d. A horizontal disallowance would be calculated for adjacent 
zones 2 and 3. It would be 40 percent of the matched positions 
between the zones--40.0 x 1.125=0.45 (450,000). The remaining 
position in zone 3 would be -4.00.
    e. A horizontal disallowance would be calculated between zones 1 
and 3. It would be 100 percent of the matched positions between the 
zones--100 x 1.00=1.00 (1,000,000).
    f. The remaining net open position for the bank would be 3.00 
($3,000,000). The total capital requirement for general market risk for 
this portfolio would be:

The vertical disallowance..................................      $50,000
Horizontal disallowance in zone 1..........................       80,000
Horizontal disallowance--zones 2 and 3.....................      450,000
Horizontal disallowance--zones 1 and 3.....................    1,000,000
Overall net open position..................................    3,000,000
                                                            ------------
    Total requirement for general market risk..............    4,580,000
                                                                        

Attachment III--Summary of Treatment for Interest Rate and Equity 
Derivatives

                               Summary of Treatment for Interest Rate Derivatives                               
----------------------------------------------------------------------------------------------------------------
                                                         Specific risk                                          
                       Instrument                            charge            General market risk charge       
----------------------------------------------------------------------------------------------------------------
Exchange-Traded Future                                                                                          
  Government security..................................  No...........  Yes, as two positions.                  
  Corporate debt security..............................  Yes..........  Yes, as two positions.                  
  Index on short-term interest rates (e.g. LIBOR)......  No...........  Yes, as two positions.                  
OTC Forward                                                                                                     
  Government security..................................  No...........  Yes, as two positions.                  

[[Page 38115]]
                                                                                                                
  Corporate debt security..............................  Yes..........  Yes, as two positions.                  
  Index on short-term interest rates...................  No...........  Yes, as two positions.                  
FRAs, Swaps............................................  No...........  Yes, as two positions.                  
Forward foreign exchange...............................  No...........  Yes, as one position in each currency.  
Options:                                                 .............  For each type of transaction, either:   
  Government security..................................  No...........     (a) Carve out together with the      
                                                                            associated hedging positions        
                                                                             --simplified method                
                                                                             --scenario analysis                
                                                                             --internal models, or              
  Corporate debt security..............................  Yes..........     (b) General market risk charge       
                                                                            according to the Delta-plus method  
                                                                            (gamma and vega receive separate    
                                                                            capital charges)                    
  Index on short-term interest rates...................  No...........                                          
----------------------------------------------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument. There remains a separate capital requirement
  for counterparty credit risk.                                                                                 



                                   Summary of Treatment for Equity Derivatives                                  
----------------------------------------------------------------------------------------------------------------
                                                         Specific risk                                          
                       Instrument                            charge            General market risk charge       
----------------------------------------------------------------------------------------------------------------
Exchange-Traded or OTC Future:                                                                                  
    Individual equity..................................  Yes..........  Yes, as underlying.                     
    Index..............................................  2.0%.........  Yes, as underlying.                     
Options:                                                 .............  For each type of transactions either:   
    Individual equity..................................  yes..........     (a) Carve out together with the      
                                                                            associated hedging positions        
                                                                             --simplified method                
                                                                             --scenario approach                
                                                                             --internal models, or              
    Index..............................................  2.0%.........  (b) General market risk requirement     
                                                                         according to the Delta-plus method     
                                                                         (gamma and vega receive separate       
                                                                         capital charges).                      
----------------------------------------------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument. There remains a separate capital requirement
  for counterparty credit risk.                                                                                 

Attachment IV--Sample Calculation of Standardized Approach for 
Commodities Risk

----------------------------------------------------------------------------------------------------------------
                                                           Spread                                      Capital  
         Time-band                    Position              rate          Capital calculation           charge  
----------------------------------------------------------------------------------------------------------------
0 up to 1 month............  None                                                                               
1 up to 3 months...........  None                                                                               
3 up to 6 months...........  Long 800..................       1.5%  800 long+800 short (matched) x            24
                                                                     1.5%=.                                     
                             Short 1000................  .........  200 short carried forward to 1-          2.4
                                                                     2 yrs, capital charge: 200 x 2             
                                                                     x 0.6%=.                                   
6 up to 12 months..........  None                                                                               
1 up to 2 yrs..............  Long 600..................  .........  200 long+200 short (matched) x             6
                                                                     1.5%=.                                     
                                                                    400 long carried forward to              4.8
                                                                     over 3 yrs capital charge: 400             
                                                                     x 2 x 0.6%=.                               
2 up to 3 yrs..............  None                                                                               
Over 3 years...............  Short 600.................  .........  400 long+400 short (matched) x            12
                                                                     1.5%=.                                     
                                                                    Net position: 200 capital                 30
                                                                     charge: 200 x 15.0%=.                      
----------------------------------------------------------------------------------------------------------------
Note: Assume all positions are in the same commodity and converted at current spot rates into U.S. dollars. The 
  total capital requirement would be $79.2.                                                                     


[[Page 38116]]


Attachment V--Sample Calculation for Delta-Plus Method for Options

    a. Assume a bank has a European short call option on a commodity 
with an exercise price of 490 and a market value of the underlying 
12 months from the expiration of the option at 500; a risk-free 
interest rate at 8% per annum, and the volatility at 20 percent. The 
current delta for this position is according to the Black-Scholes 
formula -0.721 (that is, the price of the option changes by -0.721 
if the price of the underlying moves by 1). The gamma is -0.0034 
(that is, the delta changes by -0.0034 from -0.721 to -0.7244 if the 
price of the underlying moves by 1). The current value of the option 
is 65.48.
    b. The first step under the delta-plus method is to multiply the 
market value of the commodity by the absolute value of the delta. 
500 x 0.721 = 360.5. The delta-weighted position is then 
incorporated into the measure described in section IV.D. of this 
Appendix E. If the bank uses the maturity approach and no other 
positions exist, the delta-weighted position is multiplied by 0.15 
to calculate the capital requirement for delta. 360.5 x 0.15 = 
54.075.
    c. The capital requirement for gamma is calculated according to 
the Taylor expansion by multiplying the absolute value of the 
assumed gamma of -0.0034 by 1.125% and by the square of the market 
value of the underlying. -0.0034 x 0.0125 x 500\2\ = 10.625.
    d. The capital requirement for vega is calculated next. The 
assumed current (implied) volatility is 20%. Since only an increase 
in volatility carries a risk of loss for a short call option, the 
volatility has to be increased by a relative shift of 25%. This 
means that the vega capital requirement has to be calculated on the 
basis of a change in volatility of 5 percentage points from 20% to 
25% in this example. According to the Black-Scholes formula used 
here, the vega equals 168. Thus, a 1% or 0.01 increase in volatility 
increases the value of the option by 1.68. Accordingly, a change in 
volatility of 5 percentage points increases the value of 5 x 1.68 = 
8.4. This is the capital requirement for vega risk. The total 
capital requirement would be $73.10 (54.075 + 10.625 + 8.4).
PART 225--BANK HOLDING COMPANIES AND CHANGE IN BANK CONTROL 
(REGULATION Y)

    1. The authority citation for part 225 continues to read as 
follows:

    Authority: 12 U.S.C. 1817(j)(13), 1818, 1828(o), 1831i, 1831p-1, 
1843(c)(8), 1844(b), 1972(1), 3106, 3108, 3310, 3331-3351, 3907, and 
3909.

    2. In part 225, appendix A to part 225 is amended by revising the 
first and second paragraphs of section I. to read as follows:

Appendix A to Part 225--Capital Adequacy Guidelines for Bank Holding 
Companies: Risk-Based Measure

I. Overview

    The Board of Governors of the Federal Reserve System has adopted 
a risk-based capital measure to assist in the assessment of the 
capital adequacy of bank holding companies (banking 
organizations).1 The principal objectives of this measure are 
to (i) make regulatory capital requirements more sensitive to 
differences in risk profiles among banking organizations; (ii) 
factor off-balance-sheet exposures into the assessment of capital 
adequacy; (iii) minimize disincentives to holding liquid, low-risk 
assets; and (iv) achieve greater consistency in the evaluation of 
the capital adequacy of major banking organizations throughout the 
world.

    \1\ Some banking organizations are also subject to capital 
requirements for market risk as set forth in appendix E of this 
part. Banking organizations that are subject to the market risk 
measure are required to follow the guidelines set forth in appendix 
E of this part for determining qualifying and eligible capital, 
calculating market risk-equivalent assets and adding them into 
weighted-risk assets, and calculating risk-based capital ratios 
adjusted for market risk. Supervisory ratios that relate capital to 
total assets for bank holding companies are outlined in appendices B 
and D of this part.
---------------------------------------------------------------------------

    The risk-based capital guidelines include both a definition of 
capital and a framework for calculating weighted risk assets by 
assigning assets and off-balance-sheet items to broad risk 
categories.2 An institution's risk-based capital ratio is 
calculated by dividing its qualifying capital (the numerator of the 
ratio) by its weighted risk assets (the denominator).3 The 
definition of qualifying capital is outlined below in section II. of 
this appendix A, and the procedures for calculating weighted risk 
assets are discussed in section III. of this appendix A. Attachment 
I to this appendix A illustrates a sample calculation of weighted 
risk assets and the risk-based capital ratio.

    \2\ The risk-based capital measure is based upon a framework 
developed jointly by supervisory authorities from the countries 
represented on the Basle Committee on Banking Regulations and 
Supervisory Practices (Basle Supervisors' Committee) and endorsed by 
the Group of Ten Central Bank Governors. The framework is described 
in a paper prepared by the Basle Supervisors' Committee entitled 
``International Convergence of Capital Measurement,'' July 1988.
    \3\ Banking organizations generally are expected to utilize 
period-end amounts in calculating their risk-based capital ratios. 
When necessary and appropriate, ratios based on average balances may 
also be calculated on a case-by-case basis. Moreover, to the extent 
banking organizations have data on average balances that can be used 
to calculate risk-based ratios, the Federal Reserve will take such 
data into account.
---------------------------------------------------------------------------

* * * * *
    3. In Part 225 a new appendix E is added to read as follows:

Appendix E to Part 225--Capital Adequacy Guidelines for Bank Holding 
Companies: Market Risk Measure

I. Introduction

A. Overview

    1. The Board of Governors of the Federal Reserve System has 
adopted a framework for determining capital requirements for the 
market risk exposure of bank holding companies (banking 
organizations).1 For this purpose, market risk is defined as 
the risk of losses in a banking organization's on- and off-balance-
sheet positions arising from movements in market prices. The market 
risks subject to these capital requirements are those associated 
with debt and equity instruments held in the banking organization's 
trading account, as well as foreign exchange risk and commodities 
risk throughout the organization, including options and other 
derivative contracts in each risk category.

    \1\ The market risk measure is based on a framework developed 
jointly by supervisory authorities from the countries represented on 
the Basle Committee on Banking Supervision (Basle Supervisors 
Committee) and endorsed by the Group of Ten Central Bank Governors. 
The framework is described in a paper prepared by the Basle 
Supervisors Committee entitled ``[Proposal to issue a] Supplement to 
the Basle Capital Accord to Cover Market Risks.'' [April] 1995.
---------------------------------------------------------------------------

    2. Effective December 31, 1997, the market risk measure will be 
applied to all bank holding companies that, on a consolidated basis:
    a. Have total assets in excess of $5 billion; and have a total 
volume of trading activities (measured as the sum of the banking 
organization's trading assets and liabilities 2 on a daily 
average basis for the quarter) that is 3.0 percent or more of the 
total assets of the banking organization, or have interest rate, 
foreign exchange, equity, and commodity off-balance-sheet derivative 
contracts relating to trading activities whose total notional 
amounts exceed $5 billion; or

    \2\ As reflected in the Consolidated Financial Statements for 
Bank Holding Companies (FR Y-9C Report).
    b. Have total assets of $5 billion or less; and have trading 
activities exceeding 10.0 percent of the total assets of the banking 
organization.
    3. Such banking organizations are still subject to the risk-
based capital measure set forth in appendix A of this part, subject 
to the exclusion of certain assets specified in this appendix E. 
However, these banking organizations must calculate their market 
risk-equivalent assets and determine risk-based capital ratios 
adjusted for market risk in accordance with this appendix E.3

    \3\ The Federal Reserve may apply all or portions of this 
appendix E to other banking organizations when deemed necessary for 
safety and soundness purposes.
---------------------------------------------------------------------------

    4. The market risk measure provides two ways for a banking 
organization to determine its exposure to market risk. A banking 
organization may use its internal risk measurement model, subject to 
the conditions and criteria set forth in section III. of this 
appendix E (referred to as the internal models approach), or when 
appropriate, a 

[[Page 38117]]
banking organization may use all or portions of the alternative 
measurement system described in section IV. of this appendix E 
(referred to as the standardized approach).
    a. With prior approval from the Federal Reserve, for regulatory 
capital purposes, a banking organization may use its internal risk 
measurement model to measure its value-at-risk 4 for each of 
the following risk factor categories; interest rates, exchange 
rates, equity prices, and commodity prices. The value-at-risk amount 
for each risk factor category should include volatilities of related 
options. The value-at-risk amount for each risk factor category is 
summed to determine the aggregate value-at-risk for the banking 
organization.

    \4\ A banking organization evaluates its current positions and 
estimates future market volatility through a value-at-risk measure, 
which is an estimate representing, with a certain degree of 
statistical confidence, the maximum amount by which the market value 
of trading positions could decline during a specific period of time. 
The value-at-risk is generated through an internal model that 
employs a series of market risk factors (for example, market rates 
and princes that affect the value of trading positions).
---------------------------------------------------------------------------

    b. The standardized approach uses a set of standardized 
calculations and assumptions to measure market risk exposure 
depending on its source; debt instruments, equities, foreign 
currencies, and commodities, including volatilities of related 
options.
    5. The Board generally expects any banking organization that is 
subject to the market risk measure, especially those with large 
trading accounts, to comply with the measure by using internal risk-
measurement models. A banking organization may not change its 
measurement approach for the purpose of minimizing capital 
requirements. In limited instances, on a case-by-case basis, the 
Federal Reserve may permit a banking organization that has internal 
models to incorporate risk measures of negligible exposures, for 
example, de minimis positions, activities in remote locations, minor 
exposures in a currency, or activities that present negligible risk 
to the banking organization, in an alternative manner, so long as it 
adequately captures the risk.
    6. The risk-based capital ratios adjusted for market risk 
determined in accordance with this appendix E are minimum 
supervisory ratios. Banking organizations generally are expected to 
operate with capital positions well above the minimum ratios. In all 
cases, banking organizations should hold capital commensurate with 
the level and nature of the risks to which they are exposed.
    7. The Federal Reserve will monitor the implementation and 
effect of these guidelines in relation to domestic and international 
developments in the banking industry. When necessary and 
appropriate, the Board will consider the need to modify this 
appendix E in light of any significant changes in the economy, 
financial markets, banking practices, or other relevant factors.
B. Market Risks Subject to a Capital Requirement.

    1. General Market Risk and Specific Risk. A banking organization 
must hold capital against exposure to general market risk and 
specific risk arising from its trading and other foreign exchange 
and commodity activities. For this purpose, general market risk 
refers to changes in the market value of covered transactions 
resulting from market movements, such as changing levels of market 
interest rates, broad equity indices, or currency exchange rates. 
Specific risk refers to credit risk, that is, the risk that the 
issuer of a debt or equity instrument might default, as well as to 
other factors that affect the market value of specific instruments 
but that do not materially alter market conditions.5

    \5\ This Appendix E does not impose specific risk capital 
requirements for foreign exchange risk and commodities positions 
because they do not have the type of issuer-specific risk associated 
with debt and equity instruments in the trade account.
---------------------------------------------------------------------------

    2. Trading Activities. a. The general market risk and specific 
risk capital requirements for trading activities are based on on- 
and off-balance-sheet positions in a banking organization's trading 
account. For this purpose, trading account means positions in 
financial instruments acquired with the intent to resell in order to 
profit from short-term price movements (or other price or interest-
rate variations), including, but not limited to:
    i. Assets acquired with the intent to resell to customers;
    ii. Positions in financial instruments arising from matched 
principal brokering and market making; or
    iii. Positions taken in order to hedge other elements of the 
trading account (that is, reduce risk by offsetting other positions 
that have exposure to changes in market rates or prices).6
Trading activities may include positions in debt instruments, 
equities, foreign currencies, and commodity instruments, or related 
derivative 7 or other off-balance-sheet contracts.

    \6\ At a banking organization's option, when non-trading account 
instruments are hedged with instruments in the trading account, on- 
or off-balance-sheet, the non-trading account instruments may be 
included in the measure for general market risk. Such non-trading 
account instruments remain subject to the credit risk capital 
charges of appendix A of this part.
    \7\ In general terms, a derivative is a financial contract whose 
value is derived from the values of one or more underlying assets or 
reference rates or indexes of asset values (referred to as ``the 
underlying''). Derivatives include standardized contracts that are 
traded on exchanges and customized, privately negotiated contracts 
known as over-the-counter (OTC) derivatives.
---------------------------------------------------------------------------

    b. Debt instruments in the trading account are all fixed-rate 
and floating-rate debt securities and instruments that behave like 
debt, including non-convertible preferred stock. Convertible bonds, 
i.e., preferred stock or debt issues that are convertible, at a 
stated price, into common shares of the issuer, should be treated as 
debt instruments if they trade like debt instruments and as equities 
if they trade like equities. Also included are derivative contracts 
of debt instruments and other off-balance-sheet instruments in the 
trading account that react to changes in interest rates. A security 
that has been sold subject to a repurchase agreement or lent subject 
to a securities lending agreement is treated as if it were still 
owned by the lender of the security. Such transactions remain 
subject to the capital requirements for credit risk for the off- 
balance-sheet portion of the transaction as set forth in section 
III.D. of appendix A of this part.
    c. Equities in the trading account are equity instruments that 
behave like equities. The instruments covered include common stocks 
(whether voting or non-voting), convertible securities that behave 
like equities, and commitments to buy or sell equity securities. 
Also included are derivative contracts of equity instruments and 
other off-balance-sheet instruments in the trading account that are 
affected by changes in equity prices. However, non-convertible 
preferred stock is included in debt instruments.
    3. Foreign Exchange and Commodities Risk. Foreign exchange or 
commodities positions, whether or not included in a banking 
organization's trading account, are subject to a capital requirement 
for the market risk of those positions.
    a. The capital requirement for foreign exchange risk applies to 
a banking organization's total currency and gold positions. This 
includes spot positions (that is, asset items and liability items, 
including accrued interest and expenses, denominated in each 
currency); forward positions (that is, forward foreign exchange 
transactions, including currency futures and the principal on 
currency swaps not included in the spot position); and certain 
guarantees. It includes future income and expenses from foreign 
currency transactions not yet accrued but already fully hedged (at 
the discretion of the reporting bank), foreign exchange derivative 
and other off-balance-sheet positions that are affected by changes 
in exchange rates, and any other item representing a profit or loss 
in foreign currencies.
    b. A banking organization may, subject to approval by the 
Federal Reserve, exclude from its foreign exchange positions any 
structural positions in foreign currencies. For this purpose, such 
structural positions are limited to transactions designed to hedge a 
banking organization's capital ratios against the effect of adverse 
exchange rate movements on subordinated debt, equity, or minority 
interests in consolidated subsidiaries and dotation capital assigned 
to foreign branches that are denominated in foreign currencies. Also 
included are any positions related to unconsolidated subsidiaries 
and to other items that are deducted from a banking organization's 
capital when calculating its capital base. In any event, such 
structural foreign currency positions must reflect long-term 
policies of the institution and not relate to trading positions.
    c. A banking organization doing negligible business in foreign 
currency and that does not take foreign exchange positions for its 
own account may be exempted from the capital requirement for foreign 
exchange risk provided that:
    i. Its foreign currency business, defined as the greater of the 
sum of its gross long positions and the sum of its gross short 
positions in all foreign currencies, does not exceed 100 percent of 
eligible capital as defined in section II. of this appendix E; and
    ii. Its overall net open foreign exchange position as determined 
in section IV.C.2. of this appendix E does not exceed 2.0 percent of 
its eligible capital. 

[[Page 38118]]

    d. The capital requirement for commodities risk applies to a 
banking organization's total commodities positions, including 
commodity futures, commodity swaps, and all other commodity 
derivatives or other off-balance-sheet positions that are affected 
by changes in commodity prices. A commodity is defined as a physical 
product that is or can be traded on a secondary market (such as 
agricultural products, minerals (including oil), and precious 
metals), but excluding gold (which is treated as foreign exchange).

