Basel Committee on Banking Supervision

Market risk: the risk of losses in on- and off-balance sheet risk positions arising from movements in market prices.

Notional value: the notional value of a derivative instrument is equal to the number of units underlying the instrument multiplied by the current market value of each unit of the underlying.

Trading desk: a group of traders or trading accounts in a business line within a bank that follows defined trading strategies with the goal of generating revenues or maintaining market presence from assuming and managing risk.

Pricing model: a model that is used to determine the value of an instrument (mark-to-market or mark-to-model) as a function of pricing parameters or to determine the change in the value of an instrument as a function of risk factors. A pricing model may be the combination of several calculations; eg a first valuation technique to compute a price, followed by valuation adjustments for risks that are not incorporated in the first step.

Financial instrument: any contract that gives rise to both a financial asset of one entity and a financial liability or equity instrument of another entity. Financial instruments include both primary financial instruments (or cash instruments) and derivative financial instruments.

Instrument: the term used to describe financial instruments, instruments on foreign exchange (FX) and commodities.

Embedded derivative: a component of a financial instrument that includes a non-derivative host contract. For example, the conversion option in a convertible bond is an embedded derivative.

Look-through approach: an approach in which a bank determines the relevant capital requirements for a position that has underlyings (such as an index instrument, multi-underlying option, or an equity investment in a fund) as if the underlying positions were held directly by the bank.

Risk factor: a principal determinant of the change in value of an instrument (eg an exchange rate or interest rate).

Risk position: the portion of the current value of an instrument that may be subject to losses due to movements in a risk factor. For example, a bond denominated in a currency different to a bank’s reporting currency has risk positions in general interest rate risk, credit spread risk (non-securitisation) and FX risk, where the risk positions are the potential losses to the current value of the instrument that could occur due to a change in the relevant underlying risk factors (interest rates, credit spreads, or exchange rates).

Risk bucket: a defined group of risk factors with similar characteristics.

Risk class: a defined list of risks that are used as the basis for calculating market risk capital requirements: general interest rate risk, credit spread risk (non-securitisation), credit spread risk (securitisation: non-correlation trading portfolio), credit spread risk (securitisation: correlation trading portfolio), FX risk, equity risk and commodity risk.

Sensitivity: a bank’s estimate of the change in value of an instrument due to a small change in one of its underlying risk factors. Delta and vega risks are sensitivities.

Delta risk: the linear estimate of the change in value of a financial instrument due to a movement in the value of a risk factor. The risk factor could be the price of an equity or commodity, or a change in an interest rate, credit spread or FX rate.

Vega risk: the potential loss resulting from the change in value of a derivative due to a change in the implied volatility of its underlying.

Curvature risk: the additional potential loss beyond delta risk due to a change in a risk factor for financial instruments with optionality. In the standardised approach in the market risk framework, it is based on two stress scenarios involving an upward shock and a downward shock to each regulatory risk factor.

Value at risk (VaR): a measure of the worst expected loss on a portfolio of instruments resulting from market movements over a given time horizon and a pre-defined confidence level.

Expected shortfall (ES): a measure of the average of all potential losses exceeding the VaR at a given confidence level.

Jump-to-default (JTD): the risk of a sudden default. JTD exposure refers to the loss that could be incurred from a JTD event.

Liquidity horizon: the time assumed to be required to exit or hedge a risk position without materially affecting market prices in stressed market conditions.

Basis risk: the risk that prices of financial instruments in a hedging strategy are imperfectly correlated, reducing the effectiveness of the hedging strategy.

Diversification: the reduction in risk at a portfolio level due to holding risk positions in different instruments that are not perfectly correlated with one another.

Hedge: the process of counterbalancing risks from exposures to long and short risk positions in correlated instruments.

Offset: the process of netting exposures to long and short risk positions in the same risk factor.

Standalone: being capitalised on a stand-alone basis means that risk positions are booked in a discrete, non-diversifiable trading book portfolio so that the risk associated with those risk positions cannot diversify, hedge or offset risk arising from other risk positions, nor be diversified, hedged or offset by them.

Real prices: a term used for assessing whether risk factors pass the risk factor eligibility test. A price will be considered real if it is (i) a price from an actual transaction conducted by the bank, (ii) a price from an actual transaction between other arm’s length parties (eg at an exchange), or (iii) a price taken from a firm quote (ie a price at which the bank could transact with an arm’s length party).

Modellable risk factor: risk factors that are deemed modellable, based on the number of representative real price observations and additional qualitative principles related to the data used for the calibration of the ES model. Risk factors that do not meet the requirements for the risk factor eligibility test are deemed as non-modellable risk factors (NMRF).

Backtesting: the process of comparing daily actual and hypothetical profits and losses with model-generated VaR measures to assess the conservatism of risk measurement systems.

Profit and loss (P&L) attribution (PLA): a method for assessing the robustness of banks’ risk management models by comparing the risk-theoretical P&L predicted by trading desk risk management models with the hypothetical P&L.

Trading desk risk management model: the trading desk risk management model (pertaining to in-scope desks) includes all risk factors that are included in the bank’s ES model with supervisory parameters and any risk factors deemed not modellable, which are therefore not included in the ES model for calculating the respective regulatory capital requirement, but are included in NMRFs.

Actual P&L (APL): the actual P&L derived from the daily P&L process. It includes intraday trading as well as time effects and new and modified deals, but excludes fees and commissions as well as valuation adjustments for which separate regulatory capital approaches have been otherwise specified as part of the rules or which are deducted from Common Equity Tier 1. Any other valuation adjustments that are market risk-related must be included in the APL. As is the case for the hypothetical P&L, the APL should include FX and commodity risks from positions held in the banking book.

Hypothetical P&L (HPL): the daily P&L produced by revaluing the positions held at the end of the previous day using the market data at the end of the current day. Commissions, fees, intraday trading and new/modified deals, valuation adjustments for which separate regulatory capital approaches have been otherwise specified as part of the rules and valuation adjustments which are deducted from CET1 are excluded from the HPL. Valuation adjustments updated daily should usually be included in the HPL. Time effects should be treated in a consistent manner in the HPL and risk-theoretical P&L.

Risk-theoretical P&L (RTPL): the daily desk-level P&L that is predicted by the valuation engines in the trading desk risk management model using all risk factors used in the trading desk risk management model (ie including the NMRFs).

Credit valuation adjustment (CVA): an adjustment to the valuation of a derivative transaction to account for the credit risk of contracting parties.

CVA risk: the risk of changes to CVA arising from changes in credit spreads of the contracting parties, compounded by changes to the value or variability in the value of the underlying of the derivative transaction.

Market risk is defined as the risk of losses arising from movements in market prices. The risks subject to market risk capital requirements include but are not limited to:

1. default risk, interest rate risk, credit spread risk, equity risk, foreign exchange (FX) risk and commodities risk for trading book instruments; and
2. FX risk and commodities risk for banking book instruments.

All transactions, including forward sales and purchases, shall be included in the calculation of capital requirements as of the date on which they were entered into. Although regular reporting will in principle take place only at intervals (quarterly in most countries), banks are expected to manage their market risk in such a way that the capital requirements are being met on a continuous basis, including at the close of each business day. Supervisory authorities have at their disposal a number of effective measures to ensure that banks do not window-dress by showing significantly lower market risk positions on reporting dates. Banks will also be expected to maintain strict risk management systems to ensure that intraday exposures are not excessive. If a bank fails to meet the capital requirements at any time, the national authority shall ensure that the bank takes immediate measures to rectify the situation.

A matched currency risk position will protect a bank against loss from movements in exchange rates, but will not necessarily protect its capital adequacy ratio. If a bank has its capital denominated in its domestic currency and has a portfolio of foreign currency assets and liabilities that is completely matched, its capital/asset ratio will fall if the domestic currency depreciates. By running a short risk position in the domestic currency, the bank can protect its capital adequacy ratio, although the risk position would lead to a loss if the domestic currency were to appreciate. Supervisory authorities are free to allow banks to protect their capital adequacy ratio in this way and exclude certain currency risk positions from the calculation of net open currency risk positions, subject to meeting each of the following conditions:

1. The risk position is taken or maintained for the purpose of hedging partially or totally against the potential that changes in exchange rates could have an adverse effect on its capital ratio.
2. The risk position is of a structural (ie non-dealing) nature such as positions stemming from:
   1. investments in affiliated but not consolidated entities denominated in foreign currencies; or
   2. investments in consolidated subsidiaries or branches denominated in foreign currencies.
3. The exclusion is limited to the amount of the risk position that neutralises the sensitivity of the capital ratio to movements in exchange rates.
4. The exclusion from the calculation is made for at least six months.
5. The establishment of a structural FX position and any changes in its position must follow the bank’s risk management policy for structural FX positions. This policy must be pre-approved by the national supervisor.
6. Any exclusion of the risk position needs to be applied consistently, with the exclusionary treatment of the hedge remaining in place for the life of the assets or other items.
7. The bank is subject to a requirement by the national supervisor to document and have available for supervisory review the positions and amounts to be excluded from market risk capital requirements.

No FX risk capital requirement need apply to positions related to items that are deducted from a bank’s capital when calculating its capital base.

Holdings of capital instruments that are deducted from a bank’s capital or risk weighted at 1250% are not allowed to be included in the market risk framework. This includes:

1. holdings of the bank’s own eligible regulatory capital instruments; and
2. holdings of other banks’, securities firms’ and other financial entities’ eligible regulatory capital instruments, as well as intangible assets, where the national supervisor requires that such assets are deducted from capital.
3. Where a bank demonstrates that it is an active market-maker, then a national supervisor may establish a dealer exception for holdings of other banks’, securities firms’, and other financial entities’ capital instruments in the trading book. In order to qualify for the dealer exception, the bank must have adequate systems and controls surrounding the trading of financial institutions’ eligible regulatory capital instruments.

In the same way as for credit risk and operational risk, the capital requirements for market risk apply on a worldwide consolidated basis.

1. Supervisory authorities may permit banking and financial entities in a group which is running a global consolidated trading book and whose capital is being assessed on a global basis to include just the net short and net long risk positions no matter where they are booked.¹
2. Supervisory authorities may grant this treatment only when the standardised approach in MAR20 to MAR23 permits a full offset of the risk position (ie risk positions of the opposite sign do not attract a capital requirement).
3. Nonetheless, there will be circumstances in which supervisory authorities demand that the individual risk positions be taken into the measurement system without any offsetting or netting against risk positions in the remainder of the group. This may be needed, for example, where there are obstacles to the quick repatriation of profits from a foreign subsidiary or where there are legal and procedural difficulties in carrying out the timely management of risks on a consolidated basis.
4. Moreover, all supervisory authorities will retain the right to continue to monitor the market risks of individual entities on a non-consolidated basis to ensure that significant imbalances within a group do not escape supervision. Supervisory authorities will be especially vigilant in ensuring that banks do not conceal risk positions on reporting dates in such a way as to escape measurement.

In determining its market risk for regulatory capital requirements, a bank may choose between two broad methodologies: the standardised approach and internal models approach (IMA) for market risk, described in MAR20 to MAR23 and MAR30 to MAR33, respectively, subject to the approval of the national authorities. Supervisors may allow banks that maintain smaller or simpler trading books to use the simplified alternative to the standardised approach as set out in MAR40.