C. Capital Requirements

    1. Capital Requirements. The minimum capital requirement for a 
bank holding company subject to the market risk measure is the sum 
of:
    a. The capital requirement for credit risk as determined in 
accordance with appendix A of this part, excluding debt and equity 
instruments in the trading book and positions in commodities, but 
including the counterparty credit risk requirements on all over-the-
counter derivative activities whether in the banking organization's 
trading account or not; and
    b. The capital requirement for market risk as determined by the 
internal models approach, the standardized approach, or a 
combination of the two approaches deemed to be appropriate by the 
Federal Reserve.
    2. Internal Models. a. For a banking organization approved to 
use the internal models approach, the capital requirement for market 
risk is the higher of:
    i. The banking organization's previous day's aggregate value-at-
risk amount calculated subject to certain supervisory requirements 
set forth in section III. of this appendix E; or
    ii. An average of the daily aggregate value-at-risk amounts, 
calculated subject to the same restrictions, measured on each of the 
preceding sixty (60) business days, multiplied by a minimum 
``multiplication factor'' of three (3).8

    \8\ The Federal Reserve may adjust the multiplication factor for 
a banking organization to increase its capital requirement based on 
an assessment of the quality and historic accuracy of the banking 
organization's risk management system.
---------------------------------------------------------------------------

    b. A banking organization approved to use the internal models 
approach may also be subject to a separate capital requirement for 
specific market risk of traded debt and equity instruments to the 
extent that the specific market risk associated with these 
instruments is not captured by the banking organization's models. 
However, for all banking organizations using internal models, the 
total specific risk charge should in no case be less than one-half 
the specific risk charges calculated according to the standardized 
approach.
    3. Standardized approach. A banking organization whose model has 
not been approved by the Federal Reserve must use the standardized 
approach for measuring its market risk. For a banking organization 
using this approach, the capital requirement for market risk is the 
sum of the market risk capital requirement for debt and equity 
instruments in the trading account, foreign exchange and commodities 
risk throughout the banking organization, and options and other 
derivative positions in each risk category as set forth in sections 
IV.A to IV.E. of this appendix E.9

    \9\ Section IV.E. provides several alternatives for measuring 
the market risk of options. Under two of the alternatives, the 
simplified and scenario methods, the underlying position of an 
option is ``carved-out,'' and is not included in the prescribed risk 
measure for the underlying. Instead it is evaluated together with 
the related option according to the procedures described for options 
to determine the capital requirement. Under the third alternative, 
the ``delta-plus'' approach, the delta-equivalent value of each 
position is included in the measurement framework for the 
appropriate risk category (that is, debt or equity instruments in 
the trading account, foreign exchange or commodities risk).
---------------------------------------------------------------------------

    4. Partial models. a. With approval from the Federal Reserve, a 
banking organization whose internal model does not cover all risk 
factor categories may use the standardized approach to measure 
market risk exposure arising from the risk factor categories that 
are not covered. The Federal Reserve will approve combining the two 
approaches only on a temporary basis in situations where the banking 
organization is developing, but has not fully implemented, a 
comprehensive value-at-risk measurement system. When a banking 
organization uses both approaches, each risk factor category (that 
is, interest rates, exchange rates, equity prices, and commodity 
prices) must be measured using one or the other approach. The 
methods may not be combined within a risk factor category. Once a 
banking organization adopts an acceptable value-at-risk model for a 
particular risk factor category, it may not revert to the 
standardized approach except in unusual circumstances and with prior 
approval of the Federal Reserve.
    b. For a banking organization using a combination of approaches, 
the capital requirement for market risk is the sum of (i) the 
appropriate value-at-risk amount (as determined under section 
I.C.2.a. of this appendix E, aggregating the value-at-risk amount 
for each risk factor category included in the internal model), and 
(ii) the capital requirement for each risk category that is 
calculated using the standardized approach.
    5. Application. The capital requirements for market risk apply 
to bank holding companies on a worldwide consolidated basis. The 
Federal Reserve may, however, evaluate market risk on an 
unconsolidated basis when necessary. For example, when there are 
obstacles to the repatriation of profits from a foreign subsidiary 
or where management structure does not allow timely management of 
risk on a consolidated basis.
    6. Other Considerations. All transactions, including forward 
sales and purchases, should be included in the calculation of market 
risk capital requirements from the date on which they were entered 
into. The Federal Reserve expects banking organizations to meet 
their capital requirements for market risk on a continuous basis 
(that is, at a minimum, at the close of each business day).
II. Qualifying Capital and the Market Risk-Adjusted Capital Ratio

A. Qualifying and Eligible Capital

    1. The principal forms of qualifying capital for market risk are 
Tier 1 capital and Tier 2 capital as defined in section II. of 
appendix A of this part and subject to the conditions and 
limitations of appendix A of this part. A banking organization may 
use Tier 3 capital for the sole purpose of meeting a portion of the 
capital requirements for market risk.10

    \10\ A banking organization may not use Tier 3 capital to 
satisfy any capital requirements for counterparty credit risk under 
appendix A of this part, including counterparty credit risk 
associated with derivative transactions in either the trading or 
non-trading accounts.
---------------------------------------------------------------------------

    2. Tier 3 capital consists of short-term subordinated debt that 
is subject to a lock-in clause providing that neither interest nor 
principal payment is due (even at maturity) if such payment would 
cause the issuing banking organization to fall or remain below the 
minimum 8.0 percent risk-based capital requirement as set forth in 
appendix A of this part and adjusted for market risk.
    3. In order to qualify as Tier 3 capital, the short-term debt 
must be unsecured, subordinated, and fully paid up; it must have an 
original maturity of at least two years; and it may not be redeemed 
before maturity without prior approval by the Federal Reserve. In 
addition, it may not contain or be covered by any covenants, terms, 
or restrictions that are inconsistent with safe and sound banking 
practices.
    4. Eligible Tier 3 capital may not exceed 250 percent of a 
banking organization's Tier 1 capital allocated for market risk and 
the maximum eligible amount of Tier 2 and Tier 3 capital together is 
limited to 100 percent of Tier 1 capital. (Examples of how to 
calculate these limits are set forth in Attachment I to this 
appendix E.) Tier 2 elements may be substituted for Tier 3 up to the 
same limit of 250 percent, so long as the overall limits for Tier 2 
capital set forth in appendix A of this part are not exceeded, that 
is, Tier 2 capital may not exceed total Tier 1 capital, and long-
term subordinated debt may not exceed 50 percent of Tier 1 capital.

B. Calculation of Eligible Capital and the Capital Ratio

    1. In order to calculate eligible capital, a banking 
organization must first calculate its minimum capital requirement 
for credit risk in accordance with appendix A of this part and then 
its capital requirement for market risk. Eligible capital is the sum 
of the banking organization's qualifying Tier 1 capital, its 
qualifying Tier 2 capital subject to the limits stated above, and 
its eligible Tier 3 capital subject to the conditions set out under 
section II. of this appendix E.
    2. A banking organization that is subject to the market risk 
measure must calculate its risk-based capital ratios as follows:
    a. Determine total weighted-risk assets using the procedures and 
criteria set forth in appendix A of this part, excluding debt and 
equity instruments in the trading book and positions in commodities, 
but including all over-the-counter derivative activities whether in 
the banking organization's trading account or not. 

[[Page 38119]]

    b. Calculate the measure for market risk using the internal 
models approach, the standardized approach, or an approved 
combination of these two approaches.
    c. Multiply the measure for market risk by 12.5 (i.e., the 
reciprocal of the 8.0 percent minimum risk-based capital ratio). The 
resulting product is referred to as ``market risk-equivalent 
assets.''
    d. Add market risk-equivalent assets to the weighted-risk assets 
compiled for credit risk purposes (section II.B.2.a. of this 
appendix E). The sum of these two amounts is the denominator of the 
risk-based capital ratios adjusted for market risk. The numerator of 
the total risk-based capital ratio is eligible capital and the 
numerator of the Tier 1 risk-based capital ratio is Tier 1 capital.

III. The Internal Models Approach

A. Use of Models

    1. With prior approval of the Federal Reserve, a banking 
organization may use its internal risk measurement model(s) for 
purposes of measuring value-at-risk and determining the associated 
regulatory capital requirements for market risk exposure.
    a. Requests for approval under section III.A.1. of this appendix 
E should include, at a minimum, a complete description of the 
banking organization's internal modeling and risk management systems 
and how these systems conform to the criteria set forth in this 
section III., an explanation of the policies and procedures 
established by the banking organization to ensure continued 
compliance with such criteria, a discussion of internal and external 
validation procedures, and a description of other relevant policies 
and procedures consistent with sound practices.
    b. The Federal Reserve will approve an internal model for 
regulatory capital purposes only after determining that the banking 
organization's internal model and risk management systems meet the 
criteria in section III. of this appendix E. Such a determination 
may require on-site examinations of the systems. The Federal Reserve 
may require modification to an internal model as deemed necessary to 
ensure compliance, on a continuing basis, with the provisions of 
this appendix E. A banking organization's internal model will be 
subject to continuing review, both on-and off-site, by the Federal 
Reserve.11

    \11\ Banking organizations that need to modify their existing 
modeling procedures to accommodate the requirements of this appendix 
E should, nonetheless, continue to use the internal models they 
consider most appropriate in evaluating risks for other purposes.
---------------------------------------------------------------------------

    2. A banking organization should ensure that the level of 
sophistication of its internal model is commensurate with the nature 
and volume of the banking organization's trading activity in the 
risk factor categories covered by this appendix E and measures 
market risk as accurately as possible. In addition, the model should 
be adjusted to reflect changing portfolio composition and changing 
market conditions.

B. Qualitative Criteria

    1. A banking organization using the internal models approach 
should have market risk management systems that are conceptually 
sound and implemented with integrity. Internal risk measurement 
models must be closely integrated into the day-to-day risk 
management process of the banking organization. For example, the 
risk measurement model must be used in conjunction with internal 
trading and exposure limits.
    2. A banking organization must meet the following minimum 
qualitative criteria before using its internal model to measure its 
exposure to market risk.\12\

    \12\ If the Federal Reserve is not satisfied with the extent to 
which a banking organization meets these criteria, the Federal 
Reserve may adjust the multiplication factor used to calculate 
market risk capital requirements or otherwise increase capital 
requirements.
---------------------------------------------------------------------------

    a. A banking organization must have a risk control unit that is 
independent from business trading units and reports directly to 
senior management of the banking organization. The unit must be 
responsible for designing and implementing the banking 
organization's risk management system and analyzing daily reports on 
the output of the banking organization's risk measurement model in 
the context of trading limits. The unit must conduct regular back-
testing.\13\

    \13\ Back-testing includes ex post comparisons of the risk 
measures generated by the model against the actual daily changes in 
portfolio value.
---------------------------------------------------------------------------

    b. Senior management must be actively involved in the risk 
control process. The daily reports produced by the risk management 
unit must be reviewed by a level of management with sufficient 
authority to enforce both reductions in positions taken by 
individual traders, as well as in the banking organization's overall 
risk exposure.
    c. The banking organization must have a routine and rigorous 
program of stress-testing\14\ to identify the effect of low-
probability events on the banking organization's trading portfolio. 
Senior management must routinely review the results of stress-
testing in the context of the potential effect of the events on bank 
capital and the appropriate procedures the banking organization 
should take to minimize losses. The policies of the banking 
organization set by management and the board of directors should 
identify appropriate stress-tests and the procedures to follow in 
response to the test results.

    \14\ Stress-testing should cover a range of factors that can 
create extraordinary losses or gains in trading portfolios or make 
the control of risk in those portfolios difficult. These factors 
include low-probability events of all types, including the various 
components of market, credit, and operational risks.
---------------------------------------------------------------------------

    d. The banking organization must have established procedures for 
ensuring compliance with a documented set of internal policies and 
controls, as well as for monitoring the overall operation of the 
risk measurement system.
    e. Not less than once a year, the banking organization must 
conduct, as part of its regular internal audit process, an 
independent review of the risk measurement system. This review must 
include both the activities of the business trading units and of the 
independent risk control unit of the banking organization.
    f. Not less than once a year, the banking organization must 
conduct a review of its overall risk management process. The review 
must consider:
    i. The adequacy of the documentation of the risk management 
system and process and the organization of the risk control unit;
    ii. The integration of market risk measures into daily risk 
management and the integrity of the management information system;
    iii. The process the banking organization employs for approving 
risk pricing models and valuation systems that are used by front- 
and back-office personnel;
    iv. The scope of market risks captured by the risk measurement 
model and the validation of any significant changes in the risk 
measurement process;
    v. The accuracy and completeness of position data, the accuracy 
and appropriateness of volatility and correlation assumptions, and 
the accuracy of valuation and risk sensitivity calculations;
    vi. The verification process the banking organization employs to 
evaluate the consistency, timeliness, and reliability of data 
sources used to run internal models, including the independence of 
such data sources; and
    vii. The verification process the banking organization uses to 
evaluate back-testing that is conducted to assess the model's 
accuracy.

C. Market Risk Factors

    1. Overview. For regulatory capital purposes, a banking 
organization's internal risk measurement system(s) must use 
sufficient risk factors to capture the risks inherent in the banking 
organization's portfolio of on- and off-balance-sheet trading 
positions and must, subject to the following guidelines, cover 
interest rates, equity prices, exchange rates, commodity prices, and 
volatilities related to options positions in each risk factor 
category. The level of sophistication of the banking organization's 
risk factors must be commensurate with the nature and scope of the 
risks taken by the banking organization.
    2. Interest Rates. a. A banking organization must use a set of 
market risk factors corresponding to interest rates in each currency 
in which it has material interest rate-sensitive on- or off-balance-
sheet positions. The risk measurement system must model the yield 
curve \15\ using one of a number of generally accepted approaches, 
for example, by estimating forward rates of zero coupon yields. The 
yield curve must be divided into various maturity segments in order 
to capture variation in the volatility of rates along the yield 
curve; there will typically be one risk factor corresponding to each 
maturity segment.

    \15\ Generally, a yield curve is a graph showing the term 
structure of interest rates by plotting the yields of all 
instruments of the same quality by maturities ranging from the 
shortest to the longest available. The resulting curve shows whether 
short-term interest rates are higher or lower than long-term 
interest rates.
---------------------------------------------------------------------------

    b. For material exposures to interest rate movements in the 
major currencies and markets, a banking organization must model the 
yield curve using a minimum of six risk factors. However, the number 
of risk factors used should ultimately be driven by the 

[[Page 38120]]
nature of the banking organization's trading strategies.\16\ The risk 
measurement system must incorporate separate risk factors to capture 
spread risk.\17\

    \16\ For example, a banking organization that has a portfolio of 
various types of securities across many points of the yield curve 
and that engages in complex arbitrage strategies would require a 
greater number of risk factors to accurately capture interest rate 
risk.
    \17\ Spread risk refers to the potential changes in value of an 
instrument or portfolio arising from differences in the behavior of 
baseline yield curves, such as those for U.S. Treasury securities, 
and yield curves reflecting sector, quality, or instrument specific 
factors. A variety of approaches may be used to capture the spread 
risk arising from less than perfectly correlated movements between 
government and other interest rates, such as specifying a completely 
separate yield curve for non-government instruments (for example, 
swaps or municipal securities) or estimating the spread over 
government rates at various points along the yield curve.
---------------------------------------------------------------------------

    3. Exchange rates. A banking organization must use market risk 
factors corresponding to the exchange rate between the domestic 
currency and each foreign currency in which the banking organization 
has a significant exposure. The risk measurement system must 
incorporate market risk factors corresponding to the individual 
foreign currencies in which the banking organization's positions are 
denominated.
    4. Equity prices. A banking organization must use risk factors 
corresponding to each of the equity markets in which it holds 
significant positions. The sophistication and nature of the modeling 
technique for a given market must correspond to the banking 
organization's exposure to the overall market as well as to the 
banking organization's concentration in individual equity issues in 
that market. At a minimum, there must be a risk factor designed to 
capture market-wide movements in equity prices (such as a market 
index), but additional risk factors could track various sectors or 
individual issues.
    5. Commodity prices. A banking organization must use market risk 
factors corresponding to each of the commodity markets in which it 
holds significant positions. The internal model must encompass 
directional risk, forward gap and interest rate risk, and basis 
risk.\18\ The model should also take into account the market 
characteristics, for example, delivery dates and the scope provided 
to traders to close out positions.

    \18\ Directional risk is the risk that a spot price will 
increase or decrease. Forward gap risk refers to the effects of 
owning a physical commodity versus owning a forward position in a 
commodity. Interest rate risk is the risk of a change in the cost of 
carrying forward positions and options. Basis risk is the risk that 
the relationship between the prices of similar commodities changes 
over time.
---------------------------------------------------------------------------

D. Quantitative Standards

    1. A banking organization may use one of a number of generally 
accepted measurement techniques including, for example, an internal 
model based on variance-covariance matrices, historical simulations, 
or Monte Carlo simulations so long as the model employed captures 
all the material market risks.\19\ The following minimum standards 
apply for purposes of using an internal model for calculating market 
risk capital requirements:

    \19\ In a variance/covariance approach, the change in value of 
the portfolio is calculated by combining the risk factor 
sensitivities of the individual positions--derived from valuation 
models--with a variance/covariance matrix based on risk factor 
volatilities and correlations. A banking organization using this 
approach would calculate the volatilities and correlations of the 
risk factors on the basis of the holding period and the observation 
period. A banking organization using a historical simulation would 
calculate the hypothetical change in value of the current portfolio 
in the light of historical movements in risk factors. This 
calculation would be done for each of the defined holding periods 
over a given historical measurement horizon to arrive at a range of 
simulated profits and losses. A banking organization using a Monte 
Carlo technique would consider historical movements to determine the 
probability of particular price and rate changes.
    a. Value-at-risk must be calculated on a daily basis using a 
99th percentile, one-tailed confidence interval 20 and the 
holding period must be ten trading days. For positions that display 
linear price characteristics, a banking organization may use value-
at-risk numbers calculated according to shorter holding periods 
scaled up to ten days by the square root of time.21

    \20\ A one-tailed confidence interval of 99 percent means that 
there is a 1 percent probability based on historical experience that 
the combination of positions in a banking organization's portfolio 
would result in a loss higher than the measured value-at-risk.
    \21\ This transformation entails multiplying a banking 
organization's value-at-risk by the square root of the ratio of the 
required holding period (ten days) to the holding period embodied in 
the value-at-risk figure. For example, the value-at-risk calculated 
according to a one-day holding period would be scaled-up by the 
``square root of time'' by multiplying the value-at-risk by 3.16 
(the square root of the ratio of a ten-day holding period to a one-
day holding period).
---------------------------------------------------------------------------

    b. Value-at-risk must be calculated using an observation period 
of at least one year to measure historical changes in rates and 
prices.
    c. A banking organization must update its historical rates and 
prices at least once every three months and must reassess them 
whenever market conditions change materially.
    2. A banking organization may use discretion in recognizing 
empirical correlations within each market risk factor 
category.22 However, empirical correlations among risk 
categories are not recognized. The value-at-risk measure for each 
risk category must be added together on a simple sum basis to 
determine the aggregate value-at-risk amount.

    \22\ While a banking organization has flexibility to use 
correlations, the Federal Reserve must be satisfied that there is 
integrity in the banking organization's process for calculating 
correlations.
---------------------------------------------------------------------------

    3. A banking organization's models must accurately capture the 
unique risks associated with options within each of the market risk 
factor categories. The following minimum criteria apply to the 
measurement of options risk:
    a. A banking organization's internal model must capture the non-
linear price characteristics of option positions using an options 
pricing technique. The banking organization must apply a minimum 
ten-day holding period to option positions or positions that display 
option-like characteristics. Banking organizations may not scale-up 
the daily value-at-risk numbers by the square root of time.
    b. A banking organization's internal model must capture the 
volatilities of the rates and prices (that is, the vega) underlying 
option positions and a banking organization should measure the 
volatilities of the underlying instruments broken down by different 
option maturities.
    4. The accuracy of a banking organization's internal model will 
be reviewed periodically by the Federal Reserve. Such review, during 
which, when appropriate, the Federal Reserve may take into 
consideration reports and opinions generated by external auditors or 
qualified consultants, will include, at a minimum:
    a. Verification that the internal validation processes described 
in section III.B.2. of this appendix E are operating in a 
satisfactory manner;
    b. Affirmation that the formulae used in the calculation process 
and for the pricing of options and other complex instruments, are 
validated by a qualified unit of the banking organization, which in 
all cases must be independent from the trading areas;
    c. Confirmation that the structure of the internal model is 
adequate with respect to the banking organization's activities and 
geographical coverage;
    d. Confirmation that the results of the banking organization's 
back-testing of its internal measurement system (that is, comparing 
value-at-risk estimates with actual profits and losses) are being 
used effectively to monitor reliability of the model's estimates 
over time; and
    e. Affirmation that, for regulatory capital purposes, the model 
processes all relevant data and that the modeling procedures conform 
with the parameters and specifications set forth in this appendix E.

IV. The Standardized Approach

A. Debt Instruments

    1. Specific Risk. a. The capital requirement for specific risk 
is based on the identity of the obligor and, in the case of 
corporate securities, on the credit rating and maturity of the 
instrument. The specific risk capital requirement is calculated by 
weighting the current market value of each individual position, 
whether long or short, by the appropriate category factor as set 
forth below and summing the weighted values. In measuring specific 
risk, the banking organization may offset and exclude from its 
calculations any matched positions in the identical issue (including 
positions in derivatives). Even if the issuer is the same, no 
offsetting is permitted between different issues since differences 
in coupon rates, liquidity, call features, etc., mean that prices 
may diverge in the short run. The categories and factors are:

------------------------------------------------------------------------
                                                                 Factor 
           Category                   Remaining maturity           [In  
                                         [contractual]          percent]
------------------------------------------------------------------------
Government....................  N/A...........................      0.00
Qualifying....................  6 months or less..............     0.25 

[[Page 38121]]
                                                                        
                                6 to 12 months................      1.00
                                over 12 months................      1.60
Other.........................  N/A...........................      8.00
------------------------------------------------------------------------


    b. The government category includes all forms of debt 
instruments of central governments of the OECD-based group of 
countries 23 including bonds, Treasury bills and other short-
term instruments, as well as local currency instruments of non-OECD 
central governments to the extent that the subsidiary depository 
institutions have liabilities booked in that currency.

    \23\ The OECD-based group of countries is defined in section 
III.B.1 of appendix A of this part.
---------------------------------------------------------------------------

    c. The qualifying category includes securities of U.S. 
government-sponsored agencies, general obligation securities issued 
by states and other political subdivisions of the OECD-based group 
of countries, multilateral development banks, and debt instruments 
issued by U.S. depository institutions or OECD-banks that do not 
qualify as capital of the issuing institution.24 It also 
includes other securities, including revenue securities issued by 
states and other political subdivisions of the OECD-based group of 
countries, that are rated investment-grade by at least two 
nationally recognized credit rating services, or rated investment-
grade by one nationally recognized credit rating agency and not less 
than investment-grade by any other credit rating agency, or, with 
the exception of securities issued by U.S. firms and subject to 
review by the Federal Reserve, unrated but deemed to be of 
comparable investment quality by the reporting banking organization 
and the issuer has securities listed on a recognized stock exchange.

    \24\ U.S. government-sponsored agencies, multilateral 
development banks, and OECD banks are defined in section III.C.2. of 
appendix A of this part.
---------------------------------------------------------------------------

    d. The other category includes debt securities not qualifying as 
government or qualifying securities. This would include non-OECD 
central government securities that do not meet the criteria for the 
government or qualifying categories. This category also includes 
instruments that qualify as capital issued by other banking 
organizations.
    e. The Federal Reserve will consider the extent of a banking 
organization's position in non-investment grade instruments 
(sometimes referred to as high yield debt). If those holdings are 
not well-diversified or otherwise represent a material position to 
the institution, the Federal Reserve may prevent a banking 
organization from offsetting positions in these instruments with 
other positions in qualifying instruments that may be offset when 
calculating its general market risk requirement. In addition, the 
Board may impose a specific risk capital requirement as high as 16.0 
percent.
    2. General Market Risk. a. A banking organization may measure 
its exposure to general market risk using, on a continuous basis, 
either the maturity method (which uses standardized risk weights 
that approximate the price sensitivity of various instruments) or 
the duration method (where the institution calculates the precise 
duration of each instrument, weighted by a specified change in 
interest rates).
    b. Both methods use a maturity-ladder that incorporates a series 
of ``time-bands'' and ``zones'' to group together securities of 
similar maturities and that are designed to take into account 
differences in price sensitivities and interest rate volatilities 
across different maturities. Under either method, the capital 
requirement for general market risk is the sum of a base charge that 
results from fully netting various risk-weighted positions and a 
series of additional charges (add-ons), which effectively 
``disallow'' part of the previous full netting to address basis and 
yield curve risk.
    c. For each currency in which a banking organization has 
significant positions, a separate capital requirement must be 
calculated. No netting of positions is permitted across different 
currencies. Offsetting positions of the same amount in the same 
issues, whether actual or notional, may be excluded from the 
calculation, as well as closely matched swaps, forwards, futures, 
and forward rate agreements (FRAs) that meet the conditions set out 
in section IV.A.3. of this appendix E.
    d. In the maturity method, the banking organization distributes 
each long or short position (at current market value) of a debt 
instrument into the time bands of the maturity ladder. Fixed-rate 
instruments are allocated according to the remaining term to 
maturity and floating-rate instruments according to the next 
repricing date. A callable bond trading above par is slotted 
according to its first call date, while a callable bond priced below 
par is slotted according to remaining maturity. Fixed-rate mortgage-
backed securities, including collateralized mortgage obligations 
(CMOs) and real estate mortgage investment conduits (REMICs), are 
slotted according to their expected weighted average lives.
    e. Once all long and short positions are slotted into the 
appropriate time band, the long positions in each time-band are 
summed and the short positions in each time-band are summed. The 
summed long and/or short positions are multiplied by the appropriate 
risk-weight factor (reflecting the price sensitivity of the 
positions to changes in interest rates) to determine the risk-
weighted long and/or short position for each time-band. The risk 
weights for each time-band are set out in Table I below:

            Table I.--Maturity Method: Time-Bands and Weights           
------------------------------------------------------------------------
                                                                 Risk   
  Zone        Coupon 3% or more     Coupon less than 3% and    weights  
                                       zero coupon bonds      [percent] 
------------------------------------------------------------------------
1.......  Up to 1 month...........  Up to 1 month..........         0.00
          1 up to 3 months........  1 up to 3 months.......         0.20
          3 up to 6 months........  3 up to 6 months.......         0.40
          6 up to 12 months.......  6 up to 12 months......         0.70
2.......  1 up to 2 years.........  1 up to 1.9 years......         1.25
          2 up to 3 years.........  1.9 up to 2.8 years....         1.75
          3 up to 4 years.........  2.8 up to 3.6 years....         2.25
3.......  4 up to 5 years.........  3.6 up to 4.3 years....         2.75
          5 up to 7 years.........  4.3 up to 5.7 years....         3.25
          7 up to 10 years........  5.7 up to 7.3 years....         3.75
          10 up to 15 years.......  7.3 up to 9.3 years....         4.50
          15 up to 20 years.......  9.3 up to 10.6 years...         5.25
          Over 20 years...........  10.6 up to 12 years....         6.00
                                    12 up to 20 years......         8.00
                                    Over 20 years..........        12.50
------------------------------------------------------------------------

    f. Within each time-band for which there are risk-weighted long 
and short positions, the risk-weighted long and short positions are 
then netted, resulting in a single net risk-weighted long or short 
position for each time-band. Since different instruments and 
different maturities may be included and netted within each time, a 
capital requirement, referred to as the vertical 

[[Page 38122]]
disallowance, is assessed to allow for basis risk. The vertical 
disallowance capital requirement is 10.0 percent of the position 
eliminated by the intra-time-band netting, that is, 10.0 percent of 
the smaller of the net risk-weighted long or net risk-weighted short 
position, or if the positions are equal, 10.0 percent of either 
position.\25\ The vertical disallowances for each time-band are 
absolute values, that is, neither long nor short. The vertical 
disallowances for all time-bands in the maturity ladder are summed 
and included as an element of the general market risk capital 
requirement.

    \25\ For example, if the sum of the weighted longs in a time-
band is $100 million and the sum of the weighted shorts is $90 
million, the vertical disallowance for the time-band is 10.0 percent 
of $90 million, or $9 million.
---------------------------------------------------------------------------

    g. Within each zone for which there are risk-weighted long and 
short positions in different time-bands, the weighted long and short 
positions in all of the time-bands within the zone are then netted, 
resulting in a single net long or short position for each zone. 
Since different instruments and different maturities may be included 
and netted within each zone, a capital requirement, referred to as 
the horizontal disallowance, is assessed to allow for the imperfect 
correlation of interest rates along the yield curve. The horizontal 
disallowance capital requirement is calculated as a percentage of 
the position eliminated by the intra-zone netting, that is, a 
percentage of the smaller of the net risk-weighted long or net risk-
weighted short position, or if the positions are equal, a percentage 
of either position.\26\ The percent disallowance factors for intra-
zone netting are set out in Table II in section IV.A.2.h. of this 
appendix E. The horizontal disallowances, like the vertical 
disallowances, are absolute values that are summed and included as 
an element of the general market risk capital requirement.

    \26\ For example, if the sum of the weighted longs in the 1-3 
month time-band in Zone 1 is $8 million and the sum of the weighted 
shorts in the 3-6 month time-band is $10 million, the horizontal 
disallowance for the zone is forty percent of $8 million, or $3.2 
million.
---------------------------------------------------------------------------

    h. Risk-weighted long and short positions in different zones are 
then netted between the zones. Zone 1 and zone 2 are netted if 
possible, reducing or eliminating the net long or short position in 
zone 1 or zone 2 as appropriate. Zone 2 and zone 3 are then netted 
if possible, reducing or eliminating the net long or short position 
in zone 2 or zone 3 as appropriate. Zone 3 and zone 1 are then 
netted if possible, reducing or eliminating the long or short 
position in zone 3 and zone 1 as appropriate. A horizontal 
disallowance capital requirement is then assessed, calculated as a 
percentage of the position eliminated by the inter-zone netting. The 
horizontal disallowance capital requirements for each zone are then 
summed as absolute values and included in the general market risk 
capital charge. The percent disallowance factors for inter-zone 
netting are set out in Table II below:

                                       Table II.--Horizontal Disallowances                                      
----------------------------------------------------------------------------------------------------------------
                                                                                                Between zones 1-
 Zone            Time-band                  Within the zone           Between adjacent zones            3       
----------------------------------------------------------------------------------------------------------------
1....  0-1 month...................  40 percent..................  40 percent.................  100 percent.    
       1-3 months.                                                                                              
       3-6 months.                                                                                              
       6-12 months.                                                                                             
2....  1-2 years...................  30 percent..................  40 percent.................  100 percent     
       2-3 years.                                                                                               
       3-4 years.                                                                                               
3....  1-5 years.                    30 percent..................  40 percent.................  100 percent     
       5-7 years.                                                                                               
       7-10 years.                                                                                              
       10-15 years.                                                                                             
       15-20 years.                                                                                             
       Over 20 years.                                                                                           
----------------------------------------------------------------------------------------------------------------

    i. Finally, the net risk-weighted long or net risk-weighted 
short positions remaining in the zones are summed to reach a single 
net risk-weighted long or net risk-weighted short position for the 
banking organization's portfolio. The sum of the absolute value of 
this position and the vertical and horizontal disallowances is the 
capital requirement for general market risk. An example of the 
calculation of general market risk under the maturity method is in 
Attachment II to this appendix E.
    j. In the duration method, the banking organization, after 
calculating each instrument's modified duration\27\ using a formula 
that is subject to supervisory review, multiplies that modified 
duration by the interest rate shock specified for an instrument of 
that duration in Table III in section IV.A.2.k. of this appendix E. 
The resulting product (representing the expected percentage change 
in the price of the instrument for the given interest rate shock) is 
then multiplied by the current market value of the instrument. The 
resulting amount is then slotted as a long or short position into a 
time-band in the maturity ladder in Table III on the basis of the 
instrument's modified duration.\28\

    \27\ The duration of an instrument is its approximate percentage 
change in price for a 100 basis point parallel shift in the yield 
curve assuming that its cash flow does not change when the yield 
curve shifts. Modified duration is duration divided by a factor of 1 
plus the interest rate.
    \28\ For example, an instrument held by a banking organization 
with a maturity of 4 years and 3 months and a current market value 
of $1,000 might have a modified duration of 3.5 years. Based on its 
modified duration, it would be subjected to the 75-basis point 
interest rate shock, resulting in an expected price change of 2.625 
percent (3.5 x 0.75). the corresponding expected change in price of 
$26.25, calculated as 2.625 percent of $1,000, would be slotted as a 
long position in the 3.3 to 4.0 year time-band of the maturity 
ladder.
---------------------------------------------------------------------------

    k. Once all of the banking organization's traded debt 
instruments have been slotted into the maturity ladder, the banking 
organization conducts the same rounds of netting and disallowances 
described in sections IV.A.2.f. through IV.A.2.h. of this appendix E 
for the maturity method, with the exception that the vertical 
disallowance requirement for the duration method is 5.0 percent 
(horizontal disallowances continue to be those set out in Table 
II).\29\ As with the maturity method, the sum of the absolute value 
of the final net position and the vertical and horizontal 
disallowances is the general market risk capital requirement:

    \29\ Two different vertical disallowances are used since the 
duration method takes into account an instrument's specific 
characteristics (maturity and coupon) and there is less opportunity 
for measurement error.

   Table III--Duration Method: Time-Bands and Assumed Changes in Yield  
------------------------------------------------------------------------
                                                               Assumed  
  Zone                        Time-band                       change in 
                                                                yield   
------------------------------------------------------------------------
1.......  Up to 1 month....................................         1.00
          1 up to 3 months.................................         1.00
          3 up to 6 months.................................         1.00
          6 up to 12 months................................         1.00
2.......  1.0 up to 1.8 years..............................         0.90
          1.8 up to 2.6 years..............................         0.80
          2.6 up to 3.3 years..............................         0.75
3.......  3.3 up to 4.0 years..............................         0.75
          4.0 up to 5.2 years..............................         0.70
          5.2 up to 6.8 years..............................         0.65
          6.8 up to 8.6 years..............................         0.60
          8.6 up to 9.9 years..............................         0.60
          9.9 up to 11.3 yrs...............................         0.60

[[Page 38123]]
                                                                        
          11.3 up to 16.6 yrs..............................         0.60
          Over 16.6 years..................................         0.60
------------------------------------------------------------------------


    3. Interest rate derivatives. a. Debt derivatives and other off-
balance-sheet positions that are affected by changes in interest 
rates are included in the measurement system under section IV.A. of 
this appendix E (except for options and the associated underlyings, 
which are included in the measurement system under the treatment 
discussed in section IV.E. of this appendix E). A summary of the 
treatment for debt derivatives is set out in Attachment III to this 
appendix E.
    b. Derivatives are converted into positions in the relevant 
underlying instrument and are included in the calculation of 
specific and general market risk capital charges as described above. 
The amount to be included is the market value of the principal 
amount of the underlying or of the notional underlying. For 
instruments where the apparent notional amount differs from the 
effective notional amount, a banking organization must use the 
effective notional amount.
    c. Futures and forward contracts (including FRAs) are broken 
down into a combination of a long position and short position in the 
notional security. The maturity of a future or a FRA is the period 
until delivery or exercise of the contract, plus the life of the 
underlying instrument.30 Where a range of instruments may be 
delivered to fulfill the contract, the banking organization may 
chose which deliverable instrument goes into the maturity or 
duration ladder as the notional underlying. In the case of a future 
on a corporate bond index, positions are included at the market 
value of the notional underlying portfolio of securities.

    \30\ For example, a long position in a June three-month interest 
rate future (taken in April) is reported as a long position in a 
government security with a maturity of five months and a short 
position in a government security with a maturity of two months.
---------------------------------------------------------------------------

    d. Swaps are treated as two notional positions in the relevant 
instruments with appropriate maturities. The receiving side is 
treated as the long position and the paying side is treated as the 
short position.31 The separate sides of cross-currency swaps or 
forward foreign exchange transactions are slotted in the relevant 
maturity ladders for the currencies concerned. For swaps that pay or 
receive a fixed or floating interest rate against some other 
reference price, for example, an equity index, the interest rate 
component is slotted into the appropriate repricing maturity 
category, with the long or short position attributable to the equity 
component being included in the equity framework set out in section 
IV.B. of this appendix E.32

    \31\ For example, an interest rate swap under which a banking 
organization is receiving floating-rate interest and paying fixed is 
treated as a long position in a floating rate instrument with a 
maturity equivalent to the period until the next interest reset date 
and a short position in a fixed-rate instrument with a maturity 
equivalent to the remaining life of the swap.
    \32\ A banking organization with a large swap book may, with 
prior approval of the Federal Reserve, use alternative formulae to 
calculate the positions to be included in the maturity or duration 
ladder. For example, a banking organization could first convert the 
payments required by the swap into present values. For that purpose, 
each payment would be discounted using zero coupon yields, and the 
payment's present value entered into the appropriate time-band using 
procedures that apply to zero (or low) coupon bonds. The net amounts 
would then be treated as bonds, and slotted into the general market 
risk framework. Such alternative treatments will, however, only be 
allowed if: (i) the Federal Reserve is fully satisfied with the 
accuracy of the system being used, (ii) the positions calculated 
fully reflect the sensitivity of the cash flows to interest rate 
changes; and (iii) the positions are denominated in the same 
currency.
---------------------------------------------------------------------------

    e. A banking organization may offset long and short positions 
(both actual and notional) in identical derivative instruments with 
exactly the same issuer, coupon, currency, and maturity before 
slotting these positions into time-bands. A matched position in a 
future and its corresponding underlying may also be fully offset 
and, thus, excluded from the calculation, except when the future 
comprises a range of deliverable instruments. However, in cases 
where, among the range of deliverable instruments, there is a 
readily identifiable underlying instrument that is most profitable 
for the trader with a short position to deliver, positions in the 
futures contract and the instrument may be offset. No offsetting is 
allowed between positions in different currencies.
    f. Offsetting positions in the same category of instruments can 
in certain circumstances be regarded as matched and treated by the 
banking organization as a single net position which should be 
entered into the appropriate time-band. To qualify for this 
treatment the positions must be based on the same underlying 
instrument, be of the same nominal value, and be denominated in the 
same currency. The separate sides of different swaps may also be 
``matched'' subject to the same conditions. In addition:
    i. For futures, offsetting positions in the notional or 
underlying instruments to which the futures contract relates must be 
for identical instruments and the instruments must mature within 
seven days of each other;
    ii. For swaps and FRAs, the reference rate (for floating rate 
positions) must be identical and the coupon closely matched (i.e., 
within 15 basis points); and
    iii. For swaps, FRAs and forwards, the next interest reset date, 
or for fixed coupon positions or forwards the remaining maturity, 
must correspond within the following limits: If the reset (remaining 
maturity) dates occur within one month, then the reset dates must be 
on the same day; if the reset dates occur between one month and one 
year later, then the reset dates must occur within seven days of 
each other, or if the reset dates occur over one year later, then 
the reset dates must occur within thirty days of each other.
    g. Interest rate and currency swaps, FRAs, forward foreign 
exchange contracts and interest rate futures are not subject to a 
specific risk charge. This exemption also applies to futures on a 
short-term (e.g., LIBOR) interest rate index. However, in the case 
of futures contracts where the underlying is a debt security, or an 
index representing a basket of debt securities, a specific risk 
charge will apply according to the category of the issuer as set out 
in section IV.A.2. of this appendix E.

B. Equities

    1. Specific risk. The measure of specific risk is calculated on 
the basis of the banking organization's gross equity positions, that 
is, the absolute sum of all long equity positions and of all short 
equity positions at current market value.33 The specific risk 
capital requirement is 8.0 percent of that sum, unless the portfolio 
is both liquid and well-diversified, in which case the specific risk 
capital requirement is 4.0 percent of the gross equity position. A 
specific risk charge of 2.0 percent applies to the net long or short 
position in a broad, diversified equity index and is viewed as 
necessary to provide for risks associated with contract 
execution.34

    \33\ Matched positions in each identical equity in each national 
market may be treated as offsetting and excluded from the capital 
calculation, with any remaining position included in the 
calculations for specific and general market risk. For example, a 
future in a given equity may be offset against an opposite cash 
position in the same equity.
    \34\ A portfolio that is liquid and well-diversified is 
characterized by a limited sensitivity to price changes of any 
single equity issue or closely related group of equity issues held 
in the portfolio. The volatility of the portfolio's value should not 
be dominated by the volatility of any individual equity issue or by 
equity issues from any single industry or economic sector. In 
general, such portfolios should be characterized by a large number 
of individual equity positions, with no single position representing 
a large portion of the portfolio's total market value. In addition, 
it would generally be the case that a sizable proportion of the 
portfolio would be comprised of issues traded on organized exchanges 
or in well-established over-the-counter markets.
    2. General Market risk. The measure of general market risk is 
based on the difference between the sum of the long positions and 
the sum of the short positions (i.e., the overall net position in an 
equity market) at current market value. An overall net position must 
be separately calculated for each national market in which the 
banking organization holds equities. The capital requirement for 
general market risk is 8.0 percent of the net position in each 
equity market.
    3. Equity derivatives. a. Equity derivatives and other off-
balance-sheet positions that are affected by changes in equity 
prices are included in the measurement system under section IV.B. of 
this appendix E (except for equity options, equity index options, 
and the associated underlying, which are included in the measurement 
system under the treatment discussed in section IV.E. of this 
appendix E).35 This includes futures and swaps on both 

[[Page 38124]]
individual equities and on equity indices. Equity derivatives should be 
converted into notional equity positions in the relevant underlying. 
A summary of the rules for equity derivatives is set out in 
Attachment III to this appendix E.

    \35\ Where equities are part of a forward contract (both 
equities to be received or to be delivered), any interest rate or 
foreign currency exposure from the other side of the contract should 
be appropriately included in the measurement system in sections 
IV.A. and IV.C. of this appendix E.
---------------------------------------------------------------------------

    b. Futures and forward contracts relating to individual equities 
should be reported at current market prices of the underlying. 
Futures relating to equity indices should be reported as the marked-
to-market value of the notional underlying equity portfolio. Equity 
swaps are treated as two notional positions, with the receiving side 
as the long position and the paying side as the short 
position.36 If one of the legs involves receiving/paying a 
fixed or floating interest rate, the exposure should be slotted into 
the appropriate repricing maturity band for debt securities. The 
stock index is covered by the equity treatment.

    \36\ For example, an equity swap in which a banking organization 
is receiving an amount based on the change in value of one 
particular equity or equity index and paying a different index will 
be treated as a long position in the former and a short position in 
the latter.
---------------------------------------------------------------------------

    c. In the case of futures-related arbitrage strategies, the 2.0 
percent specific risk charge applicable to broad diversified equity 
indices may be applied to only one index. The opposite position is 
exempt from a specific risk charge. The strategies qualifying for 
this treatment are:
    i. When the banking organization takes an opposite position in 
exactly the same index at different dates; and
    ii. When the banking organization has an opposite position in 
different but similar indices at the same date, subject to 
supervisory oversight.
    d. If a banking organization engages in a deliberate arbitrage 
strategy, in which a futures contract on a broad diversified equity 
index matches a basket of securities, it may exclude both positions 
from the standardized approach on condition that the trade has been 
deliberately entered into and separately controlled and the 
composition of the basket of stocks represents at least 90 percent 
of the market value of the index. In such a case, the minimum 
capital requirement is 4.0 percent (that is, 2.0 percent of the 
gross value of the positions on each side) to reflect risk 
associated with executing the transaction. This applies even if all 
of the securities comprising the index are held in identical 
proportions. Any excess value of the securities comprising the 
basket over the value of the futures contract or excess value of the 
futures contract over the value of the basket is treated as an open 
long or short position.
    e. If a banking organization takes a position in depository 
receipts 37 against an opposite position in the underlying 
equity, it may offset the position.

    \37\ Depository receipts are instruments issued by a trust 
company or other depository institution evidencing the deposit of 
foreign securities and facilitating trading in such instruments on 
U.S. stock exchanges.
---------------------------------------------------------------------------

C. Foreign Exchange Risk

    1. The capital requirement for foreign exchange risk covers the 
risk of holding or taking positions in foreign currencies, including 
gold, and is based on a banking organization's net open long 
positions or net open short positions in each currency, whether or 
not those positions are in the trading portfolio, plus the net open 
position in gold, regardless of sign.38

    \38\ Gold is treated as a foreign exchange position rather than 
a commodity because its volatility is more in line with foreign 
currencies and banking organizations manage it in a manner similar 
to foreign currencies.
    2. A banking organization's net open position in each currency 
(and gold) is calculated by summing:
    a. The net spot position (i.e., all asset items less all 
liability items, including accrued interest earned but not yet 
received and accrued expenses, denominated in the currency in 
question);
    b. All foreign exchange derivative instruments and other off-
balance-sheet positions that are affected by changes in exchange 
rates are included in the measurement system under section IV.C. of 
this appendix E (except for options and their associated 
underlyings, which are included in the measurement system under the 
treatment discussed in section IV.E. of this appendix E). Forward 
currency positions should be valued at current spot market exchange 
rates. For a banking organization in which the basis of its normal 
management accounting is to use net present values, forward 
positions may be discounted to net present values as an acceptable 
way of measuring currency positions for regulatory capital purposes;
    c. Guarantees (and similar instruments) that are certain to be 
called and are likely to be irrevocable;
    d. Net future income/expenses not yet accrued but already fully 
hedged (at the discretion of the banking organization). A banking 
organization that includes future income and expenses must do so on 
a consistent basis without selecting expected future flows in order 
to reduce the banking organization's position; and
    e. Any other item representing a profit or loss in foreign 
currencies.
    3. For measuring a banking organization's open positions, 
positions in composite currencies, such as the ECU, may be either 
treated as a currency in their own right or split into their 
component parts on a consistent basis. Positions in gold are 
measured in the same manner as described in section IV.D. of this 
appendix E.39

    \39\ Where gold is part of a forward contract (quantity of gold 
to be received or to be delivered), any interest rate or foreign 
currency exposure from the other side of the contract should be 
included in the measurement system in section IV.A. (as a zero 
coupon instrument) and IV.C. of this appendix E.
---------------------------------------------------------------------------

    4. The capital requirement is determined by converting the 
nominal amount (or net present value) of the net open position in 
each foreign currency (and gold) at spot rates into the reporting 
currency. The capital requirement is 8.0 percent of the sum of:
    a. The greater of the sum of the net short open positions or, 
the sum of the net long open positions; and
    b. The net open position in gold, regardless of sign.40

    \40\ For examples, a banking organizations has the following net 
currency positions: Yen=+50, DM=+100, GB=+150, FFR=-20, US$=-180, 
and gold=-35. The banking organization would sum its long positions 
(total=+300) and sum its short positions (total=-200). The banking 
organization's capital requirement for foreign exchange market risk 
would be: (300 (the larger of the summed long and short positions) + 
35 (gold)) x 8.0%=26.80.
---------------------------------------------------------------------------

    5. Where a banking organization is assessing its foreign 
exchange risk on a consolidated basis, it may be technically 
impractical in the case of some marginal operations to include the 
currency positions of a foreign branch or subsidiary of the banking 
organization. In such cases, the internal limit in each currency may 
be used as a proxy for the positions, provided there is adequate ex 
post monitoring of actual positions complying with such limits. In 
these circumstances, the limits should be added, regardless of sign, 
to the net open position in each currency.

D. Commodities Risk.

    1. Measurement methods. This section provides a minimum capital 
requirement to cover the risk of holding or taking positions in 
commodities. There are two methods under the standardized approach 
for measuring commodity market risk--the simplified method and the 
maturity method. These methods are only appropriate for banking 
organizations that conduct a limited amount of commodities business. 
All other banking organizations must adopt an internal measurement 
system conforming to the criteria in section III. of this appendix 
E.
    2. Base capital requirement. Under both the simplified and 
maturity methods, each long and short commodity position (spot and 
forward) is expressed in terms of the standard unit of measurement 
(such as barrels, kilos, or grams). The open positions in each 
category of commodities are then converted at current spot rates 
into U.S. currency, with long and short positions offset to arrive 
at the net open position in each commodity. Positions in different 
categories of commodities may not, generally, be offset.41 
Under either method, the base capital requirement is 15.0 percent of 
the net open position, long or short, in each commodity.42

    \41\ However, offsetting is permitted between different sub-
categories of the same commodity in cases where the sub-categories 
are deliverable against each other.
    \42\ When the funding of a commodity position opens a banking 
organization to interest rate or foreign exchange exposure the 
relevant positions should be included in the measures of interest 
rate and foreign exchange risk described in section IV.A. and IV.C 
of this appendix E. When a commodity is part of a forward contract, 
any interest or foreign currency exposure from the other side of the 
contract should be appropriately included in the measurement systems 
in sections IV.A. and IV.C. of this appendix E.
---------------------------------------------------------------------------

    3. Simplified method. To protect a banking organization against 
basis risk, interest rate risk, and forward gap risk, each category 
of commodity is also subject to a 3.0 percent capital requirement on 
the banking organization's gross positions, long plus short, in the 
particular commodity. In 

[[Page 38125]]
valuing gross positions in commodity derivatives for this purpose, a 
banking organization should use the current spot price. The total 
capital requirement for commodities risk is the sum of the 15.0 
percent base charges for each net commodity position and the 3.0 
percent requirements on the gross commodity positions.
    4. Maturity method. a. Under this method, a banking organization 
must slot each long and short commodity position (converted into 
U.S. currency at current spot rates) into a maturity ladder. The 
time-bands for the maturity ladder are; from zero to one month, one 
up to three months, three up to six months, six up to twelve months, 
one up to two years, two up to three years, and over three years. A 
separate maturity ladder is used for each category of commodity. 
Physical commodities are allocated to the first time-band.
    b. In order to capture forward gap and interest rate risk within 
a time-band (together sometimes referred to as curvature/spread 
risk), offsetting long and short positions in each time-band are 
subject to an additional capital requirement. Beginning with the 
shortest-term time-band and continuing with subsequent time-bands, 
the amount of the matched short positions plus the amount of the 
matched long position is multiplied by a spread rate of 1.5 percent.
    c. The unmatched net position from shorter-term time-bands must 
be carried forward to offset exposures in longer-term time-bands. A 
capital requirement of 0.6 percent of the net position carried 
forward is added for each time-band that the net position is carried 
forward.43 The total capital requirement for commodities risk 
is the sum of the 15.0 percent base capital requirement for each net 
commodity position and the additional requirements for matched 
positions and for unmatched positions carried forward. An example of 
this calculation is in Attachment IV to this appendix E.