1. To determine the appropriateness of the simplified alternative for use by a bank for the purpose of its market risk capital requirements, supervisors may wish to consider the following indicative criteria:
   1. The bank should not be a global systemically important bank (G-SIB).
   2. The bank should not use the IMA for any of its trading desks.
   3. The bank should not hold any correlation trading positions.
2. The use of the simplified alternative is subject to supervisory approval and oversight. Supervisors can mandate that banks with relatively complex or sizeable risks in particular risk classes apply the full standardised approach instead of the simplified alternative, even if those banks meet the indicative eligibility criteria referred to above.

All banks, except for those that are allowed to use the simplified alternative as set out in MAR11.7, must calculate the capital requirements using the standardised approach. Banks that are approved by the supervisor to use the IMA for market risk capital requirements must also calculate and report the capital requirement values calculated as set out below.

1. A bank that uses the IMA for any of its trading desks must also calculate the capital requirement under the standardised approach for all instruments across all trading desks, regardless of whether those trading desks are eligible for the IMA.
2. In addition, a bank that uses the IMA for any of its trading desks must calculate the standardised approach capital requirement for each trading desk that is eligible for the IMA as if that trading desk were a standalone regulatory portfolio (ie with no offsetting across trading desks). This will:
   1. serve as an indication of the fallback capital requirement for those desks that fail the eligibility criteria for inclusion in the bank’s internal model as outlined in MAR30, MAR32 and MAR33;
   2. generate information on the capital outcomes of the internal models relative to a consistent benchmark and facilitate comparison in implementation between banks and/or across jurisdictions;
   3. monitor over time the relative calibration of standardised and modelled approaches, facilitating adjustments as needed; and
   4. provide macroprudential insight in an ex ante consistent format.

All banks must calculate the market risk capital requirement using the standardised approach for the following:

1. securitisation exposures; and
2. equity investments in funds that cannot be looked through but are assigned to the trading book in accordance to the conditions set out in RBC25.8(5)(b).

For the purposes of market risk capital calculations, a trading desk is a group of traders or trading accounts that implements a well defined business strategy operating within a clear risk management structure.

Trading desks are defined by the bank but subject to the regulatory approval of the supervisor for capital purposes.

1. A bank should be allowed to propose the trading desk structure per their organisational structure, consistent with the requirements set out in MAR12.4.
2. A bank must prepare a policy document for each trading desk it defines, documenting how the bank satisfies the key elements in MAR12.4.
3. Supervisors will treat the definition of the trading desk as part of the initial model approval for the trading desk, as well as ongoing approval:
   1. Supervisors may determine, based on the size of the bank’s overall trading operations, whether the proposed trading desk definitions are sufficiently granular.
   2. Supervisors should check that the bank’s proposed definition of trading desk meets the criteria listed in key elements set out in MAR12.4.

Within this supervisory approved trading desk structure, banks may further define operational subdesks without the need for supervisory approval. These subdesks would be for internal operational purposes only and would not be used in the market risk capital framework.

The key attributes of a trading desk are as follows:

1. A trading desk for the purposes of the regulatory capital charge is an unambiguously defined group of traders or trading accounts.
   1. A trading account is an indisputable and unambiguous unit of observation in accounting for trading activity.
   2. The trading desk must have one head trader and can have up to two head traders provided their roles, responsibilities and authorities are either clearly separated or one has ultimate oversight over the other.
      (i)

      The head trader must have direct oversight of the group of traders or trading accounts.

      (ii)

      Each trader or each trading account in the trading desk must have a clearly defined specialty (or specialities).

   3. Each trading account must only be assigned to a single trading desk. The desk must have a clearly defined risk scope consistent with its pre-established objectives. The scope should include specification of the desk’s overall risk class and permitted risk factors.
   4. There is a presumption that traders (as well as head traders) are allocated to one trading desk. A bank can deviate from this presumption and may assign an individual trader to work across several trading desks provided it can be justified to the supervisor on the basis of sound management, business and/or resource allocation reasons. Such assignments must not be made for the only purpose of avoiding other trading desk requirements (eg to optimise the likelihood of success in the backtesting and profit and loss attribution tests).
   5. The trading desk must have a clear reporting line to bank senior management, and should have a clear and formal compensation policy clearly linked to the pre-established objectives of the trading desk.
2. A trading desk must have a well defined and documented business strategy, including an annual budget and regular management information reports (including revenue, costs and risk-weighted assets).
   1. There must be a clear description of the economics of the business strategy for the trading desk, its primary activities and trading/hedging strategies.
      (i)

      Economics: what is the economics behind the strategy (eg trading on the shape of the yield curve)? How much of the activities are customer driven? Does it entail trade origination and structuring, or execution services, or both?

      (ii)

      Primary activities: what is the list of permissible instruments and, out of this list, which are the instruments most frequently traded?

      (iii)

      Trading/hedging strategies: how would these instruments be hedged, what are the expected slippages and mismatches of hedges, and what is the expected holding period for positions?

   2. The management team at the trading desk (starting from the head trader) must have a clear annual plan for the budgeting and staffing of the trading desk.
   3. A trading desk’s documented business strategy must include regular Management Information reports, covering revenue, costs and risk-weighted assets for the trading desk.
3. A trading desk must have a clear risk management structure.
   1. Risk management responsibilities: the bank must identify key groups and personnel responsible for overseeing the risk-taking activities at the trading desk.
   2. A trading desk must clearly define trading limits based on the business strategy of the trading desk and these limits must be reviewed at least annually by senior management at the bank. In setting limits, the trading desk must have:
      (i)

      well defined trading limits or directional exposures at the trading desk level that are based on the appropriate market risk metric (eg sensitivity of credit spread risk and/or jump-to-default for a credit trading desk), or just overall notional limits; and

      (ii)

      well defined trader mandates.

   3. A trading desk must produce, at least weekly, appropriate risk management reports. This would include, at a minimum: profit and loss reports, which would be periodically reviewed, validated and modified (if necessary) by Product Control; and internal and regulatory risk measure reports, including trading desk value-at-risk (VaR) / expected shortfall (ES), trading desk VaR/ES sensitivities to risk factors, backtesting and p-value.

The bank must prepare, evaluate, and have available for supervisors the following for all trading desks:

1. inventory ageing reports;
2. daily limit reports including exposures, limit breaches, and follow-up action;
3. reports on intraday limits and respective utilisation and breaches for banks with active intraday trading; and
4. reports on the assessment of market liquidity.

Any foreign exchange or commodity positions held in the banking book must be included in the market risk capital requirement as set out in MAR11.1. For regulatory capital calculation purposes, these positions will be treated as if they were held on notional trading desks within the trading book.

The risk-weighted assets for market risk under the standardised approach are determined by multiplying the capital requirements calculated as set out in MAR20 to MAR23 by 12.5.

The standardised approach must be calculated and reported to the relevant supervisor on a monthly basis. Subject to supervisory approval, the standardised approach for market risks arising from non-banking subsidiaries of a bank may be calculated and reported to the relevant supervisor on a quarterly basis.

A bank must also determine its regulatory capital requirements for market risk according to the standardised approach for market risk at the demand of its supervisor.

The standardised approach capital requirement is the simple sum of three components: the capital requirement under the sensitivities-based method, the default risk capital (DRC) requirement and the residual risk add-on (RRAO).

1. The capital requirement under the sensitivities-based method must be calculated by aggregating three risk measures - delta, vega and curvature, as set out in MAR21:
   1. Delta: a risk measure based on sensitivities of an instrument to regulatory delta risk factors.
   2. Vega: a risk measure based on sensitivities to regulatory vega risk factors.
   3. Curvature: a risk measure which captures the incremental risk not captured by the delta risk measure for price changes in an option. Curvature risk is based on two stress scenarios involving an upward shock and a downward shock to each regulatory risk factor.
   4. The above three risk measures specify risk weights to be applied to the regulatory risk factor sensitivities. To calculate the overall capital requirement, the risk-weighted sensitivities are aggregated using specified correlation parameters to recognise diversification benefits between risk factors. In order to address the risk that correlations may increase or decrease in periods of financial stress, a bank must calculate three sensitivities-based method capital requirement values, based on three different scenarios on the specified values for the correlation parameters as set out in MAR21.6 and MAR21.7.
2. The DRC requirement captures the jump-to-default risk for instruments subject to credit risk as set out in MAR22.2. It is calibrated based on the credit risk treatment in the banking book in order to reduce the potential discrepancy in capital requirements for similar risk exposures across the bank. Some hedging recognition is allowed for similar types of exposures (corporates, sovereigns, and local governments/municipalities).
3. Additionally, the Committee acknowledges that not all market risks can be captured in the standardised approach, as this might necessitate an unduly complex regime. An RRAO is thus introduced to ensure sufficient coverage of market risks for instruments specified in MAR23.2. The calculation method for the RRAO is set out in MAR23.8.

For the purpose of calculating the credit spread risk capital requirement under the sensitivities based method and the DRC requirement, the correlation trading portfolio is defined as the set of instruments that meet the requirements of (1) or (2) below.

1. The instrument is a securitisation position that meets the following requirements:
   1. The instrument is not a re-securitisation position, nor a derivative of securitisation exposures that does not provide a pro rata share in the proceeds of a securitisation tranche, where the definition of securitisation positon is identical to that used in the credit risk framework.
   2. All reference entities are single-name products, including single-name credit derivatives, for which a liquid two-way market exists,² including traded indices on these reference entities.
   3. The instrument does not reference an underlying that is treated as a retail exposure, a residential mortgage exposure, or a commercial mortgage exposure under the standardised approach to credit risk.
   4. The instrument does not reference a claim on a special purpose entity.
2. The instrument is a non-securitisation hedge to a position described above.

The sensitivities of financial instruments to a prescribed list of risk factors are used to calculate the delta, vega and curvature risk capital requirements. These sensitivities are risk-weighted and then aggregated, first within risk buckets (risk factors with common characteristics) and then across buckets within the same risk class as set out in MAR21.8 to MAR21.14. The following terminology is used in the sensitivities-based method:

1. Risk class: seven risk classes are defined (in MAR21.39 to MAR21.89).
   1. General interest rate risk (GIRR)
   2. Credit spread risk (CSR): non-securitisations
   3. CSR: securitisations (non-correlation trading portfolio, or non-CTP)
   4. CSR: securitisations (correlation trading portfolio, or CTP)
   5. Equity risk
   6. Commodity risk
   7. Foreign exchange (FX) risk
2. Risk factor: variables (eg an equity price or a tenor of an interest rate curve) that affect the value of an instrument as defined in MAR21.8 to MAR21.14.
3. Bucket: a set of risk factors that are grouped together by common characteristics (eg all tenors of interest rate curves for the same currency), as defined in MAR21.39 to MAR21.89.
4. Risk position: the portion of the risk of an instrument that relates to a risk factor. Methodologies to calculate risk positions for delta, vega and curvature risks are set out in MAR21.3 to MAR21.5 and MAR21.15 to MAR21.26.
   1. For delta and vega risks, the risk position is a sensitivity to a risk factor.
   2. For curvature risk, the risk position is based on losses from two stress scenarios.
5. Risk capital requirement: the amount of capital that a bank should hold as a consequence of the risks it takes; it is computed as an aggregation of risk positions first at the bucket level, and then across buckets within a risk class defined for the sensitivities-based method as set out in MAR21.3 to MAR21.7.