    \43\ For example, if $200 short is carried forward from the 3-6 
month time-band to the 1-2 year time-band, the capital charge would 
be $200  x  .006  x  2 = $2.40.
---------------------------------------------------------------------------

    5. Commodity derivatives. Commodity derivatives and other off-
balance-sheet positions that are affected by changes in commodity 
prices are included in the measurement system under section IV.D. of 
this appendix E (except for options and the associated underlying, 
which are included in the measurement system under the treatment 
discussed in section IV.E. of this appendix E). Commodity 
derivatives are converted into notional commodity positions. Under 
the maturity method, the positions are slotted into maturity time-
bands as follows:
    a. Futures and forward contracts relating to individual 
commodities are incorporated in the measurement system as notional 
amounts (of, for example, barrels or kilos) that are converted to 
U.S. dollars at current spot rates and are assigned a maturity 
according to expiration date;
    b. Commodity swaps where one side of the contract is a fixed 
price and the other side is the current market price are 
incorporated as a series of positions equal to the notional amount 
of the contract at current spot rates, with one position 
corresponding to each payment on the swap and slotted in the 
maturity ladder accordingly. The positions are long positions if the 
banking organization is paying a fixed price and receiving a 
floating price, and short positions if the banking organization is 
receiving a fixed price and paying a floating price; 44 and

    \44\ If one of the sides of the transaction involves receiving/
paying a fixed or floating interest rate, that exposure should be 
slotted into the appropriate repricing maturity band in section 
IV.A. of this appendix E.
---------------------------------------------------------------------------

    c. Commodity swaps where the sides of the transaction are in 
different commodities are included in the relevant reporting ladder. 
No offsetting is allowed unless the commodities are in the same sub-
category.

E. Options

    1. Three alternatives are available for a banking organization 
to use in measuring its market risk for options activities. A 
banking organization that only has purchased options may use the 
simplified method set forth in section IV.E.2. of this appendix E. A 
banking organization that also writes options may use the scenario 
method described in section IV.E.3. of this appendix E or the delta-
plus method set forth in section IV.E.4. of this appendix E.45 
These methods may only be used by banking organizations which, in 
relative terms, have limited options activities. Banking 
organizations with more significant options business are expected to 
adopt an internal measurement system conforming to the criteria in 
section III. of this appendix E. Regardless of the method used, 
specific risk related to the issuer of an instrument still applies 
to options positions for equities, equity indices and corporate debt 
securities as set forth in sections IV.A. and IV.B. of this appendix 
E. There remains a separate capital requirement for counterparty 
credit risk as set forth in appendix A to this part.

    \45\ Unless all their written option positions are hedged by 
perfectly matched long positions in exactly the same options, in 
which case there is no capital requirement for market risk.
---------------------------------------------------------------------------

    2. Under the simplified and scenario methods, the positions for 
the options and the associated underlying, cash or forward, are not 
included in the measurement framework for debt securities, equities, 
foreign exchange or commodities risk as set forth in sections IV.A. 
through IV.D. of this appendix E. Rather, they are subject to 
capital requirements as calculated in this section. The capital 
requirements calculated under this section IV.E. should then be 
added to the capital requirements for debt securities, equities, 
foreign exchange and commodities risk as appropriate. Under the 
delta-plus method, the delta equivalent position 46 for each 
option is included in the measurement frameworks set forth in 
sections IV.A. through IV.D. of this appendix E.

    \46\ The delta equivalent of an option is the option's delta 
value multiplied by its principal or notional value. The delta value 
of an option represents the expected change in the option's price as 
a proportion of a small change in the price of the underlying 
instrument. For example, an option whose price changes $1 for every 
$2 dollar change in the price of the underlying instrument has a 
delta of 0.50.
---------------------------------------------------------------------------

    3. A banking organization that has only a limited amount and 
range of purchased options may use the following simplified approach 
to measure its market risk exposure.
    a. For a banking organization with a long cash position and a 
long put or with a short cash position and a long call, the capital 
requirement is the market value of the underlying instrument 
multiplied by the sum of the specific and general market risk 
requirements for the underlying (that is, the specific and general 
market risk requirements that would have applied to the underlying 
directly under sections IV.A. through IV.D. of this appendix 
E.47), less the amount the option is in the money (if any) 
bounded at zero.48

    \47\ Some options (e.g., where the underlying is an interest 
rate, a currency, or a commodity) bear no specific risk but specific 
risk will be present in the case of options on corporate debt 
securities and for options on equities and equity indices.
    \48\ For example, if a holder of 100 shares currently valued at 
$10 each has an equivalent put option with a strike price of $11, 
the capital charge would be: $1,000 x 16.0 percent (e.g., 8.0 
percent specific plus 8.0 percent general market risk) = $160, less 
the amount the option is in the money ($11-$10) x 100 = $100, i.e., 
the capital charge would be $60. A similar methodology applies for 
options whose underlying is a foreign currency, a debt security or a 
commodity.
---------------------------------------------------------------------------

    b. For a banking organization with a long call or a long put, 
the capital charge is the lesser of:
    i. The market value of the underlying security multiplied by the 
sum of specific and general market risk requirements for the 
underlying (that is, the specific and general market risk 
requirements that would have applied to the underlying directly 
under sections IV.A. through IV.D. of this appendix E 49); or

    \49\ See footnote 47 in section IV.E.3.a of this appendix E.
---------------------------------------------------------------------------

    ii. The market value of the option.
    c. Under this measure, the capital requirement for currency 
options is 8.0 percent of the market value of the underlying and for 
commodity options is 15.0 percent of the market value of the 
underlying.
    4. Under the scenario approach, a banking organization revalues 
its options and related hedging positions by changing the underlying 
rate or price over a specified range and by assuming different 
levels of volatility for that rate or price.
    a. For each of its option portfolios, a banking organization 
constructs a grid based on a fixed range of changes in the 
portfolio's risk factors and calculates changes in the value of the 
option portfolio at each point within the grid. For this purpose, an 
option portfolio consists of an option and any related hedging 
positions or multiple options and related hedging positions that are 
grouped together according to their remaining maturity or the type 
of underlying.
    b. Options based on interest rates and debt instruments are 
grouped into portfolios according to the maturity zones that are set 
forth in section IV.A. of this appendix E. (Zone 1 instruments have 
a remaining maturity of up to 1 year, zone 2 instruments 

[[Page 38126]]
have a remaining maturity from 1 year up to 4 years, and zone 3 
instruments have a remaining maturity of 4 years or more.) These 
options and the associated hedging positions should be evaluated 
under the assumption that the relevant interest rates move 
simultaneously. For options based on equities, separate grids are 
constructed for each individual equity issue and index. For options 
based on exchange rates, separate grids are constructed for 
individual exchange rates. For options based on commodities, 
separate grids are constructed for each category of commodity (as 
defined in sections I.B.3. and IV.D. of this appendix E).
    c. For option portfolios with options based on equities, 
exchange rates, and commodities, the first dimension of the grid 
consists of rate or price changes within a specified range above and 
below the current market value of the underlying; for equities, the 
range is  12.0 percent (or in the case of an index 
 8.0 percent), for exchange rates the range is 
 8.0 percent, and for commodities the range is 
 15.0 percent. For option portfolios with options based 
on interest rates, the range for the first dimension of the grid 
depends on the remaining maturity zone. The range for zone 1 is 
 100 basis points, the range for zone 2 is  
90 basis points, and the range for zone 3 is  75 basis 
points. For all option portfolios, the range is divided into at 
least ten equally spaced intervals. The second dimension of each 
grid is a shift in the volatility of the underlying rate or price 
equal to  25.0 percent of the current volatility.50

    \50\ For example, if the underlying in an equity instrument with 
a current market value of $100 and a volatility of 20 percent, the 
first dimension of the grid would range from $88 to $112, divided 
into ten intervals of $2.40 and the second dimension would assume 
volatilities of 15 percent, 20 percent, and 25 percent.
---------------------------------------------------------------------------

    d. For each assumed volatility and rate or price change (a 
scenario), the banking organization revalues each option portfolio. 
The market risk capital requirement for the portfolio is the largest 
loss in value from among the scenario revaluations. The total market 
risk capital requirement for all option portfolios is the sum of the 
individual option portfolio capital requirements.
    e. The Federal Reserve will review the application of the 
scenario approach, particularly regarding the precise way the 
analysis is constructed. A banking organization using the scenario 
approach should meet the appropriate qualitative criteria set forth 
in section III.B. of this appendix E.
    5. Under the delta-plus method, a banking organization that 
writes options may include delta-weighted options positions within 
each measurement framework as set forth in sections IV.A. through 
IV.D. of this appendix E.
    a. Options positions should be measured as a position equal to 
the market value of the underlying instrument multiplied by the 
delta. In addition, a banking organization must measure the 
sensitivities of the option's gamma (the change of the delta for a 
given change in the price of the underlying) and vega (the 
sensitivity of the option price with respect to a change in 
volatility) to calculate the total capital requirement. These 
sensitivities may be calculated according to an exchange model 
approved by the Federal Reserve or to the banking organization's own 
options pricing model, subject to review by the Federal Reserve.
    b. For options with debt instruments or interest rates as the 
underlying instrument, delta-weighted options positions should be 
slotted into the debt instrument time-bands in section IV.A. of this 
appendix E using a two-legged approach (as is used for other 
derivatives), requiring one entry at the time the underlying 
contract takes effect and one at the time the underlying contract 
matures.51 Floating rate instruments with caps or floors should 
be treated as a combination of floating rate securities and a series 
of European-style options.52 A banking organization must also 
calculate the gamma and vega for each such option position 
(including hedge positions). The results should be slotted into 
separate maturity ladders by currency. For options such as caps and 
floors whose underlying instrument is an interest rate, the delta 
and gamma should be expressed in terms of a hypothetical underlying 
security. Subsequently:

    \51\ For example, in April, a purchased call option on a June 
three-month interest-rate future would be considered on the basis of 
its delta-equivalent value to be a long position with a maturity of 
five months and a short position with a maturity of two months. The 
written option would be slotted as a long position with a maturity 
of two months and a short position with a maturity of five months.
    \52\ For example, the holder of a three-year floating rate bond 
indexed to six-month LIBOR with a cap of 15 percent would treat the 
bond as a debt security that reprices in six months, and a series of 
five written call options on a FRA with a strike rate of 15 percent, 
each slotted as a short position at the expiration date of the 
option and as a long position at the time the FRA matures.
    i. For gamma risk, for each time-band, net gammas that are 
negative are multiplied by the risk weights set out in Table IV in 
section IV.E.5.b.iv. of this appendix E and by the square of the 
market value of the underlying instrument (net positive gammas may 
be disregarded);
    ii. For volatility risk, a banking organization calculates the 
capital requirements for vega in each time-band assuming a 
proportional shift in volatility of  25.0 percent;
    iii. The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the sum of the individual capital requirements for 
vega risk for each time-band; and
    iv. The delta plus method risk weights are:

                Table IV.--Delta Plus Method Risk Weights               
------------------------------------------------------------------------
                                     Modified                           
                                     duration     Assumed    Risk-weight
            Time-band                (average     interest       for    
                                   assumed for  rate change    gamma\1\ 
                                    time band)      (%)                 
------------------------------------------------------------------------
Under 1 month....................         0.00         1.00      0.00000
1 up to 3 months.................         0.20         1.00      0.00020
3 up to 6 months.................         0.40         1.00      0.00080
6 up to 12 months................         0.70         1.00      0.00245
1 up to 2 years..................         1.40         0.90      0.00794
2 up to 3 years..................         2.20         0.80      0.01549
3 up to 4 years..................         3.00         0.75      0.02531
4 up to 5 years..................         3.65         0.75      0.03747
5 up to 7 years..................         4.65         0.70      0.05298
7 up to 10 years.................         5.80         0.65      0.07106
10 up to 15 years................         7.50         0.60      0.10125
15 up to 20 years................         8.75         0.60      0.13781
Over 20 years....................        10.00         0.60      0.18000
------------------------------------------------------------------------
\1\ According to the Taylor expansion, the risk weights are calculated  
  as \1/2\ (modified duration  x  assumed interest rate change) \2\ 100.

    c. For options with equities as the underlying, delta-weighted 
option positions should be incorporated in the measure of market 
risk set forth in section IV.B. of this appendix E. Individual 
equity issues and indices should be treated as separate underlyings. 
In addition to the capital requirement for delta risk, a banking 

[[Page 38127]]
organization should apply a further capital charge for gamma and vega 
risk:
    i. For gamma risk, the net gammas that are negative for each 
underlying are multiplied by 0.72 percent (in the case of an 
individual equity) or 0.32 percent (in the case of an index as the 
underlying) and by the square of the market value of the underlying;
    ii. For volatility risk, a banking organization calculates the 
capital requirement for vega for each underlying, assuming a 
proportional shift in volatility of 25.0 percent; and
    iii. The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the individual capital requirements for vega risk.
    d. For options of foreign exchange and gold positions, the net 
delta (or delta-based) equivalent of the total book of foreign 
currency and gold options is incorporated into the measurement of 
the exposure in a single currency position as set forth in section 
IV.C. of this appendix E. The gamma and vega risks should be 
measured as follows:
    i. For gamma risk, for each underlying exchange rate, net gammas 
that are negative are multiplied by 0.32 percent and by the square 
of the market value of the positions;
    ii. For volatility risk, a banking organization calculates the 
capital requirements for vega for each currency pair and gold 
assuming a proportional shift in volatility of  25.0 
percent; and
    iii. The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the sum of the individual capital requirements for 
vega risk.
    e. For options on commodities, the delta-weighted positions are 
incorporated in one of the measures described in section IV.D. of 
this appendix E. In addition, a banking organization must apply a 
capital requirement for gamma and vega risk:
    i. For gamma risk, net gammas that are negative for each 
underlying are multiplied by 1.125 percent and by the square of the 
market value of the commodity;
    ii. For volatility risk, a banking organization calculates the 
capital requirements for vega for each commodity assuming a 
proportional shift in volatility of +/- 25.0 percent; and
    iii. The capital requirement is the absolute value of the sum of 
the individual capital requirements for net negative gammas plus the 
absolute value of the sum of the individual capital requirements for 
vega risk.
    f. Under certain conditions and to a limited extent, the Federal 
Reserve may permit banking organizations that are significant 
traders in options with debt securities or interest rates as the 
underlying to net positive and negative gammas and vegas across 
time-bands. Such netting must be based on prudent and conservative 
assumptions and the banking organization must materially meet the 
qualitative standards set forth in section III.B. of this appendix 
E.
    g. A banking organization may base the calculation of vega risk 
on a volatility ladder in which the implied change in volatility 
varies with the maturity of the option. The assumed proportional 
shift in volatility must be at least +/- 25.0 percent at the short 
end of the maturity spectrum. The proportional shift for longer 
maturities must be at least as stringent in statistical terms as the 
25.0 percent shift at the short end.
    h. A banking organization should also monitor the risks of rho 
(the rate of change of the value of the option with respect to the 
interest rate) and theta (the rate of change of the value of the 
option with respect to time).

Attachments to Appendix E

Attachment I--Sample Calculation of Eligible Tier 1, Tier 2, and Tier 3 
Capital for the Risk-Based Capital Ratio Adjusted for Market Risk

    a. In each example the weighted-risk assets are $8000 and the 
market risk-adjusted assets are $625 (capital requirement for market 
risk = $50, $50 x 12.5 = $625):
    Example 1: A banking organization has the following qualifying 
capital: Tier 1 = $600, Tier 2 = $100, Tier 3 = $1000.
    (1) The minimum capital requirement for credit risk is $640 
($8000 x 8.0%). This requirement could be satisfied with $540 of 
Tier 1 capital and $100 of Tier 2 capital.
    (2) The remaining capital available for market risk would be: 
Tier 1 = $60, Tier 2 = 0, and Tier 3 = $1000. The minimum capital 
requirement for market risk is $50 ($625 x 8.0%). Eligible Tier 3 
capital would be limited to $125 ($50 x 2.5).
    (3) The Tier 1 capital required to support market risk could be 
satisfied by allocating $14 ($50 x .285), with eligible Tier 3 
capital used for market risk being $36 ($50 - $14).
    (4) Total qualifying and eligible capital would be: $540 (Tier 
1) + $100 (Tier 2) + $60 (Tier 1, comprising $14 allocated for 
market risk and $46 unallocated) + $36 (Tier 3) = $736. The banking 
organization's ratio of qualifying and eligible capital to weighted-
risk assets adjusted for market risk would be: $736/$8,625) = 8.5%.
    Example 2: A banking organization has the following qualifying 
capital: Tier 1 = $500, Tier 2 = $140, Tier 3 = $600.
    (1) The minimum capital requirement for credit risk is $640 
($8000 x 8.0%). This requirement could be satisfied with $500 of 
Tier 1 capital and $140 of Tier 2 capital.
    (2) The remaining capital available for market risk would be: 
Tier 1 = 0, Tier 2 = $0, and Tier 3 = $600. Eligible Tier 3 capital 
would be limited to $0 (0 x 2.5). Because there is no Tier 1 capital 
required to support market risk, no eligible Tier 3 capital may be 
used for market risk.
    (3) Total qualifying and eligible capital would be: $500 (Tier 
1) + $140 (Tier 2) = $640. The banking organization's ratio of 
qualifying and eligible capital to weighted-risk assets adjusted for 
market risk would be: $640/$8,625) = 7.4%.
    b. In both of the examples described in paragraph a. of this 
attachment the total of Tier 2 and Tier 3 capital for credit and 
market risk is not greater than 100 percent of Tier 1 capital for 
credit and market risk and the total of Tier 2 capital for credit 
risk is not greater than 100 percent of Tier 1 capital for credit 
risk.
Attachment II--Sample Calculation of General Market Risk for Debt 
Instruments Using the Maturity Method

    a. A banking organization with the following positions would 
slot them into a maturity ladder as shown below:
    i. Qualifying bond, $13.33mn market value, remaining maturity 8 
years, coupon 8%;
    ii. Government bond, $75mn market value, remaining maturity 2 
months, coupon 7%;
    iii. Interest rate swap, $150mn, banking organization receives 
floating rate interest and pays fixed, next interest reset after 12 
months, remaining life of swap is 8 years (assumes the current 
interest rate is identical to the one the swap is based on); and
    iv. Long position in interest rate future, $50mn, delivery date 
after 6 months, life of underlying government security is 3.5 years 
(assumes the current interest rate is identical to the one the swap 
is based on).

--------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                             Risk wght      Risk-weighted         Net time-band                         
      Zone                          Time-band and position                      (%)           position              positions        Net zone positions 
--------------------------------------------------------------------------------------------------------------------------------------------------------
1...............  10-1 mth.................................................       0.00                                                                  
                  1-3 mth Long 75 Gov.bond.................................       0.20  Long 0.15...........  Long 0.15...........  Long 1.00           
                  3-6 mt Short 50 Future...................................       0.40  Short 0.20..........  Short 0.20..........                      
                  6-12 mths Long 150 Swap..................................       0.70  Long 1.05...........  Long 1.05...........                      
2...............  1-2 yrs..................................................       1.25                                                                  
                  2-3 yrs..................................................       1.75                                                                  
                  3-4 yrs Long 50..........................................       2.25  Long 1.125..........  Long 1.125..........  Long 1.125          
                  Future                                                                                                                                
3...............  4-5 yrs..................................................       2.75                                                                  
                  5-7 yrs..................................................       3.25                                                                  
                  7-10 yrs Short 150 Swap Long 13.13 Qual Bond.............       3.75  Short 5.625.........  Short 5.125.........  Short 5.125         
                                                                                        Long 0.50...........                                            
                  10-15 yrs................................................       4.50                                                                  

[[Page 38128]]
                                                                                                                                                        
                  15-20 yrs................................................       5.25                                                                  
                  over 20 yrs..............................................       6.00                                                                  
--------------------------------------------------------------------------------------------------------------------------------------------------------



    b. A vertical disallowance would be calculated for time-band 7-
10 years. It would be 10 percent of the matched positions in the 
time-band--10.0x0.5=0.05 ($50,000).
    c. A horizontal disallowance would be calculated for zone 1. It 
would be 40 percent of the matched positions in the zone--
40.0x0.20=0.80 ($80,000). The remaining net position in Zone 1 would 
be +1.00 .
    d. A horizontal disallowance would be calculated for adjacent 
zones 2 and 3. It would be 40 percent of the matched positions 
between the zones--40.0x1.125=0.45 (450,000). The remaining position 
in zone 3 would be -4.00.
    e. A horizontal disallowance would be calculated between zones 1 
and 3. It would be 100 percent of the matched positions between the 
zones--100x1.00=1.00 (1,000,000).
    f. The remaining net open position for the banking organization 
would be 3.00 ($3,000,000).
    The total capital requirement for general market risk for this 
portfolio would be:

The vertical disallowance..................................      $50,000
Horizontal disallowance in zone 1..........................       80,000
Horizontal disallowance between zones 2 and 3..............      450,000
Horizontal disallowance between zones 1 and 3..............    1,000,000
The overall net open position..............................    3,000,000
    Total requirement for general market risk..............    4,580,000
                                                                        

Attachment III--Summary of Treatment for Interest Rate and Equity 
Derivatives

           Summary of Treatment for Interest Rate Derivatives           
------------------------------------------------------------------------
                              Specific risk                             
         Instrument               charge      General market risk charge
------------------------------------------------------------------------
Exchange-Traded Future:                                                 
    Government security.....  No...........  Yes, as two positions.     
    Corporate debt security.  Yes..........  Yes, as two positions.     
    Index on short-term       No...........  Yes, as two positions.     
     interest rates (e.g.                                               
     LIBOR).                                                            
OTC Forward:                                                            
    Government security.....  No...........  Yes, as two positions.     
    Corporate debt security.  Yes..........  Yes, as two positions.     
    Index on short-term       No...........  Yes, as two positions.     
     interest rates.                                                    
    FRAs, Swaps.............  No...........  Yes, as two positions.     
    Forward foreign exchange  No...........  Yes, as one position in    
                                              each currency.            
Options:                                                                
    Government security.....  No...........  For each type of           
                                              transaction, either:      
    Corporate debt security.  Yes..........  (a) Carve out together with
                                              the associated hedging    
                                              positions                 
    Index on short-term       No...........  --simplified method--      
     interest rates.                          scenario analysis--       
                                              internal models, or       
                                             (b) General market risk    
                                              charge according to the   
                                              Delta-plus method (gamma  
                                              and vega receive separate 
                                              capital charges)          
------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument.     
  There remains a separate capital requirement for counterparty credit  
  risk.                                                                 


               Summary of Treatment for Equity Derivatives              
------------------------------------------------------------------------
                              Specific risk                             
         Instrument               charge      General market risk charge
------------------------------------------------------------------------
Exchange-Traded or OTC                                                  
 Future:                                                                
    Individual equity.......  Yes..........  Yes, as underlying.        
    Index...................  2.0%.........  Yes, as underlying.        
Options:                                                                
    Individual equity.......  yes..........  For each type of           
                                              transactions either:      
    Index...................  2.0%.........  (a) Carve out together with
                                              the associated hedging    
                                              positions                 
                                             --simplified method--      
                                              scenario approach--       
                                              internal models, or       
                                             (b) General market risk    
                                              requirement according to  
                                              the Delta-plus method     
                                              (gamma and vega receive   
                                              separate capital charges).
                                                                        
------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument.     
  There remains a separate capital requirement for counterparty credit  
  risk.                                                                 

Attachment IV--Sample Calculation of Standardized Approach for 
Commodities Risk

----------------------------------------------------------------------------------------------------------------
                                                            Spread                                      Capital 
         Time band                     Position              rate           Capital calculation          charge 
----------------------------------------------------------------------------------------------------------------
0 up to 1 month............  None                                                                               
1 up to 3 months...........  None                                                                               
3 up to 6 months...........  Long 800...................       1.5%  800 long+800 short (matched) x           24
                                                                      1.5%=.                                    
                             Short 1000.................             200 Short carried forward to 1-2         24
                                                                      yrs, capital charge: 200 x 2 x            
                                                                      0.6%=.                                    
6 up to 12 months..........  None.......................                                                        
1 up to 2 yrs..............  Long 600...................             200 long+200 short (matched) x            6
                                                                      1.5%=.                                    

[[Page 38129]]
                                                                                                                
                                                                     400 long carried forward to over        4.8
                                                                      3 yrs capital charge: 400 x 2 x           
                                                                      0.6%=.                                    
2 up to 3 yrs..............  None                                                                               
over 3 years...............  Short 600..................             400 long+400 short                       12
                                                                      (matched)+1.5%=.                          
                                                                     Net position: 200 capital                30
                                                                      charge: 200 x 15.0%=.                     
----------------------------------------------------------------------------------------------------------------
Note: Assume all positions are in the same commodity and converted at current spot rates into U.S. dollars. 
The total capital requirement would be $79.2.                                                                     


Attachment V--Sample Calculation for Delta-Plus Method for Options

    a. Assume a banking organization has a European short call 
option on a commodity with an exercise price of 490 and a market 
value of the underlying 12 months from the expiration of the option 
at 500; a risk-free interest rate at 8% per annum, and the 
volatility at 20 percent. The current delta for this position is 
according to the Black-Scholes formula -0.721 (that is, the price of 
the option changes by -0.721 if the price of the underlying moves by 
1). The gamma is -0.0034 (that is, the delta changes by -0.0034 from 
-0.721 to -0.7244 if the price of the underlying moves by 1). The 
current value of the option is 65.48.
    b. The first step under the delta-plus method is to multiply the 
market value of the commodity by the absolute value of the delta. 
500 x 0.721=360.5. The delta-weighted position is then incorporated 
into the measure described in section IV.D. of this Appendix E. If 
the banking organization uses the maturity approach and no other 
positions exist, the delta-weighted position is multiplied by 0.15 
to calculate the capital requirement for delta. 360.5 x 0.15=54.075.
    c. The capital requirement for gamma is calculated according to 
the Taylor expansion by multiplying the absolute value of the 
assumed gamma of -0.0034 by 1.125% and by the square of the market 
value of the underlying. 0.0034 x 0.0125 x 500\2\=10.625
    d. The capital requirement for vega is calculated next. The 
assumed current (implied) volatility is 20%. Since only an increase 
in volatility carries a risk of loss for a short call option, the 
volatility has to be increased by a relative shift of 25%. This 
means that the vega capital requirement has to be calculated on the 
basis of a change in volatility of 5 percentage points from 20% to 
25% in this example. According to the Black-Scholes formula used 
here, the vega equals 168. Thus, a 1% or 0.01 increase in volatility 
increases the value of the option by 1.68. Accordingly, a change in 
volatility of 5 percentage points increases the value of 
5 x 1.68=8.4. This is the capital requirement for vega risk. The 
total capital requirement would be $73.10 (54.075+10.625+8.4).

    By Order of the Board of Governors of the Federal Reserve 
System, July 12, 1995.
William W. Wiles,
Secretary of the Board.
FEDERAL DEPOSIT INSURANCE CORPORATION

12 CFR Chapter III

    For the reasons indicated in the preamble, the FDIC Board of 
Directors hereby proposes to amend part 325 of chapter III of Title 12 
of the Code of Federal Regulations as follows:

PART 325--CAPITAL MAINTENANCE

    1. The authority citation for part 325 continues to read as 
follows:

    Authority: 12 U.S.C. 1815(a), 1815(b), 1816, 1818(a), 1818(b), 
1818(c), 1818(t), 1819(Tenth), 1828(c), 1828(d), 1828(i), 1828(n), 
1828(o), 1831o, 3907, 3909, 4808; Pub. L. 102-233, 105 Stat. 1761, 
1789, 1790 (12 U.S.C. 1831n note); Pub. L. 102-242, 105 Stat. 2236, 
2355, 2386 (12 U.S.C. 1828 note).

    2. Appendix A to part 325 is amended in the introductory text, by 
adding a new paragraph after the third undesignated paragraph to read 
as follows:

Appendix A to Part 325--Statement of Policy on Risk-Based Capital

* * * * *
    In addition, when certain banks that engage in trading 
activities calculate their risk-based capital ratio under this 
appendix A, they must also refer to appendix C of this part, which 
incorporates capital charges for certain market risks into the risk-
based capital ratio. When calculating their risk-based capital ratio 
under this appendix A, such banks are required to refer to appendix 
C of this part for supplemental rules to determine qualifying and 
eligible capital, calculate risk-weighted assets, calculate market-
risk equivalent assets and add them to risk- weighted assets, and 
calculate risk-based capital ratios adjusted for market risk.
* * * * *
    3. A new appendix C is added to part 325 to read as follows:

Appendix C to Part 325--Risk-Based Capital for State Non-Member Banks: 
Market Risk

    (i) The Federal Deposit Insurance Corporation (FDIC) has adopted 
a framework to supplement the risk-based capital requirements set 
out in appendix A of this part with capital requirements for the 
market risk exposure of state non-member banks.1 For this 
purpose, market risk refers to the risk of losses in a bank's on- 
and off-balance-sheet positions arising from movements in market 
prices. The market risks subject to these capital requirements are 
those associated with debt and equity instruments held in the bank's 
trading account, as well as foreign exchange risk and commodities 
risk throughout the bank, including options and other derivative 
contracts in each risk category. As is further detailed in section 
II of this appendix C, debt and equity instruments and commodities 
positions subject to the measure for market risk under this appendix 
C are generally excluded from the calculation of risk-weighted 
assets under appendix A of this part.

    \1\ The market risk measure is based on a framework developed 
jointly by supervisory authorities from the countries represented on 
the Basle Committee on Banking Supervision (Basle Supervisors 
Committee) and endorsed by the Group of Ten Central Bank Governors. 
The framework is described in a paper prepared by the Basle 
Supervisors Committee entitled ``Proposal to issue a Supplement to 
the Basle Capital Accord to Cover Market Risks''. April 1995.
---------------------------------------------------------------------------

    (ii) This appendix C provides two ways for a bank to determine 
its exposure to market risk. A bank may use its internal risk 
measurement model, subject to the conditions and criteria set forth 
in section III of this appendix C (referred to as the internal 
models approach), or when appropriate, a bank may use all or 
portions of the alternative measurement system described in section 
IV of this appendix C (referred to as the standardized approach).
    (iii) With prior approval from the FDIC, for regulatory capital 
purposes, a bank may use its internal risk measurement model to 
measure its value-at-risk 2 for each of the following risk 
factor categories: interest rates, exchange rates, equity prices, 
and commodity prices. The value-at-risk amount for each risk factor 
category should include volatilities of related options. The value-
at-risk amount for each risk factor category is summed to determine 
the aggregate value-at- risk for the bank.

    \2\ A bank evaluates its current positions and estimates future 
market volatility through a value-at-risk measure, which is an 
estimate representing, with a certain degree of statistical 
confidence, the maximum amount by which the market value of trading 
positions could decline during a specific period of time. The value-
at-risk is generated through an internal model that employs a series 
of market risk factors (for example, market rates and prices that 
affect the value of trading positions).
    (iv) The standardized approach uses a set of standardized 
calculations and assumptions to measure market risk exposure 
depending on its source: debt instruments, equities, foreign 
currencies, and commodities, including volatilities of related 
options.3

    \3\ There are three alternatives for measuring the market risk 
of options under the standardized approach. Under two of the 
alternatives, the simplified and scenario methods, the underlying 
position of an option is ``carved-out,'' and is not included in the 
prescribed risk measure for the underlying debt, equity, foreign 
exchange or commodity. Instead it is evaluated together with the 
related option according to the procedures described for options to 
determine the capital requirement. Under the third alternative, the 
``delta-plus'' approach, the delta-equivalent value of each position 
is included in the measurement framework for the prescribed risk 
measure for the underlying.

[[Page 38130]]

---------------------------------------------------------------------------

    (v) The FDIC generally expects any bank that is subject to this 
appendix C, especially those with large trading accounts, to compute 
the measure for market risk by using internal risk-measurement 
models. A bank may not change its measurement approach for the 
purpose of minimizing capital requirements. In limited instances, on 
a case-by-case basis, the FDIC may permit a bank that has internal 
models to incorporate alternative measures for market risk of 
negligible exposures (for example, de minimis positions, activities 
in remote locations, minor exposures in a currency, or activities 
that present negligible risk to the bank), so long as it adequately 
captures the risk.
    (vi) The FDIC will monitor the implementation and effect of 
these guidelines in relation to domestic and international 
developments in the banking industry. When necessary and 
appropriate, the FDIC will consider the need to modify this appendix 
C in light of any significant changes in the economy, financial 
markets, banking practices, or other relevant factors.

I. Scope of the Market Risk Capital Requirement

A. Banks Subject to This Appendix C

    1. Effective December 31, 1997, this appendix C will be applied 
to any FDIC-insured state-chartered bank that is not a member of the 
Federal Reserve System (excluding insured branches of foreign banks) 
and that, on a consolidated basis, either:
    a. Has total assets in excess of $5 billion, and:
    i. Has a total volume of trading activities (measured as the sum 
of the bank's trading assets and liabilities 4 on a daily 
average basis for the quarter) that is 3.0 percent or more of the 
total assets of the bank; or

    \4\ As reflected in the bank's quarterly Consolidated Reports of 
Condition and Income (call report.)
---------------------------------------------------------------------------

    ii. Has interest rate, foreign exchange, equity, and commodity 
off-balance-sheet derivative contracts relating to trading 
activities whose total notional amounts exceed $5 billion; or
    b. Has total assets of $5 billion or less and has a total volume 
of trading activities exceeding 10.0 percent of the total assets of 
the bank.
    2. Such banks identified in paragraph 1 (hereinafter referred to 
as ``banks''), when calculating their risk-based capital ratio under 
appendix A of this part, are required to refer to this appendix C 
for supplemental rules to determine their qualifying and eligible 
capital, calculate risk-weighted assets, calculate market-risk 
equivalent assets and add them to risk-weighted assets, and 
calculate risk-based capital ratios adjusted for market risk.5

    \5\ The FDIC may apply all or portions of this appendix C to 
other state non-members banks when deemed necessary for safety and 
soundness purposes.
---------------------------------------------------------------------------

B. Market Risks Subject to a Capital Requirement

    1. General Market Risk and Specific Risk. A bank must hold 
capital against exposure to general market risk and specific risk 
arising from its trading and other foreign exchange and commodity 
activities. For this purpose, general market risk refers to changes 
in the market value of covered transactions resulting from market 
movements, such as changing levels of market interest rates, broad 
equity indices, or currency exchange rates. Specific risk refers to 
credit risk, that is, the risk that the issuer of a debt or equity 
instrument might default, as well as to other factors that affect 
the market value of specific instruments but that do not materially 
alter market conditions.6

    \6\ This appendix C does not impose specific risk capital 
requirements for foreign exchange risk and commodities positions 
because they do no have the type of issuer-specific risk associated 
with debt and equity instruments in the trading account.
---------------------------------------------------------------------------

    2. Trading Activities. a. The measure for market risk in trading 
activities is based on on- and off-balance-sheet positions in a 
bank's trading account. For this purpose, the trading account 
consists of positions in financial instruments acquired with the 
intent to resell in order to profit from short-term price movements 
(or other price or interest-rate variations), including, but not 
limited to:
    i. Assets acquired with the intent to resell to customers;
    ii. Positions in financial instruments arising from matched 
principal brokering and market making; or
    iii. Positions taken in order to hedge other elements of the 
trading account (that is, reduce risk by offsetting other positions 
that have exposure to changes in market rates or prices).7

    \7\ Subject to FDIC review, when on- or off-balance-sheet non-
trading account instruments are deliberately used to hedge trading 
account instruments, the non-trading account instruments may be 
included in the measure for general market risk, but if so included, 
are not included in the measure for specific risk and instead remain 
an element of risk-weighted assets under section II of appendix A of 
this part. Instruments such as swaps used to hedge non-trading 
account activities should be excluded from the measure for market 
risk if they are not part of the trading account.
---------------------------------------------------------------------------

    b. Trading account activities may include positions in debt 
instruments, equities, foreign currencies, and commodity 
instruments, or related derivative 8 or other off-balance-sheet 
contracts.

    \8\ In general terms, a derivative is a financial contract whose 
value is derived from the values of one or more underlying assets or 
reference rates or indexes of asset values (referred to as ``the 
underlying''). Derivatives include standardized contracts that are 
traded on exchanges and customized, privately negotiated contracts 
known as over-the-counter (OTC) derivatives.
---------------------------------------------------------------------------

    c. The debt instruments in the trading account category consists 
of all fixed-rate and floating-rate debt securities and instruments 
that behave like debt, including non-convertible preferred stock. 
Convertible bonds, i.e., preferred stock or debt issues that are 
convertible, at a stated price, into common shares of the issuer, 
should be treated as debt instruments if they trade like debt 
instruments and as equities if they trade like equities. Also 
included are derivative contracts of debt instruments and other off-
balance-sheet instruments in the trading account that react to 
changes in interest rates (for example, forward rate agreements 
(FRAs), bond futures, interest rate and cross-currency swaps and 
forward foreign exchange positions). A security that has been sold 
subject to a repurchase agreement or lent subject to a securities 
lending agreement is treated as if it were still owned by the lender 
of the security, but the off-balance-sheet portion of the 
transaction remains an element of risk-weighted assets as set forth 
in section II. of appendix A of this part.
    d. The equities in the trading account category consist of 
equity instruments that behave like equities. The instruments 
covered include common stocks (whether voting or non-voting), 
convertible securities that behave like equities, and commitments to 
buy or sell equity securities. Also included are derivative 
contracts of equity instruments and other off-balance-sheet 
instruments in the trading account that are affected by changes in 
equity prices. However, non- convertible preferred stock is included 
in debt instruments.
    3. Foreign Exchange and Commodities Risk. Foreign exchange or 
commodities positions, whether or not included in a bank's trading 
account, are subject to a measure for market risk of those 
positions.
    a. The measure for market risk of foreign exchange applies to a 
bank's total currency and gold positions. This includes spot 
positions (that is, asset items and liability items, including 
accrued interest and expenses, denominated in each currency); 
forward positions (that is, forward foreign exchange transactions, 
including currency futures and the principal on currency swaps not 
included in the spot position); and certain guarantees. It also 
includes future income and expenses from foreign currency 
transactions not yet accrued but already fully hedged (at the 
discretion of the reporting bank), foreign exchange derivative and 
other off-balance-sheet positions that are affected by changes in 
exchange rates, and any other item representing a profit or loss in 
foreign currencies.
    b. A bank doing negligible business in foreign currency and that 
does not take foreign exchange positions for its own account may be 
exempted from the market risk measure for foreign exchange risk 
provided that:
    i. Its foreign currency business, defined as the greater of the 
sum of its gross long positions and the sum of its gross short 
positions in all foreign currencies as determined under section 
IV.C.2 of this appendix C, does not exceed 100 percent of eligible 
capital as defined in section II. of this appendix C; and
    ii. Its overall net open foreign exchange position as determined 
under section IV.C.3. of this appendix C does not exceed 2.0 percent 
of eligible capital. 

[[Page 38131]]

    c. A bank may, subject to approval by the FDIC, exclude from its 
foreign exchange positions any structural positions in foreign 
currencies. For this purpose, such structural positions are limited 
to transactions designed to hedge a bank's capital ratios against 
the effect of adverse exchange rate movements on subordinated debt, 
equity, or minority interests in consolidated subsidiaries and 
dotation capital assigned to foreign branches that are denominated 
in foreign currencies. Also included are any positions related to 
unconsolidated subsidiaries and to other items that are deducted 
from a bank's capital when calculating its capital base. In any 
event, such structural foreign currency positions must reflect long-
term policies of the institution and not relate to trading 
positions.
    d. The measure for market risk of commodities applies to a 
bank's total commodities positions, including commodity futures, 
commodity swaps, and all other commodity derivatives or other off-
balance-sheet positions that are affected by changes in commodity 
prices. A commodity is defined as a physical product that is or can 
be traded on a secondary market (such as agricultural products, 
minerals (including oil), and precious metals), but excluding gold 
(which is treated as foreign exchange).

II. Qualifying Capital and the Market Risk-Adjusted Capital Ratio

A. Qualifying and Eligible Capital

    1. The principal forms of qualifying capital for market risk are 
Tier 1 capital and Tier 2 capital as defined in, and subject to the 
conditions and limitations of, section I of appendix A of this part. 
A bank may use Tier 3 capital for the sole purpose of meeting a 
portion of the capital requirements for market risk. Tier 3 capital 
may be allocated only to support market-risk equivalent assets, and 
may in no event be allocated to support capital requirements 
associated with risk-weighted assets under appendix A of this part.
    2. Tier 3 capital consists of short-term subordinated debt that 
is subject to a lock-in clause providing that neither interest nor 
principal payment is due (even at maturity) if such payment would 
cause the issuing bank to fall or remain below the minimum 8.0 
percent risk-based capital requirement as set forth in appendix A of 
this part and adjusted for market risk.
    3. In order to qualify as Tier 3 capital, the short-term debt 
must be unsecured, subordinated, and fully paid up; it must have an 
original maturity of at least two years; and it may not be redeemed 
before maturity without prior approval by the FDIC. In addition, it 
may not contain or be covered by any covenants, terms, or 
restrictions that are inconsistent with safe and sound banking 
practices.

B. Calculation of Eligible Capital and the Capital Ratio

    A bank that is subject to the market risk measure must calculate 
its risk-based capital ratio and eligible capital as follows:
    1. Determine total risk-weighted assets under appendix A of this 
part, excluding from risk-weighted assets:
    a. All debt and equity instruments in the trading account 
required to be included under the measure for market risk, with the 
exception of over-the-counter derivatives or non-trading account 
instruments used to hedge trading account instruments and included 
in the measure for general market risk at the bank's option; and
    b. All positions in commodities required to be included under 
the measure for market risk.
    2. Calculate the total measure for market risk using the 
internal models approach, the standardized approach, or an approved 
combination of these two approaches:
    a. Internal Models. i. For a bank approved to use the internal 
models approach under section III of this appendix C, the total 
measure for market risk is the higher of:
    A. The bank's previous day's aggregate value-at-risk amount; or
    B. An average of the daily aggregate value-at-risk amounts 
measured on each of the preceding 60 business days multiplied by a 
minimum ``multiplication factor'' of 3. The FDIC may adjust the 
multiplication factor for a bank to increase its capital requirement 
based on an assessment of the quality and historic accuracy of the 
bank's risk management system.
    ii. Additionally, if a bank's internal model does not capture 
the specific risk of debt and equity instruments in the trading 
account,\9\ the specific risk measure as calculated under the 
standardized approach may be added to the bank's measure for market 
risk.

    \9\ If a bank uses an internal model that measures specific risk 
of debt and equity instruments in the trading account, the measure 
should in no case be less than one-half the specific risk measure as 
calculated under the standardized approach (taking into account the 
effect of the multiplier under paragraph B.2.a.ii. of this section).
---------------------------------------------------------------------------

    b. Standardized Approach. A bank that has not obtained the 
FDIC's approval to use an internal model must use the standardized 
approach for measuring its market risk. For a bank using this 
approach, the total measure for market risk is the sum of the market 
risk measures for debt and equity instruments in the trading 
account, foreign exchange and commodities risk throughout the bank, 
and options and other derivative positions in each risk category as 
set forth in sections IV.A through IV.E. of this appendix C.
    c. Partial Models. With approval from the FDIC, a bank whose 
internal model does not cover all risk factor categories may use the 
standardized approach for measuring market risk arising from the 
risk factor categories that are not covered. The FDIC will approve 
combining the two approaches only on a temporary basis in situations 
in which the institution is developing but has not fully implemented 
a comprehensive internal model. When a bank uses both approaches, 
each risk factor category (i.e., interest rates, equity prices, 
exchange rates, and commodity prices) must be measured using one or 
the other approach. The methods may not be combined within a single 
risk factor category. Once a bank adopts an acceptable internal 
model for a particular risk factor category, it may not revert to 
the standardized approach except in unusual circumstances and with 
the prior approval of the FDIC.\10\ For a bank using a combination 
of approaches, the total measure for market risk is the sum of:

    \10\ Banks that have modeling capabilities are expected to use 
their internal models for measuring market risk for regulatory 
capital purposes. However, the FDIC may permit a bank to use another 
measurement technique for de minimis positions, activities in remote 
locations, minor exposures in a currency, or in activities that 
present negligible risk to the bank.
---------------------------------------------------------------------------

    i. The appropriate value-at-risk measure (as determined in 
paragraph B.2.a. of this section, aggregating the value-at-risk 
measure for each risk factor category included in the internal 
model); and
    ii. The measure for market risk for each risk factor category 
that is calculated using the standardized approach.
    3. Calculate the market-risk equivalent assets by multiplying 
the total measure for market risk by 12.5 (i.e., the reciprocal of 
the 8.0 percent minimum risk-based capital ratio).
    4. Add the market-risk equivalent assets to total risk-weighted 
assets (as determined in paragraph B.1. of this section). The sum of 
these two amounts is the denominator of the total risk-based capital 
ratio, adjusted for market risk.
    5.a. In order to calculate eligible capital to be included in 
the numerator of the ratio, a bank must first allocate the 
qualifying Tier 1 and Tier 2 capital necessary to support total 
risk-weighted assets (as determined in paragraph B.1. of this 
section) in accordance with the terms and restrictions of section I 
of appendix A of this part, achieving at least the minimum 
supervisory ratio in section III. of appendix A of this part. 
Remaining Tier 1, eligible Tier 2, and eligible Tier 3 capital 
should then be allocated to support market-risk equivalent assets 
(as determined in paragraph B.3. of this section), achieving at 
least a minimum supervisory ratio of 8.0 percent, subject to the 
following restrictions:
    i. Eligible Tier 3 capital may not exceed 250 percent of a 
bank's Tier 1 capital allocated for market risk;
    ii. Tier 2 elements may be substituted for Tier 3 up to the same 
250 percent limit, so long as the overall limits for Tier 2 capital 
set out in section I of appendix A of this part are not exceeded 
(i.e., Tier 2 capital may not exceed total Tier 1 capital, and long-
term subordinated debt may not exceed 50 percent of Tier 1 capital); 
and
    iii. The maximum eligible amount of Tier 2 and Tier 3 capital, 
summed together, may not exceed 100 percent of Tier 1 capital.
    b. Eligible capital for the total risk-based capital ratio is 
then the sum of the bank's qualifying Tier 1 capital, its qualifying 
Tier 2 capital subject to the limits stated in this paragraph and 
eligible Tier 3 capital subject to the limits stated in this 
paragraph B.5.\11\

    \11\ Examples of the method used to calculate eligible capital 
are set forth in attachment I to this appendix C.
---------------------------------------------------------------------------

C. Consolidation and Reporting

    1. The capital requirements for market risk apply to banks on a 
worldwide consolidated basis. The FDIC may, however, evaluate market 
risk on an unconsolidated basis when necessary (for example, when 
there are 

[[Page 38132]]
obstacles to the repatriation of profits from a foreign subsidiary or 
where management structure does not allow timely management of risk 
on a consolidated basis).
    2. All transactions, including forward sales and purchases, 
should be included in the calculation of market risk capital 
requirements from the date on which they were entered into. Although 
banks subject to the capital requirements for market risk will 
continue to report their capital on a quarterly basis, the FDIC 
expects banks to meet their capital requirements for market risk on 
a continuous basis (that is, at a minimum, at the close of each 
business day).
    3. The risk-based capital ratios adjusted for market risk are 
minimum supervisory ratios. The FDIC expects banks to operate with 
capital positions well above the minimum ratios. In all cases, banks 
should hold capital commensurate with the level and nature of the 
risks to which they are exposed.