In applying the sensitivities-based method, all instruments held in trading desks as set out in MAR12 and subject to the sensitivities-based method (ie excluding instruments where the value at any point in time is purely driven by an exotic underlying as set out in MAR23.3), are subject to delta risk capital requirements. Additionally, the instruments specified in (1) to (4) are subject to vega and curvature risk capital requirements:

1. Any instrument with optionality.³
2. Any instrument with an embedded prepayment option⁴ – this is considered an instrument with optionality according to above (1). The embedded option is subject to vega and curvature risk with respect to interest rate risk and CSR (non-securitisation and securitisation) risk classes. When the prepayment option is a behavioural option the instrument may also be subject to the residual risk add-on (RRAO) as per MAR23. The pricing model of the bank must reflect such behavioural patterns where relevant. For securitisation tranches, instruments in the securitised portfolio may have embedded prepayment options as well. In this case the securitisation tranche may be subject to the RRAO.
3. Instruments whose cash flows cannot be written as a linear function of underlying notional. For example, the cash flows generated by a plain-vanilla option cannot be written as a linear function (as they are the maximum of the spot and the strike). Therefore, all options are subject to vega risk and curvature risk. Instruments whose cash flows can be written as a linear function of underlying notional are instruments without optionality (eg cash flows generated by a coupon bearing bond can be written as a linear function) and are not subject to vega risk nor curvature risk capital requirements.
4. Curvature risks may be calculated for all instruments subject to delta risk, not limited to those subject to vega risk as specified in (1) to (3) above. For example, where a bank manages the non-linear risk of instruments with optionality and other instruments holistically, the bank may choose to include instruments without optionality in the calculation of curvature risk. This treatment is allowed subject to all of the following restrictions:
   1. Use of this approach shall be applied consistently through time.
   2. Curvature risk must be calculated for all instruments subject to the sensitivities-based method.

As set out in MAR21.1, the capital requirement under the sensitivities-based method is calculated by aggregating delta, vega and curvature capital requirements. The relevant paragraphs that describe this process are as follows:

1. The risk factors for delta, vega and curvature risks for each risk class are defined in MAR21.8 to MAR21.14.
2. The methods to risk weight sensitivities to risk factors and aggregate them to calculate delta and vega risk positions for each risk class are set out in MAR21.4 and MAR21.15 to MAR21.95, which include the definition of delta and vega sensitivities, definition of buckets, risk weights to apply to risk factors, and correlation parameters.
3. The methods to calculate curvature risk are set out in MAR21.5 and MAR21.96 to MAR21.101, which include the definition of buckets, risk weights and correlation parameters.
4. The risk class level capital requirement calculated above must be aggregated to obtain the capital requirement at the entire portfolio level as set out in MAR21.6 and MAR21.7.

For each risk class, a bank must determine its instruments’ sensitivity to a set of prescribed risk factors, risk weight those sensitivities, and aggregate the resulting risk-weighted sensitivities separately for delta and vega risk using the following step-by-step approach:

1. For each risk factor (as defined in MAR21.8 to MAR21.14), a sensitivity is determined as set out in MAR21.15 to MAR21.38.
2. Sensitivities to the same risk factor must be netted to give a net sensitivity s_k across all instruments in the portfolio to each risk factor k. In calculating the net sensitivity, all sensitivities to the same given risk factor (eg all sensitivities to the one-year tenor point of the three-month Euribor swap curve) from instruments of opposite direction should offset, irrespective of the instrument from which they derive. For instance, if a bank’s portfolio is made of two interest rate swaps on three-month Euribor with the same fixed rate and same notional but of opposite direction, the GIRR on that portfolio would be zero.
3. The weighted sensitivity WS_k is the product of the net sensitivity s_k and the corresponding risk weight RW_k as defined in MAR21.39 to MAR21.95.
4. Within bucket aggregation: the risk position for delta (respectively vega) bucket b, K_b, must be determined by aggregating the weighted sensitivities to risk factors within the same bucket using the prescribed correlation set out in the following formula, where the quantity within the square root function is floored at zero:
5. Across bucket aggregation: The delta (respectively vega) risk capital requirement is calculated by aggregating the risk positions across the delta (respectively vega) buckets within each risk class, using the corresponding prescribed correlations as set out in the following formula, where:
   1. for all risk factors in bucket b, and in bucket c.
   2. If these values for and described in above MAR21.4(5)(a) produce a negative number for the overall sum of , the bank is to calculate the delta (respectively vega) risk capital requirement using an alternative specification whereby:
      (i)

      for all risk factors in bucket b; and

      (ii)

      for all risk factors in bucket c.

      

For each risk class, to calculate curvature risk capital requirements a bank must apply an upward shock and a downward shock to each prescribed risk factor and calculate the incremental loss for instruments sensitive to that risk factor above that already captured by the delta risk capital requirement using the following step-by-step approach:

1. For each instrument sensitive to curvature risk factor k, an upward shock and a downward shock must be applied to k. The size of shock (ie risk weight) is set out in MAR21.98 and MAR21.99.
   1. For example for GIRR, all tenors of all the risk free interest rate curves within a given currency (eg three-month Euribor, six-month Euribor, one year Euribor, etc for the euro) must be shifted upward applying the risk weight as set out in MAR21.99. The resulting potential loss for each instrument, after the deduction of the delta risk positions, is the outcome of the upward scenario. The same approach must be followed on a downward scenario.
   2. If the price of an instrument depends on several risk factors, the curvature risk must be determined separately for each risk factor.
2. The net curvature risk capital requirement, determined by the values and for a bank's portfolio for risk factor k described in above MAR21.5(1) is calculated by the formula below. It calculates the aggregate incremental loss beyond the delta capital requirement for the prescribed shocks, where
   1. i is an instrument subject to curvature risks associated with risk factor k;
   2. is the current level of risk factor k;
   3. is the price of instrument i at the current level of risk factor k;
   4. and denote the price of instrument i after is shifted (ie "shocked") upward and downward respectively;
   5. is the risk weight for curvature risk factor k for instrument i; and
   6. is the delta sensitivity of instrument i with respect to the delta risk factor that corresponds to curvature risk factor k, where:
      (i)

      for the FX and equity risk classes, is the delta sensitivity of instrument i; and

      (ii)

      for the GIRR, CSR and commodity risk classes, is the sum of delta sensitivities to all tenors of the relevant curve of instrument i with respect to curvature risk factor k.

      

      

3. Within bucket aggregation: the curvature risk exposure must be aggregated within each bucket using the corresponding prescribed correlation as set out in the following formula, where:
   1. The bucket level capital requirement ( ) is determined as the greater of the capital requirement under the upward scenario ( ) and the capital requirement under the downward scenario ( ). Notably, the selection of upward and downward scenarios is not necessarily the same across the high, medium and low correlations scenarios specified in MAR21.6.
      (i)

      Where , this shall be termed "selecting the upward scenario".

      (ii)

      Where , this shall be termed "selecting the downward scenario".

      (iii)

      In the specific case where if , it is deemed that the upward scenario is selected; otherwise the downward scenario is selected.

   2. takes the value 0 if and both have negative signs and the value 1 otherwise.

      

      

4. Across bucket aggregation: curvature risk positions must then be aggregated across buckets within each risk class, using the corresponding prescribed correlations , where:
   1. for all risk factors in bucket b, when the upward scenario has been selected for bucket b in above (3)(a). otherwise; and
   2. takes the value 0 if and both have negative signs and 1 otherwise.

In order to address the risk that correlations increase or decrease in periods of financial stress, the aggregation of bucket level capital requirements and risk class level capital requirements per each risk class for delta, vega, and curvature risks as specified in MAR21.4 to MAR21.5 must be repeated, corresponding to three different scenarios on the specified values for the correlation parameter (correlation between risk factors within a bucket) and (correlation across buckets within a risk class).

1. Under the “medium correlations” scenario, the correlation parameters and as specified in MAR21.39 to MAR21.101 apply.
2. Under the “high correlations” scenario, the correlation parameters and that are specified in MAR21.39 to MAR21.101 are uniformly multiplied by 1.25, with and subject to a cap at 100%.
3. Under the “low correlations” scenario, the correlation parameters and that are specified in MAR21.39 to MAR21.101 are replaced by and .

The total capital requirement under the sensitivities-based method is aggregated as follows:

1. For each of three correlation scenarios, the bank must simply sum up the separately calculated delta, vega and curvature capital requirements for all risk classes to determine the overall capital requirement for that scenario.
2. The sensitivities-based method capital requirement is the largest capital requirement from the three scenarios.
   1. For the calculation of capital requirements for all instruments in all trading desks using the standardised approach as set out in MAR11.8(1) and MAR20.2 and MAR33.40, the capital requirement is calculated for all instruments in all trading desks.
   2. For the calculation of capital requirements for each trading desk using the standardised approach as if that desk were a standalone regulatory portfolio as set out in MAR11.8(2), the capital requirements under each correlation scenario are calculated and compared at each trading desk level, and the maximum for each trading desk is taken as the capital requirement.

GIRR factors

1. Delta GIRR: the GIRR delta risk factors are defined along two dimensions: (i) a risk-free yield curve for each currency in which interest rate-sensitive instruments are denominated and (ii) the following tenors: 0.25 years, 0.5 years, 1 year, 2 years, 3 years, 5 years, 10 years, 15 years, 20 years and 30 years, to which delta risk factors are assigned.⁵
   1. The risk-free yield curve per currency should be constructed using money market instruments held in the trading book that have the lowest credit risk, such as overnight index swaps (OIS). Alternatively, the risk-free yield curve should be based on one or more market-implied swap curves used by the bank to mark positions to market. For example, interbank offered rate (BOR) swap curves.
   2. When data on market-implied swap curves described in above (1)(a) are insufficient, the risk-free yield curve may be derived from the most appropriate sovereign bond curve for a given currency. In such cases the sensitivities related to sovereign bonds are not exempt from the CSR capital requirement: when a bank cannot perform the decomposition y=r+cs, any sensitivity to y is allocated both to the GIRR and to CSR classes as appropriate with the risk factor and sensitivity definitions in the standardised approach. Applying swap curves to bond-derived sensitivities for GIRR will not change the requirement for basis risk to be captured between bond and credit default swap (CDS) curves in the CSR class.
   3. For the purpose of constructing the risk-free yield curve per currency, an OIS curve (such as Eonia or a new benchmark rate) and a BOR swap curve (such as three-month Euribor or other benchmark rates) must be considered two different curves. Two BOR curves at different maturities (eg three-month Euribor and six-month Euribor) must be considered two different curves. An onshore and an offshore currency curve (eg onshore Indian rupee and offshore Indian rupee) must be considered two different curves.
2. The GIRR delta risk factors also include a flat curve of market-implied inflation rates for each currency with term structure not recognised as a risk factor.
   1. The sensitivity to the inflation rate from the exposure to implied coupons in an inflation instrument gives rise to a specific capital requirement. All inflation risks for a currency must be aggregated to one number via simple sum.
   2. This risk factor is only relevant for an instrument when a cash flow is functionally dependent on a measure of inflation (eg the notional amount or an interest payment depending on a consumer price index). GIRR risk factors other than for inflation risk will apply to such an instrument notwithstanding.
   3. Inflation rate risk is considered in addition to the sensitivity to interest rates from the same instrument, which must be allocated, according to the GIRR framework, in the term structure of the relevant risk-free yield curve in the same currency.
3. The GIRR delta risk factors also include one of two possible cross-currency basis risk factors⁶ for each currency (ie each GIRR bucket) with the term structure not recognised as a risk factor (ie both cross-currency basis curves are flat).
   1. The two cross-currency basis risk factors are basis of each currency over USD or basis of each currency over EUR. For instance, an AUD-denominated bank trading a JPY/USD cross-currency basis swap would have a sensitivity to the JPY/USD basis but not to the JPY/EUR basis.
   2. Cross-currency bases that do not relate to either basis over USD or basis over EUR must be computed either on "basis over USD" or "basis over EUR" but not both. GIRR risk factors other than for cross-currency basis risk will apply to such an instrument notwithstanding.
   3. Cross-currency basis risk is considered in addition to the sensitivity to interest rates from the same instrument, which must be allocated, according to the GIRR framework, in the term structure of the relevant risk-free yield curve in the same currency.
4. Vega GIRR: within each currency, the GIRR vega risk factors are the implied volatilities of options that reference GIRR-sensitive underlyings; as defined along two dimensions:⁷
   1. The maturity of the option: the implied volatility of the option as mapped to one or several of the following maturity tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years.
   2. The residual maturity of the underlying of the option at the expiry date of the option: the implied volatility of the option as mapped to two (or one) of the following residual maturity tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years.
5. Curvature GIRR:
   1. The GIRR curvature risk factors are defined along only one dimension: the constructed risk-free yield curve per currency with no term structure decomposition. For example, the euro, Eonia, three-month Euribor and six-month Euribor curves must be shifted at the same time in order to compute the euro-relevant risk-free yield curve curvature risk capital requirement. For the calculation of sensitivities, all tenors (as defined for delta GIRR) are to be shifted in parallel.
   2. There is no curvature risk capital requirement for inflation and cross-currency basis risks.
6. The treatment described in above (1)(b) for delta GIRR also applies to vega GIRR and curvature GIRR risk factors.

CSR non-securitisation risk factors

1. Delta CSR non-securitisation: the CSR non-securitisation delta risk factors are defined along two dimensions:
   1. the relevant issuer credit spread curves (bond and CDS); and
   2. the following tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years.
2. Vega CSR non-securitisation: the vega risk factors are the implied volatilities of options that reference the relevant credit issuer names as underlyings (bond and CDS); further defined along one dimension - the maturity of the option. This is defined as the implied volatility of the option as mapped to one or several of the following maturity tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years.
3. Curvature CSR non-securitisation: the CSR non-securitisation curvature risk factors are defined along one dimension: the relevant issuer credit spread curves (bond and CDS). For instance, the bond-inferred spread curve of an issuer and the CDS-inferred spread curve of that same issuer should be considered a single spread curve. For the calculation of sensitivities, all tenors (as defined for CSR) are to be shifted in parallel.

CSR securitisation: non-CTP risk factors

1. For securitisation instruments that do not meet the definition of CTP as set out in MAR20.5 (ie, non-CTP), the sensitivities of delta risk factors (ie CS01) must be calculated with respect to the spread of the tranche rather than the spread of the underlying of the instruments.
2. Delta CSR securitisation (non-CTP): the CSR securitisation delta risk factors are defined along two dimensions:
   1. Tranche credit spread curves; and
   2. The following tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years to which delta risk factors are assigned.
3. Vega CSR securitisation (non-CTP): Vega risk factors are the implied volatilities of options that reference non-CTP credit spreads as underlyings (bond and CDS); further defined along one dimension - the maturity of the option. This is defined as the implied volatility of the option as mapped to one or several of the following maturity tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years.
4. Curvature CSR securitisation (non-CTP): the CSR securitisation curvature risk factors are defined along one dimension, the relevant tranche credit spread curves (bond and CDS). For instance, the bond-inferred spread curve of a given Spanish residential mortgage-backed security (RMBS) tranche and the CDS-inferred spread curve of that given Spanish RMBS tranche would be considered a single spread curve. For the calculation of sensitivities, all the tenors are to be shifted in parallel.

CSR securitisation: CTP risk factors

1. For securitisation instruments that meet the definition of a CTP as set out in MAR20.5, the sensitivities of delta risk factors (ie CS01) must be computed with respect to the names underlying the securitisation or nth-to-default instrument.
2. Delta CSR securitisation (CTP): the CSR correlation trading delta risk factors are defined along two dimensions:
   1. the relevant underlying credit spread curves (bond and CDS); and
   2. the following tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years, to which delta risk factors are assigned.
3. Vega CSR securitisation (CTP): the vega risk factors are the implied volatilities of options that reference CTP credit spreads as underlyings (bond and CDS), as defined along one dimension, the maturity of the option. This is defined as the implied volatility of the option as mapped to one or several of the following maturity tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years.
4. Curvature CSR securitisation (CTP): the CSR correlation trading curvature risk factors are defined along one dimension, the relevant underlying credit spread curves (bond and CDS). For instance, the bond-inferred spread curve of a given name within an iTraxx series and the CDS-inferred spread curve of that given underlying would be considered a single spread curve. For the calculation of sensitivities, all the tenors are to be shifted in parallel.

Equity risk factors

1. Delta equity: the equity delta risk factors are:
   1. all the equity spot prices; and
   2. all the equity repurchase agreement rates (equity repo rates).
2. Vega equity:
   1. The equity vega risk factors are the implied volatilities of options that reference the equity spot prices as underlyings as defined along one dimension, the maturity of the option. This is defined as the implied volatility of the option as mapped to one or several of the following maturity tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years.
   2. There is no vega risk capital requirement for equity repo rates.
3. Curvature equity:
   1. The equity curvature risk factors are all the equity spot prices.
   2. There is no curvature risk capital requirement for equity repo rates.

Commodity risk factors

1. Delta commodity: the commodity delta risk factors are all the commodity spot prices. However for some commodities such as electricity (which is defined to fall within bucket 3 (energy – electricity and carbon trading) in MAR21.82 the relevant risk factor can either be the spot or the forward price, as transactions relating to commodities such as electricity are more frequent on the forward price than transactions on the spot price. Commodity delta risk factors are defined along two dimensions:
   1. legal terms with respect to the delivery location⁸ of the commodity; and
   2. time to maturity of the traded instrument at the following tenors: 0 years, 0.25 years, 0.5 years, 1 year, 2 years, 3 years, 5 years, 10 years, 15 years, 20 years and 30 years.
2. Vega commodity: the commodity vega risk factors are the implied volatilities of options that reference commodity spot prices as underlyings. No differentiation between commodity spot prices by the maturity of the underlying or delivery location is required. The commodity vega risk factors are further defined along one dimension, the maturity of the option. This is defined as the implied volatility of the option as mapped to one or several of the following maturity tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years.
3. Curvature commodity: the commodity curvature risk factors are defined along only one dimension, the constructed curve (ie no term structure decomposition) per commodity spot prices. For the calculation of sensitivities, all tenors (as defined for delta commodity) are to be shifted in parallel.

FX risk factors

1. Delta FX: the FX delta risk factors are defined below.
   1. The FX delta risk factors are all the exchange rates between the currency in which an instrument is denominated and the reporting currency. For transactions that reference an exchange rate between a pair of non-reporting currencies, the FX delta risk factors are all the exchange rates between:
      (i)

      the reporting currency; and

      (ii)

      both the currency in which an instrument is denominated and any other currencies referenced by the instrument.⁹

   2. Subject to supervisory approval, FX risk may alternatively be calculated relative to a base currency instead of the reporting currency. In such case the bank must account for not only:
      (i)

      the FX risk against the base currency; but also

      (ii)

      the FX risk between the reporting currency and the base currency (ie translation risk).

   3. The resulting FX risk calculated relative to the base currency as set out in (b) is converted to the capital requirements in the reporting currency using the spot reporting/base exchange rate reflecting the FX risk between the base currency and the reporting currency.
   4. The FX base currency approach may be allowed under the following conditions:
      (i)

      To use this alternative, a bank may only consider a single currency as its base currency; and

      (ii)

      The bank shall demonstrate to the relevant supervisor that calculating FX risk relative to their proposed base currency provides an appropriate risk representation for their portfolio (for example, by demonstrating that it does not inappropriately reduce capital requirements relative to those that would be calculated without the base currency approach) and that the translation risk between the base currency and the reporting currency is taken into account.

2. Vega FX: the FX vega risk factors are the implied volatilities of options that reference exchange rates between currency pairs; as defined along one dimension, the maturity of the option. This is defined as the implied volatility of the option as mapped to one or several of the following maturity tenors: 0.5 years, 1 year, 3 years, 5 years and 10 years.
3. Curvature FX: the FX curvature risk factors are defined below.
   1. The FX curvature risk factors are all the exchange rates between the currency in which an instrument is denominated and the reporting currency. For transactions that reference an exchange rate between a pair of non-reporting currencies, the FX risk factors are all the exchange rates between:
      (i)

      the reporting currency; and

      (ii)

      both the currency in which an instrument is denominated and any other currencies referenced by the instrument.

   2. Where supervisory approval for the base currency approach has been granted for delta risks, FX curvature risks shall also be calculated relative to a base currency instead of the reporting currency, and then converted to the capital requirements in the reporting currency using the spot reporting/base exchange rate.
4. No distinction is required between onshore and offshore variants of a currency for all FX delta, vega and curvature risk factors.

Sensitivities for each risk class must be expressed in the reporting currency of the bank.

For each risk factor defined in MAR21.8 to MAR21.14, sensitivities are calculated as the change in the market value of the instrument as a result of applying a specified shift to each risk factor, assuming all the other relevant risk factors are held at the current level as defined in MAR21.17 to MAR21.38.

In calculating the risk capital requirement under the sensitivities-based method in MAR21, the bank must determine each delta and vega sensitivity and curvature scenario based on instrument prices or pricing models that an independent risk control unit within a bank uses to report market risks or actual profits and losses to senior management.

A key assumption of the standardised approach for market risk is that a bank’s pricing models used in actual profit and loss reporting provide an appropriate basis for the determination of regulatory capital requirements for all market risks. To ensure such adequacy, banks must at a minimum establish a framework for prudent valuation practices that include the requirements of CAP50.