III. The Internal Models Approach

A. Use of Models
    1. With prior approval of the FDIC, a bank may use its internal 
risk measurement model(s) for measuring value-at-risk to be used as 
the measure for market risk.
    a. Requests for approval should include, at a minimum, a 
complete description of the bank's internal modeling and risk 
management systems and how these systems conform to the criteria set 
forth in this section III, an explanation of the policies and 
procedures established by the bank to ensure continued compliance 
with such criteria, a discussion of internal and external validation 
procedures, and a description of other relevant policies and 
procedures consistent with sound practices.
    b. The FDIC will approve an internal model for regulatory 
capital purposes only after determining that the bank's internal 
model and risk management systems meet the criteria in this section 
III. Such a determination may require on-site examinations of the 
systems. The FDIC may require modification to an internal model as 
deemed necessary to ensure compliance, on a continuing basis, with 
the provisions of this appendix C. A bank's internal model will be 
subject to continuing review, both on- and off-site, by the 
FDIC.\12\

    \12\ Banks that need to modify their existing modeling 
procedures to accommodate the requirements of this appendix C 
should, nonetheless, continue to use the internal models they 
consider most appropriate in evaluating risks for other purposes.
---------------------------------------------------------------------------

    2. A bank should ensure that the level of sophistication of its 
internal model is commensurate with the nature and volume of the 
bank's trading activity in the risk factor categories covered by 
this appendix C and measures market risk as accurately as possible. 
In addition, the model should be adjusted to reflect changing 
portfolio composition and changing market conditions.

B. Qualitative Criteria

    1. A bank using the internal models approach should have market 
risk management systems that are conceptually sound and implemented 
with integrity. Internal risk measurement models must be closely 
integrated into the day-to-day risk management process of the bank. 
For example, the risk measurement model must be used in conjunction 
with internal trading and exposure limits.
    2. A bank must meet the following minimum qualitative criteria 
before using its internal model as the measure for market risk:\13\

    \13\ If the FDIC is not satisfied with the extent to which a 
bank meets these criteria, the FDIC may adjust the multiplication 
factor used in section II.B.2.a.ii. of this appendix C to determine 
the total measure for market risk or otherwise increase capital 
requirements.
---------------------------------------------------------------------------

    a. A bank must have a risk control unit that is independent from 
business trading units and reports directly to senior management of 
the bank. The unit must be responsible for designing and 
implementing the bank's risk management system and analyzing daily 
reports on the output of the bank's risk measurement model in the 
context of trading limits. The unit must conduct regular back-
testing.\14\

    \14\ Back-testing includes ex post comparisons of the risk 
measures generated by the model against the actual daily changes in 
portfolio value.
---------------------------------------------------------------------------

    b. Senior management must be actively involved in the risk 
control process. The daily reports produced by the risk management 
unit must be reviewed by a level of management with sufficient 
authority to enforce both reductions in positions taken by 
individual traders, as well as in the bank's overall risk exposure.
    c. The bank must have a routine and rigorous program of stress-
testing to identify the effect of low-probability events on the 
bank's trading portfolio. Bank stress-testing should cover a range 
of factors that can create extraordinary losses or gains in trading 
portfolios or make the control of risk in those portfolios 
difficult. These factors include low-probability events of all 
types, including the various components of market, credit, and 
operational risks. Senior management must routinely review the 
results of stress-testing in the context of the potential effect of 
the events on bank capital and the appropriate procedures the bank 
should take to minimize losses. The policies of the bank set by 
management and the bank's board of directors should identify 
appropriate stress-tests and the procedures to follow in response to 
the test results.
    d. The bank must have established procedures for ensuring 
compliance with a documented set of internal policies and controls, 
as well as for monitoring the overall operation of the risk 
measurement system.
    e. Not less than once a year, the bank must conduct, as part of 
its regular internal audit process, an independent review of the 
risk measurement system. This review must include both the 
activities of the business trading units and of the independent risk 
control unit of the bank.
    f. Not less than once a year, the bank must conduct a review of 
its overall risk management process. The review must consider:
    i. The adequacy of the documentation of the risk management 
system and process, and the organization of the risk control unit;
    ii. The integration of market risk measures into daily risk 
management and the integrity of the management information system;
    iii. The process the bank employs for approving risk pricing 
models and valuation systems that are used by front- and back-office 
personnel;
    iv. The scope of market risks captured by the risk measurement 
model and the validation of any significant changes in the risk 
measurement process;
    v. The accuracy and completeness of position data, the accuracy 
and appropriateness of volatility and correlation assumptions, and 
the accuracy of valuation and risk sensitivity calculations;
    vi. The verification process the bank employs to evaluate the 
consistency, timeliness, and reliability of data sources used to run 
internal models, including the independence of such data sources; 
and
    vii. The verification process the bank uses to evaluate back-
testing that is conducted to assess the model's accuracy.

C. Market Risk Factors

    1. Generally. For regulatory capital purposes, a bank's internal 
risk measurement system must use sufficient risk factors to capture 
the risks inherent in the bank's portfolio of on- and off-balance-
sheet trading positions and must, subject to the following 
guidelines, cover interest rates, equity prices, exchange rates, 
commodity prices, and volatilities related to options positions in 
each risk factor category. The level of sophistication of the bank's 
risk factors must be commensurate with the nature and scope of the 
risks taken by the bank.
    2. Interest Rates. a. A bank must use a set of market risk 
factors corresponding to interest rates in each currency in which it 
has material interest rate-sensitive on- or off-balance-sheet 
positions. The risk measurement system must model the yield curve 
\15\ using one of a number of generally accepted approaches, for 
example, by estimating forward rates of zero coupon yields. The 
yield curve must be divided into various maturity segments in order 
to capture variation in the volatility of rates along the yield 
curve; there will typically be one risk factor corresponding to each 
maturity segment.

    \15\ Generally, a yield curve is a graph showing the term 
structure of interest rates by plotting the yields of all 
instruments of the same quality by maturities ranging from the 
shortest to the longest available. The resulting curve shows whether 
short-term interest rates are higher or lower than long-term 
interest rates.
---------------------------------------------------------------------------

    b. For significant exposures to interest rate movements in the 
major currencies and markets, a bank must model the yield curve 
using a minimum of six risk factors. However, the number of risk 
factors used should ultimately be driven by the nature of the bank's 
trading strategies.\16\ The risk measurement system must incorporate 
separate risk factors to capture spread risk.\17\

    \16\ For example, a bank that has a portfolio of various types 
of securities across many points of the yield curve and that engages 
in complex arbitrage strategies would require a greater number of 
risk factors to accurately capture interest rate risk.
    \17\ For these purposes, spread risk refers to the potential 
changes in value of an instrument or portfolio arising from 
differences in the behavior of baseline yield curves, such as those 
for U.S. Treasury securities, and yield curves reflecting sector, 
quality, or instrument specific factors. A variety of approaches may 
be used to capture the spread risk arising from less than perfectly 
correlated movements between government and other interest rates, 
such as specifying a completely separate yield curve for non-
government instruments (for example, swaps or municipal securities) 
or estimating the spread over government rates at various points 
along the yield curve.

[[Page 38133]]

---------------------------------------------------------------------------

    3. Exchange Rates. A bank must use market risk factors 
corresponding to the exchange rate between the domestic currency and 
each foreign currency in which the bank has a significant exposure. 
The risk measurement system must incorporate market risk factors 
corresponding to the individual foreign currencies in which the 
bank's positions are denominated.
    4. Equity Prices. A bank must use risk factors corresponding to 
each of the equity markets in which it holds significant positions. 
The sophistication and nature of the modeling technique for a given 
market must correspond to the bank's exposure to the overall market 
as well as to the bank's concentration in individual equity issues 
in that market. At a minimum, there must be a risk factor designed 
to capture market-wide movements in equity prices (such as a market 
index), but additional risk factors could track various sectors or 
individual issues.
    5. Commodity Prices. A bank must use market risk factors 
corresponding to each of the commodity markets in which it holds 
significant positions. The internal model must encompass directional 
risk, forward gap and interest rate risk, and basis risk.\18\ The 
model should also take into account the market characteristics, for 
example, delivery dates and the scope provided to traders to close 
out positions.

    \18\ For these purposes, directional risk refers to the risk 
that a spot price will increase or decrease. Forward gap risk refers 
to the effects of owning a physical commodity versus owning a 
forward position in a commodity. Interest rate risk refers to the 
risk of a change in the cost of carrying forward positions and 
options. Basis risk refers to the risk that the relationship between 
the prices of similar commodities changes over time.
---------------------------------------------------------------------------

D. Quantitative Standards

    1. A bank may use one of a number of generally accepted 
measurement techniques including, for example, an internal model 
based on variance-covariance matrices, historical simulations, or 
Monte Carlo simulations, so long as the model employed captures all 
significant market risks.\19\ The following minimum standards apply 
for purposes of using an internal model for calculating market risk 
capital requirements:

    \19\ For these purposes, a variance/covariance approach refers 
to an approach in which the change in value of the portfolio is 
calculated by combining the risk factor sensitivities of the 
individual positions--derived from valuation models--with a 
variance/covariance matrix based on risk factor volatilities and 
correlations. A bank using this approach would calculate the 
volatilities and correlations of the risk factors on the basis of 
the holding period and the observation period. The historical 
simulation approach refers to an approach in which a bank would 
calculate the hypothetical change in value of the current portfolio 
in light of historical movements in risk factors. This calculation 
would be done for each of the defined holding periods over a given 
historical measurement horizon to arrive at a range of simulated 
profits and losses. The Monte Carlo approach refers to an approach 
in which a bank would consider historical movements to determine the 
probability of particular price and rate changes.
---------------------------------------------------------------------------

    a. Value-at-risk must be calculated on a daily basis using a 
99th percentile, one-tailed confidence interval \20\ and the holding 
period must be ten trading days. For positions that display linear 
price characteristics, a bank may use value-at-risk numbers 
calculated according to shorter holding periods scaled up to ten 
days by the square root of time.\21\

    \20\ A one-tailed confidence interval of 99 percent means that 
there is a 1 percent probability based on historical experience that 
the combination of positions in a bank's portfolio would result in a 
loss higher than the measured value-at-risk.
    \21\ This transformation entails multiplying a bank's value-at-
risk by the square root of the ratio of the required holding period 
(ten days) to the holding period embodied in the value-at-risk 
figure. For example, the value-at-risk calculated according to a 
one-day holding period would be scaled-up by the ``square root of 
time'' by multiplying the value-at-risk by 3.16 (the square root of 
the ratio of a ten-day holding period to a one-day holding period).
---------------------------------------------------------------------------

    b. Value-at-risk must be calculated using an observation period 
of at least one year to measure historical changes in rates and 
prices.
    c. A bank must update its historical rates and prices at least 
once every three months and must reassess them whenever there is a 
change in market conditions of any significance.
    2. A bank may use its discretion in recognizing empirical 
correlations within each market risk factor category, provided that 
the FDIC is satisfied that there is integrity in the bank's process 
for calculating correlations. However, empirical correlations among 
risk categories are not recognized. The value-at-risk measure for 
each risk category must be added together on a simple sum basis to 
determine the aggregate value-at-risk amount.
    3. A bank's model must accurately capture the unique risks 
associated with options within each of the market risk factor 
categories. The following minimum criteria apply to the measurement 
of options risk:
    a. A bank's internal model must capture the non-linear price 
characteristics of option positions using an options pricing 
technique. The bank must apply a minimum ten-day holding period to 
option positions or positions that display option-like 
characteristics. Banks may not scale-up the daily value-at-risk 
numbers by the square root of time.
    b. A bank's internal model must, for example, capture the 
sensitivity of the value of the options positions to changes in the 
volatility of the options' underlying rates or prices (that is, the 
vega) and must measure the volatilities of options positions broken 
down by different maturities.
    4. The accuracy of a bank's internal model will be reviewed 
periodically by the FDIC. Such review--during which, when 
appropriate, the FDIC may take into consideration reports and 
opinions generated by external auditors or qualified consultants--
will include at a minimum:
    a. Verification that the internal validation processes described 
in paragraph B.2. of this section are operating in a satisfactory 
manner;
    b. Assurance that the formulae used in the calculation process 
and for the pricing of options and other complex instruments, are 
validated by a qualified unit of the bank, which in all cases must 
be independent from the trading areas;
    c. Confirmation that the structure of the internal model is 
adequate with respect to the bank's activities and geographical 
coverage;
    d. Confirmation that the results of the bank's back-testing of 
its internal measurement system (that is, comparing value-at-risk 
estimates with actual profits and losses) are being used effectively 
to monitor reliability of the model's estimates over time; and
    e. Assurance that, for regulatory capital purposes, the model 
processes all relevant data and that the modeling procedures conform 
with the parameters and specifications set forth in this appendix C.

IV. The Standardized Approach

A. Debt Instruments

    1. Specific Risk. a. The specific risk element of the measure 
for market risk is based on the identity of the obligor and, in the 
case of corporate securities, on the credit rating and maturity of 
the instrument. The specific risk element is calculated by weighting 
the current market value of each individual position, whether long 
or short, by the appropriate factor as set forth below and summing 
the weighted values. In determining specific risk, the bank may 
offset and exclude from its calculations any matched positions in 
the identical issue (including positions in derivatives). Even if 
the issuer is the same, no offsetting is permitted between different 
issues since differences in coupon rates, liquidity, call features, 
etc., mean that prices may diverge in the short run. The categories 
and factors are:

------------------------------------------------------------------------
                                    Remaining maturity        Factor (in
           Category                    (contractual)           percent) 
------------------------------------------------------------------------
Government...................  N/A.........................         0.00
Qualifying...................  6 months or less............         0.25
                               6 to 12 months..............         1.00
                               over 12 months..............         1.60
Other........................  N/A.........................         8.00
------------------------------------------------------------------------

    b. The government category consists of all forms of debt 
instruments of central governments of the OECD-based group of 
countries \22\ including bonds, Treasury bills and other short-term 
instruments, as well as local currency instruments of non-OECD 
central governments to the extent that the bank has liabilities 
booked in that currency.

    \22\ As defined in section III.B. and III.C. of appendix A of 
this part.
---------------------------------------------------------------------------

    c. The qualifying category consists of securities of U.S. 
government-sponsored 

[[Page 38134]]
agencies, general obligation securities issued by states and other 
political subdivisions of the OECD-based group of countries, 
multilateral development banks, and debt instruments issued by U.S. 
depository institutions or OECD-banks that do not qualify as capital 
of the issuing institution.\23\ It also includes other securities, 
including revenue securities issued by states and other political 
subdivisions of the OECD-based group of countries, that are:

    \23\ U.S. government-sponsored agencies, multilateral 
development banks, and OECD banks are defined in section III.C. of 
appendix A of this part.
---------------------------------------------------------------------------

    i. Rated investment-grade by at least two nationally recognized 
credit rating services, or rated investment-grade by one nationally 
recognized credit rating agency and not less than investment-grade 
by any other credit rating agency; or
    ii. With the exception of securities issued by U.S. firms and 
subject to review by the FDIC, unrated but deemed to be of 
comparable investment quality by the reporting bank and issued by an 
entity which has securities listed on a recognized stock exchange.
    d. The other category consists of debt securities not meeting 
the criteria for government or qualifying securities. This would 
include non-OECD central government securities that do not meet the 
criteria for the government or qualifying categories. This category 
also includes instruments that qualify as capital issued by other 
banking organizations.
    e. The FDIC will consider the extent of a bank's position in 
non-investment grade instruments (sometimes referred to as ``high 
yield debt''). If those holdings are not well- diversified or 
otherwise represent a significant position to the institution, the 
FDIC may prevent a bank from offsetting positions in these 
instruments with other positions in qualifying instruments that may 
be offset when calculating its general market risk element. In 
addition, the FDIC may impose a specific risk factor as high as 16.0 
percent.
    2. General Market Risk. a. A bank may determine the general 
market risk element of the measure for market risk by using, on a 
continuous basis, either the maturity method (which uses 
standardized risk weights that approximate the price sensitivity of 
various instruments) or, subject to the FDIC's review, the duration 
method (in which the institution calculates the precise duration of 
each instrument, weighted by a specified change in interest rates).
    b. Both methods use a maturity-ladder that incorporates a series 
of ``time bands'' and ``zones'' to group together securities of 
similar maturities and that are designed to take into account 
differences in price sensitivities and interest rate volatilities 
across different maturities. Under either method, the general market 
risk element is the sum of a base charge that results from fully 
netting various risk-weighted positions and a series of additional 
charges (add-ons), which effectively ``disallow'' part of the 
previous full netting to address basis and yield curve risk.
    c. For each currency in which a bank has significant positions, 
a separate maturity ladder must be constructed. No netting of 
positions is permitted across different currencies. Offsetting 
positions of the same amount in the same issues, whether actual or 
notional, may be excluded from the calculation, as well as closely 
matched swaps, forwards, futures, and forward rate agreements (FRAs) 
that meet the conditions set out in paragraph A.3. of this section.
    d. In the maturity method, the bank distributes each long or 
short position (at current market value) of a debt instrument into 
the time bands of the maturity ladder. Fixed-rate instruments are 
allocated according to the remaining term to maturity and floating-
rate instruments according to the next repricing date. A callable 
bond trading above par is allocated according to its first call 
date, while a callable bond priced below par is allocated according 
to remaining maturity. Fixed-rate mortgage-backed securities, 
including collateralized mortgage obligations (CMOs) and real estate 
mortgage investment conduits (REMICs), are allocated according to 
their expected weighted average lives.
    e. Once all long and short positions are allocated into the 
appropriate time band, the long positions in each time band are 
summed and the short positions in each time band are summed. The 
summed long and/or short positions are multiplied by the appropriate 
risk-weight factor (reflecting the price sensitivity of the 
positions to changes in interest rates) to determine the risk-
weighted long and/or short position for each time band. The risk 
weights for each time band are set out in Table 1:

            Table 1.--Maturity Method: Time Bands and Weights           
------------------------------------------------------------------------
                                     Coupon less than 3 % and     Risk  
  Zone        Coupon 3% or more          zero-coupon bonds      weights 
------------------------------------------------------------------------
1.......  Up to 1 month............  Up to 1 month...........       0.00
          1 up to 3 months.........  1 up to 3 months........       0.20
          3 up to 6 months.........  3 up to 6 months........       0.40
          6 up to 12 months........  6 up to 12 months.......       0.70
2.......  1 up to 2 years..........  1 up to 1.9 years.......       1.25
          2 up to 3 years..........  1.9 up to 2.8 years.....       1.75
          3 up to 4 years..........  2.8 up to 3.6 years.....       2.25
3.......  4 up to 5 years..........  3.6 up to 4.3 years.....       2.75
          5 up to 7 years..........  4.3 up to 5.7 years.....       3.25
          7 up to 10 years.........  5.7 up to 7.3 years.....       3.75
          10 up to 15 years........  7.3 up to 9.3 years.....       4.50
          15 up to 20 years........  9.3 up to 10.6 years....       5.25
          Over 20 years............  10.6 up to 12 years.....       6.00
                                     12 up to 20 years.......       8.00
                                     Over 20 years...........      12.50
------------------------------------------------------------------------

    f. Next, within each time band for which there are risk-weighted 
long and short positions, the risk-weighted long and short positions 
are then netted, resulting in a single net risk-weighted long or 
short position for each time band. Since different instruments and 
different maturities may be included and netted within each time 
band, an addition to the risk measure, referred to as the vertical 
disallowance, is assessed to allow for basis risk. The vertical 
disallowance is 10.0 percent of the position eliminated by the 
intra-time band netting, that is, 10.0 percent of the smaller of the 
net risk-weighted long or net risk-weighted short position, or if 
the positions are equal, 10.0 percent of either position.24 The 
vertical disallowances for each time band are absolute values, that 
is, neither long nor short. The vertical disallowances for all time 
bands in the maturity ladder are summed and included as an element 
of the general market risk element.

    \24\ For example, if the sum of the weighted longs in a time 
band is $100 million and the sum of the weighted shorts is $90 
million, the vertical disallowance for the time band is 10.0 percent 
of $90 million, or $9 million.
---------------------------------------------------------------------------

    g. Next, within each zone for which there are risk-weighted long 
and short positions in different time bands, the weighted long and 
short positions in all of the time bands 

[[Page 38135]]
within the zone are then netted, resulting in a single net long or 
short position for each zone. Since different instruments and 
different maturities may be included and netted within each zone, an 
addition to the risk measure, referred to as the horizontal 
disallowance, is assessed to allow for the imperfect correlation of 
interest rates along the yield curve. The horizontal disallowance is 
calculated as a percentage of the position eliminated by the intra-
zone netting, that is, a percentage of the smaller of the net risk- 
weighted long or net risk-weighted short position, or if the 
positions are equal, a percentage of either position.25 The 
percent disallowance factors for intra-zone netting are set out in 
table 2. The horizontal disallowances, like the vertical 
disallowances, are absolute values that are summed and included as 
an element of the general market risk element.