Delta GIRR: the sensitivity is defined as the PV01. PV01 is measured by changing the interest rate r at tenor t (r_t) of the risk-free yield curve in a given currency by 1 basis point (ie 0.0001 in absolute terms) and dividing the resulting change in the market value of the instrument (V_i) by 0.0001 (ie 0.01%) as follows, where:

1. r_t is the risk-free yield curve at tenor t;
2. cs_t is the credit spread curve at tenor t; and
3. V_i is the market value of the instrument i as a function of the risk-free interest rate curve and credit spread curve:

Delta CSR non-securitisation, securitisation (non-CTP) and securitisation (CTP): the sensitivity is defined as CS01. The CS01 (sensitivity) of an instrument i is measured by changing a credit spread cs at tenor t (cs_t) by 1 basis point (ie 0.0001 in absolute terms) and dividing the resulting change in the market value of the instrument (V_i) by 0.0001 (ie 0.01%) as follows:

Delta equity spot: the sensitivity is measured by changing the equity spot price by 1 percentage point (ie 0.01 in relative terms) and dividing the resulting change in the market value of the instrument (V_i) by 0.01 (ie 1%) as follows, where:

1. k is a given equity;
2. EQ_k is the market value of equity k; and
3. V_i is the market value of instrument i as a function of the price of equity k.

Delta equity repo rates: the sensitivity is measured by applying a parallel shift to the equity repo rate term structure by 1 basis point (ie 0.0001 in absolute terms) and dividing the resulting change in the market value of the instrument V_i by 0.0001 (ie 0.01%) as follows, where:

1. k is a given equity;
2. is the repo term structure of equity k; and
3. V_iis the market value of instrument i as a function of the repo term structure of equity k.

Delta commodity: the sensitivity is measured by changing the commodity spot price by 1 percentage point (ie 0.01 in relative terms) and dividing the resulting change in the market value of the instrument V_i by 0.01 (ie 1%) as follows, where:

1. k is a given commodity;
2. CTY_k is the market value of commodity k; and
3. V_i is the market value of instrument i as a function of the spot price of commodity k:

Delta FX: the sensitivity is measured by changing the exchange rate by 1 percentage point (ie 0.01 in relative terms) and dividing the resulting change in the market value of the instrument V_i by 0.01 (ie 1%), where:

1. k is a given currency;
2. FX_k is the exchange rate between a given currency and a bank’s reporting currency or base currency, where the FX spot rate is the current market price of one unit of another currency expressed in the units of the bank’s reporting currency or base currency; and
3. V_i is the market value of instrument i as a function of the exchange rate k:

The option-level vega risk sensitivity to a given risk factor¹⁰ is measured by multiplying vega by the implied volatility of the option as follows, where:

1. vega, , is defined as the change in the market value of the option as a result of a small amount of change to the implied volatility ; and
2. the instrument’s vega and implied volatility used in the calculation of vega sensitivities must be sourced from pricing models used by the independent risk control unit of the bank.

The following sets out how to derive vega risk sensitivities in specific cases:

1. Options that do not have a maturity, are assigned to the longest prescribed maturity tenor, and these options are also assigned to the RRAO.
2. Options that do not have a strike or barrier and options that have multiple strikes or barriers, are mapped to strikes and maturity used internally to price the option, and these options are also assigned to the RRAO.
3. CTP securitisation tranches that do not have an implied volatility, are not subject to vega risk capital requirement. Such instruments may not, however, be exempt from delta and curvature risk capital requirements.

When computing a first-order sensitivity for instruments subject to optionality, banks should assume that the implied volatility either:

1. remains constant, consistent with a “sticky strike” approach; or
2. follows a “sticky delta” approach, such that implied volatility does not vary with respect to a given level of delta.

For the calculation of vega sensitivities, the distribution assumptions (ie log-normal assumptions or normal assumptions) for pricing models are applied as follows:

1. For the computation of a vega GIRR or CSR sensitivity, banks may use either the log-normal or normal assumptions.
2. For the computation of a vega equity, commodity or FX sensitivity, banks must use the log-normal assumption.¹¹

If, for internal risk management, a bank computes vega sensitivities using different definitions than the definitions set out in this standard, the bank may transform the sensitivities computed for internal risk management purposes to deduce the sensitivities to be used for the calculation of the vega risk measure.

All vega sensitivities must be computed ignoring the impact of credit valuation adjustments (CVA).

In the delta and curvature risk context: for index instruments and multi-underlying options, a look-through approach should be used. However, a bank may opt not to apply the look-through approach for instruments referencing any listed and widely recognised and accepted equity or credit index, where:

1. it is possible to look-through the index (ie the constituents and their respective weightings are known);
2. the index contains at least 20 constituents;
3. no single constituent contained within the index represents more than 25% of the total index;
4. the largest 10% of constituents represents less than 60% of the total index; and
5. the total market capitalisation of all the constituents of the index is no less than USD 40 billion.

For a given instrument, irrespective of whether a look-through approach is adopted or not, the sensitivity inputs used for the delta and curvature risk calculation must be consistent.

Where a bank opts not to apply the look-through approach in accordance with MAR21.31, a single sensitivity shall be calculated to each widely recognised and accepted index that an instrument references. The sensitivity to the index should be assigned to the relevant delta risk bucket defined in MAR21.53 and MAR21.72 as follows:

1. Where more than 75% of constituents in that index (taking into account the weightings of that index) would be mapped to a specific sector bucket (ie bucket 1 to bucket 11 for equity risk, or bucket 1 to bucket 16 for CSR), the sensitivity to the index shall be mapped to that single specific sector bucket and treated like any other single-name sensitivity in that bucket.
2. In all other cases, the sensitivity may be mapped to an "index" bucket (ie bucket 12 or bucket 13 for equity risk; or bucket 17 or bucket 18 for CSR). The same principle as above (1) applies when allocating sensitivities to a specific index bucket.
   1. For equity risk, an equity index should be mapped to the large market cap and advanced economy indices bucket (ie bucket 12) if at least 75% of the constituents in that index (taking into account the weightings of that index) are both large cap and advanced economy equities. Otherwise, it should be mapped to the other equity indices bucket (ie bucket 13).
   2. For CSR, a credit index should be mapped to the investment grade indices bucket (ie bucket 17) if at least 75% of the constituents in that index (taking into account the weightings of that index) are investment grade. Otherwise, it should be mapped to the high yield indices bucket (ie bucket 18).

A look-through approach must always be used for indices that do not meet the criteria set out in MAR21.31(2) to MAR21.31(5), and for any multi-underlying instruments that reference a bespoke set of equities or credit positions.

1. Where a look-through approach is adopted, for index instruments and multi-underlying options other than the CTP, the sensitivities to constituent risk factors from those instruments or options are allowed to net with sensitivities to single-name instruments without restriction.
2. Index CTP instruments cannot be broken down into its constituents (ie the index CTP should be considered a risk factor as a whole) and the above-mentioned netting at the issuer level does not apply either.
3. Where a look-through approach is adopted, it shall be applied consistently through time¹² , and shall be used for all identical instruments that reference the same index.

For equity investments in funds that can be looked through as set out in RBC25.8(5)(a), banks must apply a look-through approach and treat the underlying positions of the fund as if the positions were held directly by the bank (taking into account the bank’s share of the equity of the fund, and any leverage in the fund structure), except for the funds that meet the following conditions:

1. For funds that hold an index instrument that meets the criteria set out under MAR21.31, banks must still apply a look-through and treat the underlying positions of the fund as if the positions were held directly by the bank, but the bank may then choose to apply the “no look-through” approach for the index holdings of the fund as set out in MAR21.33.
2. For funds that track an index benchmark, a bank may opt not to apply the look-through approach and opt to measure the risk assuming the fund is a position in the tracked index only where:
   1. the fund has an absolute value of a tracking difference (ignoring fees and commissions) of less than 1%; and
   2. the tracking difference is checked at least annually and is defined as the annualised return difference between the fund and its tracked benchmark over the last 12 months of available data (or a shorter period in the absence of a full 12 months of data).

For equity investments in funds that cannot be looked through (ie do not meet the criterion set out in RBC25.8(5)(a)), but that the bank has access to daily price quotes and knowledge of the mandate of the fund (ie meet both the criteria set out in RBC25.8(5)(b)), banks may calculate capital requirements for the fund in one of three ways:

1. If the fund tracks an index benchmark and meets the requirement set out in MAR21.35(2)(a) and (b), the bank may assume that the fund is a position in the tracked index, and may assign the sensitivity to the fund to relevant sector specific buckets or index buckets as set out in MAR21.33.
2. Subject to supervisory approval, the bank may consider the fund as a hypothetical portfolio in which the fund invests to the maximum extent allowed under the fund’s mandate in those assets attracting the highest capital requirements under the sensitivities-based method, and then progressively in those other assets implying lower capital requirements. If more than one risk weight can be applied to a given exposure under the sensitivities-based method, the maximum risk weight applicable must be used.
   1. This hypothetical portfolio must be subject to market risk capital requirements on a stand-alone basis for all positions in that fund, separate from any other positions subject to market risk capital requirements.
   2. The counterparty credit and CVA risks of the derivatives of this hypothetical portfolio must be calculated using the simplified methodology set out in accordance with CRE60.7(c) of the banking book equity investment in funds treatment.
3. A bank may treat their equity investment in the fund as an unrated equity exposure to be allocated to the “other sector” bucket (bucket 11). In applying this treatment, banks must also consider whether, given the mandate of the fund, the default risk capital (DRC) requirement risk weight prescribed to the fund is sufficiently prudent (as set out in MAR22.8), and whether the RRAO should apply (as set out in MAR23.6).

As per the requirement in RBC25.8(5), net long equity investments in a given fund in which the bank cannot look through or does not meet the requirements of RBC25.8(5) for the fund must be assigned to the banking book. Net short positions in funds, where the bank cannot look through or does not meet the requirements of RBC25.8(5), must be excluded from any trading book capital requirements under the market risk framework, with the net position instead subjected to a 100% capital requirement.

In the vega risk context:

1. Multi-underlying options (including index options) are usually priced based on the implied volatility of the option, rather than the implied volatility of its underlying constituents and a look-through approach may not need to be applied, regardless of the approach applied to the delta and curvature risk calculation as set out in MAR21.31 through MAR21.34.¹³
2. For indices, the vega risk with respect to the implied volatility of the multi-underlying options will be calculated using a sector specific bucket or an index bucket defined in MAR21.53 and MAR21.72 as follows:
   1. Where more than 75% of constituents in that index (taking into account the weightings of that index) would be mapped to a single specific sector bucket (ie bucket 1 to bucket 11 for equity risk; or bucket 1 to bucket 16 for CSR), the sensitivity to the index shall be mapped to that single specific sector bucket and treated like any other single-name sensitivity in that bucket.
   2. In all other cases, the sensitivity may be mapped to an “index” bucket (ie bucket 12 or bucket 13 for equity risk or bucket 17 or bucket 18 for CSR).

MAR21.41 to MAR21.89 set out buckets, risk weights and correlation parameters for each risk class to calculate delta risk capital requirement as set out in MAR21.4.

The prescribed risk weights and correlations in MAR21.41 to MAR21.89 have been calibrated to the liquidity adjusted time horizon related to each risk class.

Each currency is a separate delta GIRR bucket, so all risk factors in risk-free yield curves for the same currency in which interest rate-sensitive instruments are denominated are grouped into the same bucket.

For calculating weighted sensitivities, the risk weights for each tenor in risk-free yield curves are set in Table 1 as follows:

The risk weight for the inflation risk factor and the cross-currency basis risk factors, respectively, is set at 1.6%.

For specified currencies by the Basel Committee,¹⁴ the above risk weights may, at the discretion of the bank, be divided by the square root of 2.

For aggregating GIRR risk positions within a bucket, the correlation parameter between weighted sensitivities and within the same bucket (ie same currency), same assigned tenor, but different curves is set at 99.90%. In aggregating delta risk positions for cross-currency basis risk for onshore and offshore curves, which must be considered two different curves as set out in MAR21.8, a bank may choose to aggregate all cross-currency basis risk for a currency (ie “Curr/USD” or “Curr/EUR”) for both onshore and offshore curves by a simple sum of weighted sensitivities.

The delta risk correlation between weighted sensitivities and within the same bucket with different tenor and same curve is set in the following Table 2¹⁵ :

Between two weighted sensitivities and within the same bucket with different tenor and different curves, the correlation is equal to the correlation parameter specified in MAR21.46 multiplied by 99.90%.¹⁶

The delta risk correlation between a weighted sensitivity to the inflation curve and a weighted sensitivity to a given tenor of the relevant yield curve is 40%.

The delta risk correlation between a weighted sensitivity to a cross-currency basis curve and a weighted sensitivity to each of the following curves is 0%:

1. a given tenor of the relevant yield curve;
2. the inflation curve; or
3. another cross-currency basis curve (if relevant).

For aggregating GIRR risk positions across different buckets (ie different currencies), the parameter is set at 50%.

For delta CSR non-securitisations, buckets are set along two dimensions - credit quality and sector - as set out in Table 3. The CSR non-securitisation sensitivities or risk exposures should first be assigned to a bucket defined before calculating weighted sensitivities by applying a risk weight.

To assign a risk exposure to a sector, banks must rely on a classification that is commonly used in the market for grouping issuers by industry sector.

1. The bank must assign each issuer to one and only one of the sector buckets in the table under MAR21.51.
2. Risk positions from any issuer that a bank cannot assign to a sector in this fashion must be assigned to the other sector (ie bucket 16).

For calculating weighted sensitivities, the risk weights for buckets 1 to 18 are set out in Table 4. Risk weights are the same for all tenors (ie 0.5 years, 1 year, 3 years, 5 years, 10 years) within each bucket:

For buckets 1 to 15, for aggregating delta CSR non-securitisations risk positions within a bucket, the correlation parameter between two weighted sensitivities and within the same bucket, is set as follows, where:²⁰

1. is equal to 1 where the two names of sensitivities k and l are identical, and 35% otherwise;
2. is equal to 1 if the two tenors of the sensitivities k and l are identical, and to 65% otherwise; and
3. is equal to 1 if the two sensitivities are related to same curves, and 99.90% otherwise.

For buckets 17 and 18, for aggregating delta CSR non-securitisations risk positions within a bucket, the correlation parameter between two weighted sensitivities and within the same bucket is set as follows, where:

1. is equal to 1 where the two names of sensitivities k and l are identical, and 80% otherwise;
2. is equal to 1 if the two tenors of the sensitivities k and l are identical, and to 65% otherwise; and
3. is equal to 1 if the two sensitivities are related to same curves, and 99.90% otherwise.

The correlations above do not apply to the other sector bucket (ie bucket 16).

1. The aggregation of delta CSR non-securitisation risk positions within the other sector bucket would be equal to the simple sum of the absolute values of the net weighted sensitivities allocated to this bucket. The same method applies to the aggregation of vega risk positions.
2. The aggregation of curvature CSR non-securitisation risk positions within the other sector bucket would be calculated by the formula below.

For aggregating delta CSR non-securitisation risk positions across buckets 1 to 18, the correlation parameter is set as follows, where:

1. is equal to 50% where the two buckets b and c are both in buckets 1 to 15 and have a different rating category (either IG or HY/NR). is equal to 1 otherwise; and
2. is equal to 1 if the two buckets belong to the same sector, and to the specified numbers in Table 5 otherwise.

   Values of where the buckets do not belong to the same sector										Table 5
   Bucket	1 / 9	2 / 10	3 / 11	4 / 12	5 / 13	6 / 14	7 / 15	8	16	17	18
   1 / 9		75%	10%	20%	25%	20%	15%	10%	0%	45%	45%
   2 / 10			5%	15%	20%	15%	10%	10%	0%	45%	45%
   3 / 11				5%	15%	20%	5%	20%	0%	45%	45%
   4 / 12					20%	25%	5%	5%	0%	45%	45%
   5 / 13						25%	5%	15%	0%	45%	45%
   6 / 14							5%	20%	0%	45%	45%
   7 / 15								5%	0%	45%	45%
   8									0%	45%	45%
   16										0%	0%
   17											75%
   18

Sensitivities to CSR arising from the CTP and its hedges are treated as a separate risk class as set out in MAR21.1. The buckets, risk weights and correlations for the CSR securitisations (CTP) apply as follows:

1. The same bucket structure and correlation structure apply to the CSR securitisations (CTP) as those for the CSR non-securitisation framework as set out in MAR21.51 to MAR21.57 with an exception of index buckets (ie buckets 17 and 18).
2. The risk weights and correlation parameters of the delta CSR non-securitisations are modified to reflect longer liquidity horizons and larger basis risk as specified in MAR21.59 to MAR21.61.

For calculating weighted sensitivities, the risk weights for buckets 1 to 16 are set out in Table 6. Risk weights are the same for all tenors (ie 0.5 years, 1 year, 3 years, 5 years, 10 years) within each bucket:

For aggregating delta CSR securitisations (CTP) risk positions within a bucket, the delta risk correlation is derived the same way as in MAR21.54 and MAR21.55, except that the correlation parameter applying when the sensitivities are not related to same curves, , is modified.

1. is now equal to 1 if the two sensitivities are related to same curves, and 99.00% otherwise.
2. The identical correlation parameters for and to CSR non-securitisation as set out in MAR21.54 and MAR21.55 apply.

For aggregating delta CSR securitisations (CTP) risk positions across buckets, the correlation parameters for are identical to CSR non-securitisation as set out in MAR21.57.

For delta CSR securitisations not in the CTP, buckets are set along two dimensions – credit quality and sector – as set out in Table 7. The delta CSR securitisation (non-CTP) sensitivities or risk exposures must first be assigned to a bucket before calculating weighted sensitivities by applying a risk weight.

To assign a risk exposure to a sector, banks must rely on a classification that is commonly used in the market for grouping tranches by type.

1. The bank must assign each tranche to one of the sector buckets in above Table 7.
2. Risk positions from any tranche that a bank cannot assign to a sector in this fashion must be assigned to the other sector (ie bucket 25).

For calculating weighted sensitivities, the risk weights for buckets 1 to 8 (senior IG) are set out in Table 8:

The risk weights for buckets 9 to 16 (non-senior investment grade) are then equal to the corresponding risk weights for buckets 1 to 8 scaled up by a multiplication by 1.25. For instance, the risk weight for bucket 9 is equal to .

The risk weights for buckets 17 to 24 (high yield and non-rated) are then equal to the corresponding risk weights for buckets 1 to 8 scaled up by a multiplication by 1.75. For instance, the risk weight for bucket 17 is equal to .

The risk weight for bucket 25 is set at 3.5%.

For aggregating delta CSR securitisations (non-CTP) risk positions within a bucket, the correlation parameter between two sensitivities and within the same bucket, is set as follows, where:

1. is equal to 1 where the two names of sensitivities k and l are within the same bucket and related to the same securitisation tranche (more than 80% overlap in notional terms), and 40% otherwise;
2. is equal to 1 if the two tenors of the sensitivities k and l are identical, and to 80% otherwise; and
3. is equal to 1 if the two sensitivities are related to same curves, and 99.90% otherwise.

The correlations above do not apply to the other sector bucket (ie bucket 25).

1. The aggregation of delta CSR securitisations (non-CTP) risk positions within the other sector bucket would be equal to the simple sum of the absolute values of the net weighted sensitivities allocated to this bucket. The same method applies to the aggregation of vega risk positions.
2. The aggregation of curvature CSR risk positions within the other sector bucket would be calculated by the formula below.

For aggregating delta CSR securitisations (non-CTP) risk positions across buckets 1 to 24, the correlation parameter is set as 0%.

For aggregating delta CSR securitisations (non-CTP) risk positions between the other sector bucket (ie bucket 25) and buckets 1 to 24, (i) the capital requirements for bucket 25 and (ii) the aggregated capital requirements for buckets 1 to 24 will be simply summed up to the overall risk class level capital requirements. There should be no diversification or hedging effects recognised in aggregating the capital requirements for the other sector bucket (ie bucket 25) with those for buckets 1 to 24.

For delta equity risk, buckets are set along three dimensions – market capitalisation, economy and sector – as set out in Table 9. The equity risk sensitivities or exposures must first be assigned to a bucket before calculating weighted sensitivities by applying a risk weight.

Market capitalisation (market cap) is defined as the sum of the market capitalisations based on the market value of the total outstanding shares issued by the same listed legal entity or a group of legal entities across all stock markets globally, where the total outstanding shares issued by the group of legal entities refer to cases where the listed entity is a parent company of a group of legal entities. Under no circumstances should the sum of the market capitalisations of multiple related listed entities be used to determine whether a listed entity is “large market cap” or “small market cap”.

Large market cap is defined as a market capitalisation equal to or greater than USD 2 billion and small market cap is defined as a market capitalisation of less than USD 2 billion.

The advanced economies are Canada, the United States, Mexico, the euro area, the non-euro area western European countries (the United Kingdom, Norway, Sweden, Denmark and Switzerland), Japan, Oceania (Australia and New Zealand), Singapore and Hong Kong SAR.

To assign a risk exposure to a sector, banks must rely on a classification that is commonly used in the market for grouping issuers by industry sector.

1. The bank must assign each issuer to one of the sector buckets in the table under MAR21.72 and it must assign all issuers from the same industry to the same sector.
2. Risk positions from any issuer that a bank cannot assign to a sector in this fashion must be assigned to the other sector (ie bucket 11).
3. For multinational multi-sector equity issuers, the allocation to a particular bucket must be done according to the most material region and sector in which the issuer operates.