    \25\ For example, if the sum of the weighted longs in the 1-3 
month time band in Zone 1 is $8 million and the sum of the weighted 
shorts in the 3-6 month time band is $10 million, the horizontal 
disallowance for the zone is forty percent of $8 million, or $3.2 
million.
---------------------------------------------------------------------------

    h. Next, risk-weighted long and short positions in different 
zones are then netted between the zones. Zone 1 and zone 2 are 
netted if possible, reducing or eliminating the net long or short 
position in zone 1 or zone 2 as appropriate. Zone 2 and zone 3 are 
then netted if possible, reducing or eliminating the net long or 
short position in zone 2 or zone 3 as appropriate. Zone 3 and zone 1 
are then netted if possible, reducing or eliminating the long or 
short position in zone 3 and zone 1 as appropriate. A horizontal 
disallowance is then assessed, calculated as a percentage of the 
position eliminated by the inter-zone netting. The horizontal 
disallowances for each zone are then summed as absolute values and 
included in the general market risk element. The percent 
disallowance factors for inter-zone netting are set out in Table 2:

                   Table 2.--Horizontal Disallowances                   
------------------------------------------------------------------------
                                                  Between               
                                    Within the    adjacent     Between  
  Zone           Time band             zone        zones     zones 1 & 3
                                    (percent)    (percent)    (percent) 
------------------------------------------------------------------------
1.......  0-1 month..............           40           40          100
          1-3 months.............                                       
          3-6 months.............                                       
          6-12 months............                                       
2.......  1-2 years..............           30           40          100
          2-3 years..............                                       
          3-4 years..............                                       
3.......  1-5 years..............           30           40          100
          5-7 years..............                                       
          7-10 years.............                                       
          10-15 years............                                       
          15-20 years............                                       
          over 20 years..........                                       
------------------------------------------------------------------------

    i. Finally, the net risk-weighted long or net risk-weighted 
short positions remaining in the zones are summed to reach a single 
net risk-weighted long or net risk-weighted short position for the 
bank's portfolio. The sum of the absolute value of this position and 
the vertical and horizontal disallowances is the general market risk 
element of the measure of market risk. An example of this 
calculation is in attachment II to this appendix.
    j. In the duration method, the bank, after calculating each 
instrument's modified duration 26 using a formula that is 
subject to FDIC review, multiplies that modified duration by the 
interest rate shock specified for an instrument of that duration in 
table 3. The resulting product (representing the expected percentage 
change in the price of the instrument for the given interest rate 
shock) is then multiplied by the current market value of the 
instrument. The resulting amount is then allocated as a long or 
short position into a time band in the maturity ladder in table 3 on 
the basis of the instrument's modified duration.27

    \26\ The duration of an instrument is its approximate percentage 
change in price for a 100 basis point parallel shift in the yield 
curve assuming that its cash flow does not change when the yield 
curve shifts. Modified duration is duration divided by a factor of 1 
plus the interest rate.
    \27\ For example, an instrument held by a bank with a maturity 
of 4 years and 3 months and a current market value of $1,000 might 
have a modified duration of 3.5 years. Based on its modified 
duration, it would be subjected to the 75-basis point interest rate 
shock, resulting in an expected price change of 2.625 percent 
(3.5 x 0.75). The corresponding expected change in price of $26.25, 
calculated as 2.625 percent of $1,000, would be slotted as a long 
position in the 3.3 to 4.0 year time band of the maturity ladder.
---------------------------------------------------------------------------

    k. Once all of the bank's traded debt instruments have been 
allocated into the maturity ladder, the bank conducts the same 
rounds of netting and disallowances described in paragraphs A.2.f. 
through h. of the maturity method in this section, with the 
exception that the vertical disallowance requirement for the 
duration method is 5.0 percent. Horizontal disallowances continue to 
be those set out in table 2. As with the maturity method, the sum of 
the absolute value of the final net position and the vertical and 
horizontal disallowances is the general market risk element of the 
measure for market risk:

   Table 3.--Duration Method: Time Bands and Assumed Changes in Yield   
------------------------------------------------------------------------
                                                               Assumed  
  Zone                        Time band                       change in 
                                                                yield   
------------------------------------------------------------------------
1.......  Up to 1 month....................................         1.00
          1 up to 3 months.................................         1.00
          3 up to 6 months.................................         1.00
          6 up to 12 months................................         1.00
2.......  1.0 up to 1.8 years..............................         0.90
          1.8 up to 2.6 years..............................         0.80
          2.6 up to 3.3 years..............................         0.75
3.......  3.3 up to 4.0 years..............................         0.75
          4.0 up to 5.2 years..............................         0.70
          5.2 up to 6.8 years..............................         0.65
          6.8 up to 8.6 years..............................         0.60
          8.6 up to 9.9 years..............................         0.60
          9.9 up to 11.3 years.............................         0.60
          11.3 up to 16.6 years............................         0.60
          Over 16.6 years 0.75.............................         0.60
------------------------------------------------------------------------

    3. Interest Rate Derivatives. a. Debt derivatives and other off-
balance-sheet positions that are affected by changes in interest 
rates are included in the measurement system under this section 
IV.A. (except for options and the associated underlyings, which are 
included in the measurement system under the treatment discussed in 
section IV.E. of this appendix C). A summary of the treatment for 
debt derivatives is set out in Attachment III to this appendix C.
    b. Derivatives are converted into positions in the relevant 
underlying instrument and are included in the calculation of the 
specific and general market risk elements. The amount to be included 
is the market value of the principal amount of the underlying or of 

[[Page 38136]]
the notional underlying. If the apparent notional amount of an 
instrument differs from the effective notional amount, a bank must 
use the effective notional amount.
    c. Futures and forward contracts (including FRAs) are broken 
down into a combination of a long position and short position in the 
notional security. The maturity of a future or a FRA is the period 
until delivery or exercise of the contract, plus the life of the 
underlying instrument.28 If a range of instruments may be 
delivered to fulfill the contract, the bank may choose which 
deliverable instrument goes into the maturity or duration ladder as 
the notional underlying. In the case of a future on a corporate bond 
index, positions are included at the market value of the notional 
underlying portfolio of securities.

    \28\ For example, a long position in a June three-month interest 
rate future (taken in April) is reported as a long position in a 
government security with a maturity of five months and a short 
position in a government security with a maturity of two months.
---------------------------------------------------------------------------

    d. i. Swaps are treated as two notional positions in the 
relevant instruments with appropriate maturities. The receiving side 
is treated as the long position and the paying side is treated as 
the short position.29 The separate sides of cross-currency 
swaps or forward foreign exchange transactions are allocated in the 
relevant maturity ladders for the currencies concerned. For swaps 
that pay or receive a fixed or floating interest rate against some 
other reference price, for example, an equity index, the long or 
short position attributable to the interest rate component is 
allocated into the appropriate repricing maturity category, with the 
long or short position attributable to the equity component being 
included in the equity framework set out in section IV.B. of this 
appendix C.

    \29\ For example, an interest rate swap under which a bank is 
receiving floating-rate interest and paying fixed is treated as a 
long position in a floating rate instrument with a maturity 
equivalent to the period until the next interest reset date and a 
short position in a fixed-rate instrument with a maturity equivalent 
to the remaining life of the swap.
---------------------------------------------------------------------------

    ii. A bank with a large swap book may, with prior approval of 
the FDIC, use alternative formulae to calculate the positions to be 
included in the maturity or duration ladder. For example, a bank 
could first convert the payments required by the swap into present 
values. For that purpose, each payment would be discounted using 
zero coupon yields, and the payment's present value entered into the 
appropriate time band using procedures that apply to zero (or low) 
coupon bonds. The net amounts would then be treated as bonds, and 
allocated into the general market risk framework. Such alternative 
treatments will, however, only be allowed if the FDIC is fully 
satisfied with the accuracy of the system being used; the positions 
calculated fully reflect the sensitivity of the cash flows to 
interest rate changes; and the positions are denominated in the same 
currency.
    e. A bank may offset long and short positions (both actual and 
notional) in identical derivative instruments with exactly the same 
issuer, coupon, currency, and maturity before allocating these 
positions into time bands. A matched position in a future and its 
corresponding underlying may also be fully offset and, thus, 
excluded from the calculation, except when the future comprises a 
range of deliverable instruments. However, if, among the range of 
deliverable instruments, there is a readily identifiable underlying 
instrument that is most profitable for the trader with a short 
position to deliver, positions in the futures contract and the 
instrument may be offset. Positions in different currencies are not 
subject to offset.
    f. Offsetting positions in the same category of instruments can 
in certain circumstances be regarded as matched and treated by the 
bank as a single net position which should be entered into the 
appropriate time band. To qualify for this treatment the positions 
must be based on the same underlying instrument, be of the same 
nominal value, and be denominated in the same currency. The separate 
sides of different swaps may also be ``matched'' subject to the same 
conditions. In addition:
    i. For futures, offsetting positions in the notional or 
underlying instruments to which the futures contract relates must be 
for identical instruments and the instruments must mature within 
seven days of each other;
    ii. For swaps and FRAs, the reference rate (for floating rate 
positions) must be identical and the coupon closely matched (i.e., 
within 15 basis points); and
    iii. For swaps, FRAs and forwards, the next interest reset date, 
or for fixed coupon positions or forwards the remaining maturity, 
must correspond within the following limits: If the reset (remaining 
maturity) dates occur within one month, then the reset dates must be 
on the same day; if the reset dates occur between one month and one 
year later, then the reset dates must occur within seven days of 
each other, or if the reset dates occur over one year later, then 
the reset dates must occur within thirty days of each other.
    g. Interest rate and currency swaps, FRAs, forward foreign 
exchange contracts and interest rate futures are not subject to a 
specific risk charge. This exemption also applies to futures on a 
short-term (e.g., LIBOR) interest rate index. However, in the case 
of futures contracts in which the underlying is a debt security, or 
an index representing a basket of debt securities, a specific risk 
charge will apply according to the category of the issuer as set out 
in paragraph A.2. of this section.

B. Equities

    1. Specific Risk. The specific risk element of the measure for 
market risk is calculated on the basis of the bank's gross equity 
positions, that is, the absolute sum of all long equity positions 
and of all short equity positions at current market value. The risk 
measure is 8.0 percent of that sum, unless the portfolio is both 
liquid and well-diversified, in which case the specific risk measure 
is 4.0 percent of the gross equity position. A specific risk measure 
of 2.0 percent applies to the net long or short position in a broad, 
diversified equity index and is viewed as necessary to provide for 
risks associated with contract execution. A portfolio that is liquid 
and well-diversified is characterized by a limited sensitivity to 
price changes of any single equity issue or closely related group of 
equity issues held in the portfolio. The volatility of the 
portfolio's value should not be dominated by the volatility of any 
individual equity issue or by equity issues from any single industry 
or economic sector. In general, such portfolios should be 
characterized by a large number of individual equity positions, with 
no single position representing a large portion of the portfolio's 
total market value. In addition, it would generally be the case that 
a sizeable proportion of the portfolio would be comprised of issues 
traded on organized exchanges or in well-established over-the-
counter markets.
    2. General Market Risk. The general market risk element of the 
measure for market risk is calculated on the difference between the 
sum of the long positions and the sum of the short positions (i.e., 
the overall net position in an equity market) at current market 
value. An overall net position must be separately calculated for 
each national market in which the bank holds equities. The general 
market risk element is 8.0 percent of the net position in each 
equity market.
    3. Matched Positions. Matched positions in each identical equity 
in each national market may be treated as offsetting and excluded 
from the capital calculation, with any remaining position included 
in the calculations for specific and general market risk. For 
example, a future in a given equity may be offset against an 
opposite cash position in the same equity.
    4. Equity Derivatives. a. Equity derivatives and other off-
balance-sheet positions that are affected by changes in equity 
prices are included in the measurement system under this section 
IV.B. (except for equity options, equity index options, and the 
associated underlying, which are included in the measurement system 
under the treatment discussed in section IV.E. of this appendix 
C).30 This includes futures and swaps on both individual 
equities and on equity indices. Equity derivatives should be 
converted into notional equity positions in the relevant underlying. 
A summary of the rules for equity derivatives is set out in 
attachment III to this appendix C.

    \30\ If equities are part of a forward contract (either equities 
to be received or to be delivered), any interest rate or foreign 
currency exposure from the other side of the contract should be 
appropriately included in sections IV.A. and IV.C. of this appendix 
C.
---------------------------------------------------------------------------

    b. Futures and forward contracts relating to individual equities 
should be reported at current market prices of the underlying. 
Futures relating to equity indices should be reported as the marked-
to-market value of the notional underlying equity portfolio. Equity 
swaps are treated as two notional positions, with the receiving side 
as the long position and the paying side as the short 
position.31 If one of the legs involves receiving/paying a 
fixed or floating interest rate, the exposure should be allocated 
into the appropriate repricing maturity band for debt securities. 

[[Page 38137]]
The stock index is covered by the equity treatment.

    \31\ For example, an equity swap in which a bank is receiving an 
amount based on the change in value of one particular equity or 
equity index and paying a different index will be treated as a long 
position in the former and a short position in the latter.
---------------------------------------------------------------------------

    c. In the case of futures-related arbitrage strategies, the 2.0 
percent specific risk charge applicable to broad diversified equity 
indices may be applied to only one index. The opposite position is 
exempt from a specific risk charge. The strategies qualifying for 
this treatment are:
    i. When the bank takes an opposite position in exactly the same 
index at different dates; or
    ii. When the bank has an opposite position in different but 
similar indices at the same date, subject to FDIC review.
    d. If a bank engages in a deliberate arbitrage strategy, in 
which a futures contract on a broad diversified equity index matches 
a basket of securities, it may exclude both positions from the 
standardized approach on condition that the trade has been 
deliberately entered into and separately controlled and the 
composition of the basket of stocks represents at least 90 percent 
of the market value of the index. In such a case, the minimum 
measure for market risk is 4.0 percent (that is, 2.0 percent of the 
gross value of the positions on each side) to reflect risk 
associated with executing the transaction. This applies even if all 
of the securities comprising the index are held in identical 
proportions. Any excess value of the securities comprising the 
basket over the value of the futures contract or excess value of the 
futures contract over the value of the basket is treated as an open 
long or short position.
    e. If a bank takes a position in depository receipts 32 
against an opposite position in the underlying equity, it may offset 
the position.

    \32\ Generally, depository receipts are instruments issued by a 
trust company or other depository institution evidencing the deposit 
of foreign securities and facilitating trading in such instruments 
on U.S. stock exchanges.
---------------------------------------------------------------------------

C. Foreign Exchange Risk

    1. The measure for market risk in foreign exchange covers the 
risk of holding or taking positions in foreign currencies, including 
gold, whether or not those positions are in the trading 
portfolio.33 The measure is calculated as 8.0 percent of the 
sum of the greater of a bank's total net open long positions or net 
open short positions in each currency and the net open position in 
gold.

    \33\ Gold is treated as a foreign exchange position rather than 
a commodity because its volatility is more in line with foreign 
currencies and banks manage it in a manner similar to foreign 
currencies.
---------------------------------------------------------------------------

    2. When calculating a bank's net open position in each currency 
and gold, positions in composite currencies, such as the ECU, may be 
either treated as a currency in their own right or split into their 
component parts on a consistent basis. Positions in gold (including 
futures and forwards) should be converted to U.S. currency at 
current spot rates. The bank's net open position in each currency is 
the sum of:
    a. The net spot position (i.e., all asset items less all 
liability items, including accrued interest earned but not yet 
received and accrued expenses, denominated in the currency in 
question);
    b. The net forward position.34 All foreign exchange 
derivative instruments and other off-balance-sheet positions that 
are affected by changes in exchange rates are included in the 
measurement system under this section IV.C. (except for options and 
their associated underlyings, which are included in the measurement 
system under the treatment discussed in section IV.E. of this 
appendix C). Forward currency positions should be valued at current 
spot market exchange rates, but for a bank in which the basis of its 
normal management accounting is to use net present values, forward 
positions may be discounted to net present values as an acceptable 
way of measuring currency positions for regulatory capital purposes;

    \34\ Where gold is part of a forward contract (quantity of gold 
to be received or to be delivered), any interest rate or foreign 
currency exposure from the other side of the contract should be 
reported as set out in section IV.A. (treating gold as a zero-coupon 
instrument) and this section.
---------------------------------------------------------------------------

    c. Guarantees (and similar instruments) that are certain to be 
called and are likely to be irrecoverable;
    d. At the discretion of the bank, net future income/expenses not 
yet accrued but already fully hedged. A bank that includes future 
income and expenses must do so on a consistent basis without 
selecting expected future flows in order to reduce the bank's 
position; and
    e. Any other item representing a profit or loss in foreign 
currencies.
    3. The measure for market risk of foreign exchange is determined 
by converting the net open position in each foreign currency at spot 
rates into U.S. currency. The risk measure is 8.0 percent of the 
overall net open foreign exchange position, which is determined by 
summing:
    a. The greater of the sum of the net long open positions or, the 
sum of the net short open positions; and
    b. The absolute value (that is, regardless of whether it is long 
or short) of the net open position in gold.35

    \35\ For example, a bank has the following net currency 
positions: Yen=+50, DM=+100, GB=+150, FFR=+-20, US$=-180, and 
gold=-35. The bank would sum its long positions (total=+300) and sum 
its short positions (total=-200). The bank's capital requirement for 
foreign exchange market risk would be: (300 (the larger of the 
summed long and short positions)+35 (gold)) x 8.0%=$26.80.
---------------------------------------------------------------------------

    4. If a bank is assessing its foreign exchange risk on a 
consolidated basis, it may be technically impractical in the case of 
some marginal operations to include the currency positions of a 
foreign branch or subsidiary of the bank. In such cases, the branch 
or subsidiary's internal limit in each currency may be used as a 
proxy for the positions, provided there is adequate ex post 
monitoring of actual positions complying with such limits. In these 
circumstances, the absolute value of the limits should be added to 
the net open position in each currency.
D. Commodities Risk

    1. Measurement Methods. The measure for market risk in 
commodities is calculated by either the simplified method or the 
maturity method. These methods are only appropriate for banks that 
conduct a limited amount of commodities business. All other banks 
must adopt an internal model measurement system conforming to the 
criteria in section III. of this appendix C.
    2. Base Measure. Under both the simplified and maturity methods, 
each long and short commodity position (spot or forward) is 
expressed in terms of the standard unit of measurement (such as 
barrels, kilos, or ounces). The positions are then converted at 
current spot rates into U.S. currency, with long and short positions 
in each category of commodities offset to arrive at the net open 
position in each commodity. Positions in different categories of 
commodities may not, generally, be offset. However, offsetting is 
permitted between different sub-categories of the same commodity if 
the sub-categories are deliverable against each other. Under the 
simplified or maturity method, the base measure for market risk is 
15.0 percent of the absolute value (i.e., neither long nor short) of 
the net open position in each commodity.36

    \36\ When the funding of a commodity position opens a bank to 
interest rate or foreign exchange exposure the relevant positions 
should be included in the measures of interest rate and foreign 
exchange risk described in sections IV.A. and IV.C. of this appendix 
C. When a commodity is part of a forward contract, any interest or 
foreign currency exposure from the other side of the contract should 
be appropriately included in sections IV.A. and IV.C. of this 
appendix C.
---------------------------------------------------------------------------

    3. Simplified Method. To protect a bank against basis risk, 
interest rate risk, and forward gap risk, the measure of market risk 
under the simplified method includes an additional 3.0 percent of 
the bank's gross positions, long plus short, in each commodity. In 
valuing gross positions in commodity derivatives for this purpose, a 
bank should use the current spot price. The total measure for 
commodities risk is thus the sum of the 15.0 percent base charges 
for each net commodity position and the 3.0 percent requirements on 
the gross commodity positions.
    4. Maturity Method. a. Under this method, a bank must allocate 
each long and short commodity position (converted into U.S. currency 
at current spot rates) into a maturity ladder with time bands as set 
out in table 4. A separate maturity ladder is used for each category 
of commodity. Physical commodities are allocated to the first time 
band:

                     Table 4.--Commodity Time Bands                     
------------------------------------------------------------------------
                               Time Bands                               
-------------------------------------------------------------------------
0-1 month                                                               
1-3 months                                                              
3-6 months                                                              
6-12 months                                                             
1-2 years                                                               
2-3 years                                                               
Over 3 years                                                            
------------------------------------------------------------------------

    b. In order to capture forward gap and interest rate risk within 
a time band (together sometimes referred to as curvature/spread 
risk), offsetting long and short positions in each time band are 
subject to an additional charge. Beginning with the shortest-term 
time band and continuing with subsequent time bands, the amount of 
the matched short 

[[Page 38138]]
positions plus the amount of the matched long position is multiplied by 
a spread rate of 1.5 percent.
    c. The unmatched net position from shorter-term time bands must 
be carried forward to offset exposures in longer-term time bands. A 
charge of 0.6 percent of the net position carried forward is added 
for each time band that the net position is carried forward.37 
The total measure for commodities risk is the sum of the 15.0 
percent base measurement for each net commodity position and the 
additional charges for matched positions and for unmatched positions 
carried forward. An example of this calculation is in attachment IV 
to this appendix C.

    \37\ For example, if $200 short is carried forward from the 3-6 
month time band to the 1-2 year time band, the capital charge would 
be $200 x .006 x 2=$2.40.
---------------------------------------------------------------------------

    5. Commodity derivatives and other off-balance-sheet positions 
that are affected by changes in commodity prices are included in the 
measurement system under this section IV.D. (except for options and 
the associated underlying, which are included in the measurement 
system under the treatment discussed in section IV.E. of this 
appendix C). Commodity derivatives are converted into notional 
commodity positions. Under the maturity method, the positions are 
allocated in maturity time bands as follows:
    a. Futures and forward contracts relating to individual 
commodities are incorporated in the measurement system as notional 
amounts (of, for example, barrels or kilos) that are converted to 
U.S. currency at current spot rates and are assigned a maturity 
according to expiration date;
    b. Commodity swaps in which one side of the contract is a fixed 
price and the other side is the current market price are 
incorporated as a series of positions equal to the notional amount 
of the contract at current spot rates, with one position 
corresponding to each payment on the swap and allocated in the 
maturity ladder accordingly. The positions are long positions if the 
bank is paying a fixed price and receiving a floating price, and 
short positions if the bank is receiving a fixed price and paying a 
floating price; 38 and

    \38\ If one of the sides of the transaction involves receiving/
paying a fixed or floating interest rate, that exposure should be 
allocated into the appropriate repricing maturity band in section 
IV.A. of this appendix C.
    c. Commodity swaps in which the sides of the transaction are in 
different commodities are included in the relevant reporting ladder. 
No offsetting is allowed unless the commodities are in the same sub-
category.

E. Options

    1. Three alternatives are available for a bank to use in 
measuring its market risk for options activities under the 
standardized approach. A bank that only has purchased options may 
use the simplified method set forth in paragraph E.2 of this 
section. A bank that also writes options may use the scenario method 
described in section IV.E.3., or the delta-plus method set forth in 
paragraph E.4. of this section.39 These methods may only be 
used by banks which, in relative terms, have limited options 
activities. Banks with more significant options business are 
expected to adopt an internal measurement system conforming to the 
criteria in section III of this appendix C. Regardless of the method 
used, specific risk related to the issuer of an instrument still 
applies to options positions for equities, equity indices and 
corporate debt securities as set forth in sections IV.A. and IV.B. 
of this appendix C. Options remain an element of risk-weighted 
assets under section II of appendix A of this part.

    \39\ Unless all their written option positions are hedged by 
perfectly matched long positions in exactly the same options, in 
which case there is no measure for market risk.
---------------------------------------------------------------------------

    2. Under the simplified and scenario methods, the positions for 
the options and the associated underlying, cash or forward, are not 
included in the measurement framework for debt securities, equities, 
foreign exchange or commodities risk as set forth in sections IV.A. 
through IV.D. of this appendix C. Rather, they are subject to the 
measure of market risk as calculated in this section. The risk 
measures calculated under this section should then be added to the 
risk measures for debt securities, equities, foreign exchange and 
commodities risk as appropriate. Under the delta-plus method, the 
delta equivalent position 40 for each option is included in the 
measurement frameworks set forth in sections IV.A. through IV.D. of 
this appendix C.