For calculating weighted sensitivities, the risk weights for the sensitivities to each of equity spot price and equity repo rates for buckets 1 to 13 are set out in Table 10:

For aggregating delta equity risk positions within a bucket, the correlation parameter between two sensitivities and within the same bucket is set at as follows

1. The correlation parameter is set at 99.90%, where:
   1. one is a sensitivity to an equity spot price and the other a sensitivity to an equity repo rates; and
   2. both are related to the same equity issuer name.
2. The correlation parameter is set out in (a) to (e) below, where both sensitivities are to equity spot price, and where:
   1. 15% between two sensitivities within the same bucket that fall under large market cap, emerging market economy (bucket number 1, 2, 3 or 4).
   2. 25% between two sensitivities within the same bucket that fall under large market cap, advanced economy (bucket number 5, 6, 7 or 8).
   3. 7.5% between two sensitivities within the same bucket that fall under small market cap, emerging market economy (bucket number 9).
   4. 12.5% between two sensitivities within the same bucket that fall under small market cap, advanced economy (bucket number 10).
   5. 80% between two sensitivities within the same bucket that fall under either index bucket (bucket number 12 or 13).
3. The same correlation parameter as set out in above (2)(a) to (e) apply, where both sensitivities are to equity repo rates.
4. The correlation parameter is set as each parameter specified in above (2)(a) to (e) multiplied by 99.90%, where:
   1. One is a sensitivity to an equity spot price and the other a sensitivity to an equity repo rate; and
   2. Each sensitivity is related to a different equity issuer name.

The correlations set out above do not apply to the other sector bucket (ie bucket 11).

1. The aggregation of equity risk positions within the other sector bucket capital requirement would be equal to the simple sum of the absolute values of the net weighted sensitivities allocated to this bucket. The same method applies to the aggregation of vega risk positions.
2. The aggregation of curvature equity risk positions within the other sector bucket (ie bucket 11) would be calculated by the formula:

For aggregating delta equity risk positions across buckets 1 to 13, the correlation parameter is set at:

1. 15% if bucket b and bucket c fall within bucket numbers 1 to 10;
2. 0% if either of bucket b and bucket c is bucket 11;
3. 75% if bucket b and bucket c are bucket numbers 12 and 13 (i.e. one is bucket 12, one is bucket 13); and
4. 45% otherwise.

For delta commodity risk, 11 buckets that group commodities by common characteristics are set out in Table 11.

For calculating weighted sensitivities, the risk weights for each bucket are set out in Table 11:

For the purpose of aggregating commodity risk positions within a bucket using a correlation parameter, the correlation parameter between two sensitivities and within the same bucket, is set as follows, where:²³

1. is equal to 1 where the two commodities of sensitivities k and l are identical, and to the intra-bucket correlations in Table 12 otherwise, where, any two commodities are considered distinct commodities if in the market two contracts are considered distinct when the only difference between each other is the underlying commodity to be delivered. For example, WTI and Brent in bucket 2 (ie energy - liquid combustibles) would typically be treated as distinct commodities;
2. is equal to 1 if the two tenors of the sensitivities k and l are identical, and to 99.00% otherwise; and
3. is equal to 1 if the two sensitivities are identical in the delivery location of a commodity, and 99.90% otherwise.

   Values of for intra-bucket correlations			Table 12
   Bucket number	Commodity bucket	Correlation ( )
   1	Energy - Solid combustibles	55%
   2	Energy - Liquid combustibles	95%
   3	Energy - Electricity and carbon trading	40%
   4	Freight	80%
   5	Metals - non-precious	60%
   6	Gaseous combustibles	65%
   7	Precious metals (including gold)	55%
   8	Grains and oilseed	45%
   9	Livestock and dairy	15%
   10	Softs and other agriculturals	40%
   11	Other commodity	15%

For determining whether the commodity correlation parameter ( ) as set out in Table 12 in MAR21.83(1)(a) should apply, this paragraph provides non-exhaustive examples of further definitions of distinct commodities as follows:

1. For bucket 3 (energy – electricity and carbon trading):
   1. Each time interval (i) at which the electricity can be delivered and (ii) that is specified in a contract that is made on a financial market is considered a distinct electricity commodity (eg peak and off-peak).
   2. Electricity produced in a specific region (eg Electricity NE, Electricity SE or Electricity North) is considered a distinct electricity commodity.
2. For bucket 4 (freight):
   1. Each combination of freight type and route is considered a distinct commodity.
   2. Each week at which a good has to be delivered is considered a distinct commodity.

For aggregating delta commodity risk positions across buckets, the correlation parameter is set as follows:

1. 20% if bucket b and bucket c fall within bucket numbers 1 to 10; and
2. 0% if either bucket b or bucket c is bucket number 11.

An FX risk bucket is set for each exchange rate between the currency in which an instrument is denominated and the reporting currency.

A unique relative risk weight equal to 15% applies to all the FX sensitivities.

For the specified currency pairs by the Basel Committee,²⁴ and for currency pairs forming first-order crosses across these specified currency pairs,²⁵ the above risk weight may at the discretion of the bank be divided by the square root of 2.

For aggregating delta FX risk positions across buckets, the correlation parameter is uniformly set to 60%.

MAR21.91 to MAR21.95 set out buckets, risk weights and correlation parameters to calculate vega risk capital requirement as set out in MAR21.4.

The same bucket definitions for each risk class are used for vega risk as for delta risk.

For calculating weighted sensitivities for vega risk, the risk of market illiquidity is incorporated into the determination of vega risk, by assigning different liquidity horizons for each risk class as set out in Table 13. The risk weight for each risk class²⁶ is also set out in Table 13.

For aggregating vega GIRR risk positions within a bucket, the correlation parameter is set as follows, where:

1. is equal to , where:
   1. is set at 1%;
   2. (respectively ) is the maturity of the option from which the vega sensitivity ( ) is derived, expressed as a number of years; and
2. is equal to , where:
   1. is set at 1%; and
   2. (respectively ) is the maturity of the underlying of the option from which the sensitivity ( ) is derived, expressed as a number of years after the maturity of the option.

For aggregating vega risk positions within a bucket of the other risk classes (ie non-GIRR), the correlation parameter is set as follows, where:

1. is equal to the correlation that applies between the delta risk factors that correspond to vega risk factors k and l. For instance, if k is the vega risk factor from equity option X and l is the vega risk factor from equity option Y then is the delta correlation applicable between X and Y; and
2. is defined as in MAR21.93:

For aggregating vega risk positions across different buckets within a risk class (GIRR and non-GIRR), the same correlation parameters for , as specified for delta correlations for each risk class in MAR21.39 to MAR21.89 are to be used for the aggregation of vega risk (eg = 50% is to be used for the aggregation of vega risk sensitivities across different GIRR buckets).

MAR21.97 to MAR21.101 set out buckets, risk weights and correlation parameters to calculate curvature risk capital requirement as set out in MAR21.5.

The delta buckets are replicated for the calculation of curvature risk capital requirement, unless specified otherwise in the preceding paragraphs within MAR21.8 to MAR21.89.

For calculating the net curvature risk capital requirement for risk factor k for FX and equity risk classes, the curvature risk weight, which is the size of a shock to the given risk factor, is a relative shift equal to the respective delta risk weight. For FX curvature, for options that do not reference a bank’s reporting currency (or base currency as set out in MAR21.14(b)) as an underlying, net curvature risk charges ( and ) may be divided by a scalar of 1.5. Alternatively, and subject to supervisory approval, a bank may apply the scalar of 1.5 consistently to all FX instruments provided curvature sensitivities are calculated for all currencies, including sensitivities determined by shocking the reporting currency (or base currency where used) relative to all other currencies.

For calculating the net curvature risk capital requirement for curvature risk factor k for GIRR, CSR and commodity risk classes, the curvature risk weight is the parallel shift of all the tenors for each curve based on the highest prescribed delta risk weight for each bucket. For example, in the case of GIRR for a given currency (ie bucket), the risk weight assigned to 0.25-year tenor (ie the most punitive tenor risk weight) is applied to all the tenors simultaneously for each risk-free yield curve (consistent with a "translation", or "parallel shift" risk calculation).

For aggregating curvature risk positions within a bucket, the curvature risk correlations are determined by squaring the corresponding delta correlation parameters . In a case where a curvature risk factor is defined differently than the corresponding delta risk factor for a given risk class (ie for CSR non-securitisations, CSR securitisations (CTP), CSR securitisations (non-CTP) and commodities as defined in MAR21.9 to MAR21.13), banks do not need to consider this delta risk factor dimension. For example, for CSR non-securitisations and CSR securitisations (CTP), consistent with MAR21.9 which defines a bucket along one dimension (ie the relevant credit spread curve), the correlation parameter as defined in MAR21.54 and MAR21.55 is not applicable to the curvature risk capital requirement calculation. Thus, the correlation parameter is determined by whether the two names of weighted sensitivities are the same. In the formula in MAR21.54 and MAR21.55, the correlation parameters and need not apply and only correlation parameter applies between two weighted sensitivities within the same bucket. This correlation parameter should be squared. In applying the high and low correlations scenario set out in MAR21.6, the curvature risk capital requirements are calculated by applying the curvature correlation parameters determined in this paragraph.

For aggregating curvature risk positions across buckets, the curvature risk correlations are determined by squaring the corresponding delta correlation parameters . For instance, when aggregating and for the GIRR, the correlation should be . In applying the high and low correlations scenario set out in MAR21.6, the curvature risk capital requirements are calculated by applying the curvature correlation parameters , (ie the square of the corresponding delta correlation parameter).

The default risk capital (DRC) requirement is intended to capture jump-to-default (JTD) risk that may not be captured by credit spread shocks under the sensitivities-based method. DRC requirements provide some limited hedging recognition. In this chapter offsetting refers to the netting of exposures to the same obligor (where a short exposure may be subtracted in full from a long exposure) and hedging refers to the application of a partial hedge benefit from the short exposures (where the risk of long and short exposures in distinct obligors do not fully offset due to basis or correlation risks).

The DRC requirement must be calculated for instruments subject to default risk:

1. Non-securitisation portfolios
2. Securitisation portfolio (non-correlation trading portfolio, or non-CTP)
3. Securitisation (correlation trading portfolio, or CTP)

The following step-by-step approach must be followed for each risk class subject to default risk. The specific definition of gross JTD risk, net JTD risk, bucket, risk weight and the method for aggregation of DRC requirement across buckets are separately set out per each risk class in subsections in MAR22.9 to MAR22.26.

1. The gross JTD risk of each exposure is computed separately.
2. With respect to the same obligator, the JTD amounts of long and short exposures are offset (where permissible) to produce net long and/or net short exposure amounts per distinct obligor.
3. Net JTD risk positions are then allocated to buckets.
4. Within a bucket, a hedge benefit ratio is calculated using net long and short JTD risk positions. This acts as a discount factor that reduces the amount of net short positions to be netted against net long positions within a bucket. A prescribed risk weight is applied to the net positions which are then aggregated.
5. Bucket level DRC requirements are aggregated as a simple sum across buckets to give the overall DRC requirement.

No diversification benefit is recognised between the DRC requirements for:

1. non-securitisations;
2. securitisations (non-CTP); and
3. securitisations (CTP).

For traded non-securitisation credit and equity derivatives, JTD risk positions by individual constituent issuer legal entity should be determined by applying a look-through approach.

For the CTP, the capital requirement calculation includes the default risk for non-securitisation hedges. These hedges must be removed from the calculation of default risk non-securitisation.

Claims on sovereigns, public sector entities and multilateral development banks may, at national discretion, be subject to a zero default risk weight in line with CRE20.7 to CRE20.15 of the credit risk standard. National authorities may apply a non-zero risk weight to securities issued by certain foreign governments, including to securities denominated in a currency other than that of the issuing government.