    \40\ The delta equivalent of an option is the option's delta 
value multiplied by its principal or notional value. The delta value 
of an option represents the expected change in the option's price as 
a proportion of a small change in the price of the underlying 
instrument. For example, an option whose price changes $1 for every 
$2 dollar change in the price of the underlying instrument has a 
delta of 0.50.
---------------------------------------------------------------------------

    3. A bank that has only a limited amount and range of purchased 
options may use the following simplified approach to measure its 
market risk exposure.
    a. For a bank with a long cash position and a long put or with a 
short cash position and a long call, the measure for market risk is 
the market value of the underlying instrument multiplied by the sum 
of the specific and general market risk requirements for the 
underlying (that is, the specific and general market risk 
requirements that would have applied to the underlying directly 
under sections IV.A. through IV.D. of this appendix C 41), less 
the amount the option is in the money (if any) bounded at 
zero.42

    \41\ Because some underlying instruments are not subject to a 
specific risk charge under sections IV.A through IV.D of this 
appendix C, such instruments will only be multiplied by the general 
market risk charge in making this calculation.
    \42\ For example, if a holder of 100 shares currently valued at 
$10 each has an equivalent put option with a strike price of $11, 
the risk measure would be: $1,000 x 16.0 percent (e.g., 8.0 percent 
specific plus 8.0 percent general market risk)=$160, less the amount 
the option is in the money ($11-$10) x 100=$100, i.e., the measure 
for market risk would be $60. A similar methodology applies for 
options for which the underlying is a foreign currency, a debt 
security or a commodity.
---------------------------------------------------------------------------

    b. For a bank with a long call or a long put, the measure for 
market risk is the lesser of:
    i. The market value of the underlying security multiplied by the 
sum of specific and general market risk requirements for the 
underlying (that is, the specific and general market risk 
requirements that would have applied to the underlying directly 
under sections IV.A. through IV.D. of this appendix C) 43; or

    \43\ See footnote 41 in section IV.E.3.a. of this appendix C.
---------------------------------------------------------------------------

    ii. The market value of the option.
    4. Under the scenario approach, a bank revalues its options and 
related hedging positions by changing the underlying rate or price 
over a specified range and by assuming different levels of 
volatility for that rate or price.
    a. For each of its option portfolios, a bank constructs a grid 
based on a fixed range of changes in the portfolio's risk factors 
and calculates changes in the value of the option portfolio at each 
point within the grid. For this purpose, an option portfolio 
consists of an option and any related hedging positions or multiple 
options and related hedging positions that are grouped together 
according to their remaining maturity or the type of underlying.
    b. Options based on interest rates and debt instruments are 
grouped into portfolios according to the maturity zones that are set 
forth in section IV.A. of this appendix C. (Zone 1 instruments have 
a remaining maturity of up to 1 year, zone 2 instruments have a 
remaining maturity from 1 year up to 4 years, and zone 3 instruments 
have a remaining maturity of 4 years or more.) These options and the 
associated hedging positions should be evaluated under the 
assumption that the relevant interest rates move simultaneously. For 
options based on equities, separate grids are constructed for each 
individual equity issue and index. For options based on exchange 
rates, separate grids are constructed for individual exchange rates. 
For options based on commodities, separate grids are constructed for 
each category of commodity (as defined in section IV.D. of this 
appendix C).
    c. For option portfolios with options based on equities, 
exchange rates, and commodities, the first dimension of the grid 
consists of rate or price changes within a specified range above and 
below the current market value of the underlying. For equities, the 
range is 12.0 percent (or in the case of an index 
8.0 percent); for exchange rates the range is 
8.0 percent; and for commodities the range is 
15.0 percent. For option portfolios with options based 
on interest rates, the range for the first dimension of the grid 
depends on the remaining maturity zone. The range for zone 1 is 
100 basis points, the range for zone 2 is 90 
basis points; and the range for zone 3 is 75 basis 
points. For all option portfolios, the range is divided into at 
least ten equally spaced intervals. The second dimension of each 
grid is a shift in the volatility of the underlying rate or price 
equal to 25.0 percent of the current volatility.44

    \44\ For example, if the underlying in an equity instrument with 
a current market value of $100 and a volatility of 20 percent, the 
first dimension of the grid would range from $88 to $112, divided 
into ten intervals of $2.40 and the second dimension would assume 
volatilities of 15 percent, 20 percent, and 25 percent.
---------------------------------------------------------------------------

    d. For each assumed volatility and rate or price change (a 
scenario), the bank revalues 

[[Page 38139]]
each option portfolio. The measure for market risk for the portfolio is 
the largest loss in value from among the scenario revaluations. The 
total measure for market risk for all option portfolios is the sum 
of the individual option portfolio measures.
    e. The FDIC will review the application of the scenario 
approach, particularly regarding the precise way the analysis is 
constructed. A bank using the scenario approach should meet the 
appropriate qualitative criteria set forth in section III.B. of this 
appendix C.
    5. Under the delta-plus method, a bank that writes options may 
include delta-weighted options positions within each measurement 
framework as set forth in sections IV.A. through IV.D. of this 
appendix C.
    a. Options positions should be measured as a position equal to 
the market value of the underlying instrument multiplied by the 
delta. In addition, a bank must measure the sensitivities of the 
option's gamma (the change of the delta for a given change in the 
price of the underlying) and vega (the sensitivity of the option 
price with respect to a change in volatility) to calculate the 
measure for market risk. These sensitivities may be calculated 
according to an exchange model approved by the FDIC or to the bank's 
own options pricing model, subject to review by the FDIC.
    b. For options with debt instruments or interest rates as the 
underlying instrument, delta-weighted options positions should be 
allocated into the debt instrument time bands in section IV.A. of 
this appendix C using a two-legged approach (as is used for other 
derivatives), requiring one entry at the time the underlying 
contract takes effect and one at the time the underlying contract 
matures.45 Floating rate instruments with caps or floors should 
be treated as a combination of floating rate securities and a series 
of European-style options.46 A bank must also calculate the 
gamma and vega for each such option position (including hedge 
positions). The results should be allocated into separate maturity 
ladders by currency. For interest rate options such as caps and 
floors, the delta and gamma should be expressed in terms of a 
hypothetical underlying security. Subsequently:

    \45\ For example, in April a purchased call option on a June 
three-month interest-rate future would be considered on the basis of 
its delta-equivalent value to a long position with a maturity of 
five months and a short position with a maturity of two months. The 
written option would be allocated as a long position with a maturity 
of two months and a short position with a maturity of five months.
    \46\ For example, the holder of a three-year floating rate bond 
indexed to six-month LIBOR with a cap of 15 percent would treat the 
bond as a debt security that reprices in six months, and a series of 
five written call options on a FRA with a strike rate of 15 percent, 
each allocated as a short position at the expiration date of the 
option and as a long position at the time the FRA matures.
---------------------------------------------------------------------------

    i. For gamma risk, for each time band, net gammas on short 
positions are multiplied by the risk weights set out in table 5 and 
by the square of the market value of the underlying instrument (net 
gammas on long positions may be disregarded);
    ii. For volatility risk, a bank calculates the risk measure for 
vega in each time band assuming a proportional shift in volatility 
of 25.0 percent;
    iii. The measure for market risk is the absolute value of the 
sum of the individual measures for net gammas on short positions 
plus the absolute value of the sum of the individual measures for 
vega risk for each time band; and
    iv. The delta plus method risk weights are:

                Table 5.--Delta Plus Method Risk Weights                
------------------------------------------------------------------------
                                     Modified                           
                                     duration     Assumed    Risk-weight
            Time-band                (average     interest       for    
                                   assumed for  rate change    gamma\1\ 
                                    time band)      (%)                 
------------------------------------------------------------------------
Under 1 month....................         0.00         1.00      0.00000
1 up to 3 months.................         0.20         1.00      0.00020
3 up to 6 months.................         0.40         1.00      0.00080
6 up to 12 months................         0.70         1.00      0.00245
1 up to 2 years..................         1.40         0.90      0.00794
2 up to 3 years..................         2.20         0.80      0.01549
3 up to 4 years..................         3.00         0.75      0.02531
4 up to 5 years..................         3.65         0.75      0.03747
5 up to 7 years..................         4.65         0.70      0.05298
7 up to 10 years.................         5.80         0.65      0.07106
10 up to 15 years................         7.50         0.60      0.10125
15 up to 20 years................         8.75         0.60      0.13781
Over 20 years....................        10.00         0.60      0.18000
------------------------------------------------------------------------
\1\ According to the Taylor expansion, the risk weights are calculated  
  as \1/2\ (modified duration x assumed interest rate change) \2\100.   

    c. For options with equities as the underlying, delta-weighted 
option positions should be incorporated in the measure of market 
risk set forth in section IV.B. of this appendix C. Individual 
equity issues and indices should be treated as separate underlyings. 
In addition to the measure for delta risk, a bank should apply a 
further charge for gamma and vega risk:
    i. For gamma risk, the net gammas on short positions for each 
underlying are multiplied by 0.72 percent (in the case of an 
individual equity) or 0.32 percent (in the case of an index as the 
underlying) and by the square of the market value of the underlying;
    ii. For volatility risk, a bank calculates the risk measure for 
vega for each underlying, assuming a proportional shift in 
volatility of 25.0 percent; and
    iii. The measure for market risk is the absolute value of the 
sum of the individual measures for net gammas on short positions 
plus the absolute value of the individual measures for vega risk.
    d. For options on foreign exchange and gold positions, the net 
delta (or delta-based) equivalent of the total book of foreign 
currency and gold options is incorporated into the measurement of 
the exposure in a net open position in each currency as set forth in 
section IV.C. of this appendix C. The gamma and vega risks should be 
measured as follows:
    i. For gamma risk, for each underlying exchange rate, net gammas 
on short positions are multiplied by 0.32 percent and by the square 
of the market value of the positions;
    ii. For volatility risk, a bank calculates the risk measure for 
vega for each currency pair and gold assuming a proportional shift 
in volatility of 25.0 percent; and
    iii. The measure for market risk is the absolute value of the 
sum of the individual measures for net gammas on short positions 
plus the absolute value of the sum of the individual measures for 
vega risk.
    e. For options on commodities, the delta-weighted positions are 
incorporated in one of the measures described in section IV.D. of 
this appendix C. In addition, a bank must apply a capital 
requirement for gamma and vega risk:
    i. For gamma risk, net gammas on short positions for each 
underlying are multiplied by 1.125 percent and by the square of the 
market value of the commodity;
    ii. For volatility risk, a bank calculates the risk measures for 
vega for each commodity assuming a proportional shift in volatility 
of 25.0 percent; and
    iii. The measure for market risk is the absolute value of the 
sum of the individual 

[[Page 38140]]
measures for net gammas on short positions plus the absolute value of 
the sum of the individual measures for vega risk.
    f. Under certain conditions and to a limited extent, the FDIC 
may permit banks that are significant traders in options with debt 
securities or interest rates as the underlying to net gammas on long 
and short positions and vegas across time bands. Such netting must 
be based on prudent and conservative assumptions and the bank must 
materially meet the qualitative standards set forth in section 
III.B. of this appendix C.
    g. A bank may base the calculation of vega risk on a volatility 
ladder in which the implied change in volatility varies with the 
maturity of the option. The assumed proportional shift in volatility 
must be at least 25.0 percent at the short end of the 
maturity spectrum. The proportional shift for longer maturities must 
be at least as stringent in statistical terms as the 25.0 percent 
shift at the short end.
    h. A bank should also monitor the risks of rho (the rate of 
change of the value of the option with respect to the interest rate) 
and theta ( the rate of change of the value of the option with 
respect to time).

Attachments to Appendix C

Attachment I--Sample Calculation of Eligible Tier 1, Tier 2, and Tier 3 
Capital for the Risk-Based Capital Ratio Adjusted for Market Risk

    a. In each example the weighted-risk assets are $8000 and the 
market risk-adjusted assets are $625 (capital requirement for market 
risk=$50 $50 x 12.5=$625):
    Example 1: A bank has the following qualifying capital: Tier 
1=$600, Tier 2=$100, Tier 3=$1000.
    (1) The minimum capital requirement for credit risk is $640 
($8000 x 8.0%). This requirement could be satisfied with $540 of 
Tier 1 capital and $100 of Tier 2 capital.
    (2) The remaining capital available for market risk would be: 
Tier 1=$60, Tier 2=0, and Tier 3=$1000. The minimum capital 
requirement for market risk is $50 ($625 x 8.0%). Eligible Tier 3 
capital would be limited to $125 ($50 x 2.5).
    (3) The Tier 1 capital required to support market risk could be 
satisfied by allocating $14 ($50 x .285), with eligible Tier 3 
capital used for market risk being $36 ($50 x $14).
    (4) Total qualifying and eligible capital would be: $540 (Tier 
1)+$100 (Tier 2)+$60 (Tier 1, comprising $14 allocated for market 
risk and $46 unallocated)+$36 (Tier 3)=$736. The bank's ratio of 
qualifying and eligible capital to weighted-risk assets adjusted for 
market risk would be: $736/$8,625)=8.5%.
    Example 2: A bank has the following qualifying capital: Tier 
1=$500, Tier 2=$140, Tier 3=$600.
    (1) The minimum capital requirement for credit risk is $640 
($8000 x 8.0%). This requirement could be satisfied with $500 of 
Tier 1 capital and $140 of Tier 2 capital.
    (2) The remaining capital available for market risk would be: 
Tier 1=0, Tier 2=$0, and Tier 3=$600. Eligible Tier 3 capital would 
be limited to $0 (0 x 2.5). Because there is no Tier 1 capital 
required to support market risk, no eligible Tier 3 capital may be 
used for market risk.
    (3) Total qualifying and eligible capital would be: $500 (Tier 
1)+$140 (Tier 2)=$640. The bank's ratio of qualifying and eligible 
capital to weighted-risk assets adjusted for market risk would be: 
$640/$8,625)=7.4%
    b. In both of the examples described in paragraph a. of this 
attachment the total of Tier 2 and Tier 3 capital for credit and 
market risk is not greater than 100 percent of Tier 1 capital for 
credit and market risk and the total of Tier 2 capital for credit 
risk is not greater than 100 percent of Tier 1 capital for credit 
risk.
Attachment II--Sample Calculation of General Market Risk for Debt 
Instruments Using the Maturity Method

    a. A bank with the following positions would allocate them into 
a maturity ladder as shown below:
    i. Qualifying bond, $13.33mn market value, remaining maturity 8 
years, coupon 8%;
    ii. Government bond, $75mn market value, remaining maturity 2 
months, coupon 7%;
    iii. Interest rate swap, $150mn, bank receives floating rate 
interest and pays fixed, next interest reset after 12 months, 
remaining life of swap is 8 years (assumes the current interest rate 
is identical to the one the swap is based on); and
    iv. Long position in interest rate future, $50mn, delivery date 
after 6 months, life of underlying government security is 3.5 years 
(assumes the current interest rate is identical to the one the swap 
is based on).

----------------------------------------------------------------------------------------------------------------
                                     Risk                                                                       
  Zone    Time band and position    weight       Risk-weighted          Net time-band        Net zone positions 
                                     [%]            position              positions                             
----------------------------------------------------------------------------------------------------------------
1.......  0-1 Month.............       0.00                                                                     
          1-3 Months............       0.20  Long 0.15............  Long 0.15............  Long 1.00            
          Long 75 Gov. Bond.....                                                                                
          3-6 Months............       0.40  Short 0.20...........  Short 0.20...........                       
          Short 50 Future.......                                                                                
          6-12 Months...........       0.70  Long 1.05............  Long 1.05............                       
          Long 150 Swap.........                                                                                
2.......  1-2 yrs...............       1.25                                                                     
          2-3 yrs...............       1.75                                                                     
          3-4 yrs...............       2.25  Long 1.125...........  Long 1.125...........  Long 1.125           
          Long 50 Future........                                                                                
3.......  4-5 yrs...............       2.75                                                                     
          5-7 yrs...............       3.25                                                                     
          7-10 yrs..............       3.75  Short 5.625..........  Short 5.125..........  Short 5.125          
          Short 150 Swap........                                                                                
          Long 13.33............             Long 0.50............                                              
          Qual. Bond............                                                                                
          10-15 yrs.............       4.50                                                                     
          15-20 yrs.............       5.25                                                                     
          Over 20 yrs...........       6.00                                                                     
----------------------------------------------------------------------------------------------------------------

    b. A vertical disallowance would be calculated for time band 7-
10 years. It would be 10 percent of the positions eliminated by 
netting in the time band--10.0 x 0.5 = 0.05 ($50,000).
    c. A horizontal disallowance would be calculated for zone 1. It 
would be 40 percent of the positions eliminated by netting in the 
zone--40.0 x 0.20 = 0.80 ($80,000). The remaining net position in 
zone 1 would be long 1.00.
    d. A horizontal disallowance would be calculated for adjacent 
zones 2 and 3. It would be 40 percent of the positions eliminated by 
netting between the zones--40.0 x 1.125 = 0.45 ($450,000). The 
remaining position in zone 3 would be short 4.00.
    e. A horizontal disallowance would be calculated between zones 1 
and 3. It would be 100 percent of the positions eliminated by 
netting between the zones--100 x 1.00 = 1.00 ($1,000,000).
    f. The remaining net open position for the bank would be 3.00 
($3,000,000). The total capital requirement for general market risk 
for this portfolio would be:

The vertical disallowance..................................      $50,000
Horizontal disallowance in zone 1..........................      80,000 

[[Page 38141]]
                                                                        
The horizontal disallowance between zones 2 and 3..........      450,000
The horizontal disallowance between zones 1 and 3..........    1,000,000
The overall net open position..............................    3,000,000
                                                            ------------
    Total requirement for general market risk..............   $4,580,000
                                                                        


Attachment III--Summary of Treatment for Interest Rate and Equity 
Derivatives

           Summary of Treatment for Interest Rate Derivatives           
------------------------------------------------------------------------
                              Specific risk                             
         Instrument               charge      General market risk charge
------------------------------------------------------------------------
Exchange-Traded Future:                                                 
    Government security.....  No...........  Yes, as two positions.     
    Corporate debt security.  Yes..........  Yes, as two positions.     
    Index on short-term       No...........  Yes, as two positions.     
     interest rates (e.g.                                               
     LIBOR).                                                            
OTC Forward:                                                            
    Government security.....  No...........  Yes, as two positions.     
    Corporate debt security.  Yes..........  Yes, as two positions.     
    Index on short-term       No...........  Yes, as two positions.     
     interest rates.                                                    
    FRAs, Swaps.............  No...........  Yes, as two positions.     
    Forward foreign exchange  No...........  Yes, as one position in    
                                              each currency.            
Options:                                                                
    Government security.....  No...........  For each type of           
                                              transaction, either:      
    Corporate debt security.  Yes..........  (a) Carve out together with
                                              the associated hedging    
                                              positions                 
    Index on short-term       No...........  --simplified method        
     interest rates.                                                    
                                             --scenario analysis        
                                             --internal models, or      
                                             (b) General market risk    
                                              charge according to the   
                                              Delta-plus method (gamma  
                                              and vega receive separate 
                                              capital charges).         
------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument.     
  There remains a separate capital requirement for counterparty credit  
  risk.                                                                 


               Summary of Treatment for Equity Derivatives              
------------------------------------------------------------------------
                              Specific risk                             
         Instrument               charge      General market risk charge
------------------------------------------------------------------------
Exchange-Traded or OTC                                                  
 Future:                                                                
    Individual equity.......  Yes..........  Yes, as underlying.        
    Index...................  2.0%.........  Yes, as underlying.        
Options:                                                                
    Individual equity.......  Yes..........  For each type of           
                                              transactions either:      
    Index...................  2.0%.........  (a) Carve out together with
                                              the associated hedging    
                                              positions                 
                                             --simplified method        
                                             --scenario approach        
                                             --internal models, or      
                                             (b) General market risk    
                                              requirement according to  
                                              the Delta-plus method     
                                              (gamma and vega receive   
                                              separate capital charges).
                                                                        
------------------------------------------------------------------------
Note: Specific risk charges relate to the issuer of the instrument.     
  There remains a separate capital requirement for counterparty credit  
  risk.                                                                 

Attachment IV--Sample Calculation of Standardized Approach for 
Commodities Risk

----------------------------------------------------------------------------------------------------------------
                                                            Spread                                      Capital 
         Time-band                     Position              rate           Capital calculation          charge 
----------------------------------------------------------------------------------------------------------------
0 up to 1 month............  None                                                                               
1 up to 3 months...........  None                                                                               
3 up to 6 months...........  Long 800...................       1.5%  800 long + 800 short (matched)           24
                                                                      x  1.5%=.                                 
                             Short 1000.................  .........  200 short carried forward to 1-2        2.4
                                                                      yrs, capital charge: 200 x 2 x            
                                                                      0.6%=.                                    
6 up to 12 months..........  None                                                                               
1 up to 2 yrs..............  Long 600...................  .........  200 long + 200 short (matched)            6
                                                                      x  1.5%=.                                 
                                                                     400 long carried forward to over        4.8
                                                                      3 yrs capital charge: 400 x 2 x           
                                                                      0.6%=.                                    
2 up to 3 yrs..............  None                                                                               
Over 3 years...............  Short 600..................  .........  400 long + 400 short (matched)           12
                                                                      x  1.5%=.                                 
                                                                     Net position: 200 capital                30
                                                                      charge: 200 x 15.0%=.                     
----------------------------------------------------------------------------------------------------------------
Note: Assume all positions are in the same commodity and converted at current spot rates into U.S. dollars. The 
  total capital requirement would be $79.2.                                                                     

Attachment V--Sample Calculation for Delta-Plus Method for Options

    a. Assume a bank has a European short call option on a commodity 
with an exercise price of 490 and a market value of the underlying 
12 months from the expiration of the option at 500; a risk-free 
interest rate at 8% per annum, and the volatility at 20 percent. The 
current delta for this position is according to the Black-Scholes 
formula -0.721 (that is, the price of the option changes by -0.721 
if the price of the underlying moves by 1). The gamma is -0.0034 
(that is, the delta changes by 

[[Page 38142]]
-0.0034 from -0.721 to -0.7244 if the price of the underlying moves by 
1). The current value of the option is 65.48.
    b. The first step under the delta-plus method is to multiply the 
market value of the commodity by the absolute value of the delta. 
500 x 0.721=360.5. The delta-weighted position is then incorporated 
into the measure described in section IV.D. of this appendix C E. If 
the bank uses the maturity approach and no other positions exist, 
the delta-weighted position is multiplied by 0.15 to calculate the 
capital requirement for delta. 360.5 x 0.15=54.075.
    c. The capital requirement for gamma is calculated according to 
the Taylor expansion by multiplying the absolute value of the 
assumed gamma of -0.0034 by 1.125% and by the square of the market 
value of the underlying. 0.0034 x 0.0125  x 5002=10.625.
    d. The capital requirement for vega is calculated next. The 
assumed current (implied) volatility is 20%. Since only an increase 
in volatility carries a risk of loss for a short call option, the 
volatility has to be increased by a relative shift of 25%. This 
means that the vega capital requirement has to be calculated on the 
basis of a change in volatility of 5 percentage points from 20% to 
25% in this example. According to the Black-Scholes formula used 
here, the vega equals 168. Thus, a 1% or 0.01 increase in volatility 
increases the value of the option by 1.68. Accordingly, a change in 
volatility of 5 percentage points increases the value of 
5 x 1.68=8.4. This is the capital requirement for vega risk. The 
total capital requirement would be $73.10 (54.075+10.625+8.4).

    By Order of the Board of Directors.

    Dated at Washington, DC, this 11th day of July 1995.
Jerry L. Langley,
Executive Secretary.
[FR Doc. 95-17542 Filed 7-24-95; 8:45 am]
BILLING CODES 4810-33-P; 6210-01-P; 6714-01-P
Last Updated 10/31/2011 communications@fdic.gov