For claims on an equity investment in a fund that is subject to the treatment specified in MAR21.36(3) (ie treated as an unrated "other sector" equity), the equity investment in the fund shall be treated as an unrated equity instrument. Where the mandate of that fund allows the fund to invest in primarily high-yield or distressed names, banks shall apply the maximum risk weight per Table 2 in MAR22.24 that is achievable under the fund's mandate (by calculating the effective average risk weight of the fund when assuming that the fund invests first in defaulted instruments to the maximum possible extent allowed under its mandate, and then in CCC-rated names to the maximum possible extent, and then B-rated, and then BB-rated). Neither offsetting nor diversification between these generated exposures and other exposures is allowed.

The gross JTD risk position is computed exposure by exposure. For instance, if a bank has a long position on a bond issued by Apple, and another short position on a bond issued by Apple, it must compute two separate JTD exposures.

For the purpose of DRC requirements, the determination of the long/short direction of positions must be on the basis of long or short with respect to whether the credit exposure results in a loss or gain in the case of a default.

1. Specifically, a long exposure is defined as a credit exposure that results in a loss in the case of a default.
2. For derivative contracts, the long/short direction is also determined by whether the contract will result in a loss in the case of a default (ie long or short position is not determined by whether the option or credit default swap (CDS), is bought or sold). Thus, for the purpose of DRC requirements, a sold put option on a bond is a long credit exposure, since a default results in a loss to the seller of the option.

The gross JTD is a function of the loss given default (LGD), notional amount (or face value) and the cumulative profit and loss (P&L) already realised on the position, where:

1. notional is the bond-equivalent notional amount (or face value) of the position; and
2. P&L is the cumulative mark-to-market loss (or gain) already taken on the exposure. P&L is equal to the market value minus the notional amount, where the market value is the current market value of the position.

   

   

For calculating the gross JTD, LGD is set as follows:

1. Equity instruments and non-senior debt instruments are assigned an LGD of 100%.
2. Senior debt instruments are assigned an LGD of 75%.
3. Covered bonds, as defined within MAR21.51, are assigned an LGD of 25%.
4. When the price of the instrument is not linked to the recovery rate of the defaulter (eg a foreign exchange-credit hybrid option where the cash flows are swap of cash flows, long EUR coupons and short USD coupons with a knockout feature that ends cash flows on an event of default of a particular obligor), there should be no multiplication of the notional by the LGD.

In calculating the JTD as set out in MAR22.11, the notional amount of an instrument that gives rise to a long (short) exposure is recorded as a positive (negative) value, while the P&L loss (gain) is recorded as a negative (positive) value. If the contractual or legal terms of the derivative allow for the unwinding of the instrument with no exposure to default risk, then the JTD is equal to zero.

The notional amount is used to determine the loss of principal at default, and the mark-to-market loss is used to determine the net loss so as to not double-count the mark-to-market loss already recorded in the market value of the position.

1. For all instruments, the notional amount is the notional amount of the instrument relative to which the loss of principal is determined. Examples are as follows:
   1. For a bond, the notional amount is the face value.
   2. For credit derivatives, the notional amount of a CDS contract or a put option on a bond is the notional amount of the derivative contract.
   3. In the case of a call option on a bond, the notional amount to be used in the JTD calculation is zero (since, in the event of default, the call option will not be exercised). In this case, a JTD would extinguish the call option's value and this loss would be captured through the mark-to-market P&L term in the JTD calculation.
2. Table 1 illustrates examples of the notional amounts and market values for a long credit position with a mark-to-market loss to be used in the JTD calculation, where:
   1. the bond-equivalent market value is an intermediate step in determining the P&L for derivative instruments;
   2. the mark-to-market value of CDS or an option takes an absolute value; and
   3. the strike amount of the bond option is expressed in terms of the bond price (not the yield).

      Examples of components for a long credit position in the JTD calculation				Table 1
      Instrument	Notional	Bond-equivalent market value	P&L
      Bond	Face value of bond	Market value of bond	Market value - face value
      CDS	Notional of CDS	Notional of CDS +  mark-to-market (MtM) value of CDS	- MtM value of CDS
      Sold put option on a bond	Notional of option	Strike amount - | MtM value of option |	(Strike - | MtM value of option | ) - Notional
      Bought call option on a bond	0	MtM value of option	MtM value of option
      P&L = bond-equivalent market value - notional. With this representation of the P&L for a sold put option, a lower strike results in a lower JTD loss.

To account for defaults within the one-year capital horizon, the JTD for all exposures of maturity less than one year and their hedges are scaled by a fraction of a year. No scaling is applied to the JTD for exposures of one year or greater.²⁷ For example, the JTD for a position with a six month maturity would be weighted by one-half, while the JTD for a position with a one year maturity would have no scaling applied to the JTD.

Cash equity positions (ie stocks) are assigned to a maturity of either more than one year or three months, at banks’ discretion.

For derivative exposures, the maturity of the derivative contract is considered in determining the offsetting criterion, not the maturity of the underlying instrument.

The maturity weighting applied to the JTD for any sort of product with a maturity of less than three months (such as short term lending) is floored at a weighting factor of one-fourth or, equivalently, three months (that means that the positions having shorter-than-three months remaining maturity would be regarded as having a remaining maturity of three months for the purpose of the DRC requirement).

Exposures to the same obligator may be offset as follows:

1. The gross JTD risk positions of long and short exposures to the same obligor may be offset where the short exposure has the same or lower seniority relative to the long exposure. For example, a short exposure in an equity may offset a long exposure in a bond, but a short exposure in a bond cannot offset a long exposure in the equity.
2. For the purposes of determining whether a guaranteed bond is an exposure to the underlying obligor or an exposure to the guarantor, the credit risk mitigation requirements set out in CRE22.71 and CRE22.73 apply.
3. Exposures of different maturities that meet this offsetting criterion may be offset as follows.
   1. Exposures with maturities longer than the capital horizon (one year) may be fully offset.
   2. An exposure to an obligor comprising a mix of long and short exposures with a maturity less than the capital horizon (equal to one year) must be weighted by the ratio of the exposure’s maturity relative to the capital horizon. For example, with the one-year capital horizon, a three-month short exposure would be weighted so that its benefit against long exposures of longer-than-one-year maturity would be reduced to one quarter of the exposure size.

In the case of long and short offsetting exposures where both have a maturity under one year, the scaling can be applied to both the long and short exposures.

Finally, the offsetting may result in net long JTD risk positions and net short JTD risk positions. The net long and net short JTD risk positions are aggregated separately as described below.

For the default risk of non-securitisations, three buckets are defined as:

1. corporates;
2. sovereigns; and
3. local governments and municipalities.

In order to recognise hedging relationship between net long and net short positions within a bucket, a hedge benefit ratio is computed as follows.

1. A simple sum of the net long JTD risk positions (not risk-weighted) must be calculated, where the summation is across the credit quality categories (ie rating bands). The aggregated amount is used in the numerator and denominator of the expression of the hedge benefit ratio (HBR) below.
2. A simple sum of the net (not risk-weighted) short JTD risk positions must be calculated, where the summation is across the credit quality categories (ie rating bands). The aggregated amount is used in the denominator of the expression of the HBR below.
3. The HBR is the ratio of net long JTD risk positions to the sum of net long JTD and absolute value of net short JTD risk positions:

For calculating the weighted net JTD, default risk weights are set depending on the credit quality categories (ie rating bands) for all three buckets (ie irrespective of the type of counterparty), as set out in Table 2:

The capital requirement for each bucket is to be calculated as the combination of the sum of the risk-weighted long net JTD, the HBR, and the sum of the risk-weighted short net JTD, where the summation for each long net JTD and short net JTD is across the credit quality categories (ie rating bands). In the following formula, DRC stands for DRC requirement; and i refers to an instrument belonging to bucket b.

No hedging is recognised between different buckets - the total DRC requirement for non-securitisations must be calculated as a simple sum of the bucket level capital requirements.

For the computation of gross JTD on securitisations, the same approach must be followed as for default risk (non-securitisations), except that an LGD ratio is not applied to the exposure. Because the LGD is already included in the default risk weights for securitisations to be applied to the securitisation exposure (see below), to avoid double counting of LGD the JTD for securitisations is simply the market value of the securitisation exposure (ie the JTD for tranche positions is their market value).

For the purposes of offsetting and hedging recognition for securitisations (non-CTP), positions in underlying names or a non-tranched index position may be decomposed proportionately into the equivalent replicating tranches that span the entire tranche structure. When underlying names are treated in this way, they must be removed from the non-securitisation default risk treatment.

For default risk of securitisations (non-CTP), offsetting is limited to a specific securitisation exposure (ie tranches with the same underlying asset pool). This means that:

1. no offsetting is permitted between securitisation exposures with different underlying securitised portfolio (ie underlying asset pools), even if the attachment and detachment points are the same; and
2. no offsetting is permitted between securitisation exposures arising from different tranches with the same securitised portfolio.

Securitisation exposures that are otherwise identical except for maturity may be offset. The same offsetting rules for non-securitisations including scaling down positions of less than one year as set out in MAR22.15 through MAR22.18 apply to JTD risk positions for securitisations (non-CTP). Offsetting within a specific securitisation exposure is allowed as follows.

1. Securitisation exposures that can be perfectly replicated through decomposition may be offset. Specifically, if a collection of long securitisation exposures can be replicated by a collection of short securitisation exposures, then the securitisation exposures may be offset.
2. Furthermore, when a long securitisation exposure can be replicated by a collection of short securitisation exposures with different securitised portfolios, then the securitisation exposure with the “mixed” securitisation portfolio may be offset by the combination of replicating securitisation exposures.
3. After the decomposition, the offsetting rules would apply as in any other case. As in the case of default risk (non-securitisations), long and short securitisation exposures should be determined from the perspective of long or short the underlying credit, eg the bank making losses on a long securitisation exposure in the event of a default in the securitised portfolio.

For default risk of securitisations (non-CTP), the buckets are defined as follows:

1. Corporates (excluding small and medium enterprises) – this bucket takes into account all regions.
2. Other buckets – these are defined along two dimensions:
   1. Asset classes: the 11 asset classes are defined as asset-backed commercial paper; auto Loans/Leases; residential mortgage-backed securities (MBS); credit cards; commercial MBS; collateralised loan obligations; collateralised debt obligation (CDO)-squared; small and medium enterprises; student loans, other retail; and other wholesale.
   2. Regions: the four regions are defined as Asia, Europe, North America and all other.

To assign a securitisation exposure to a bucket, banks must rely on a classification that is commonly used in the market for grouping securitisation exposures by type and region of underlying.

1. The bank must assign each securitisation exposure to one and only one of the buckets above and it must assign all securitisations with the same type and region of underlying to the same bucket.
2. Any securitisation exposure that a bank cannot assign to a type or region of underlying in this fashion must be assigned to the “other bucket”.

The capital requirement for default risk of securitisations (non-CTP) is determined using a similar approach to that for non-securitisations. The DRC requirement within a bucket is calculated as follows:

1. The hedge benefit discount HBR, as defined in MAR22.23, is applied to net short securitisation exposures in that bucket.
2. The capital requirement is calculated as in MAR22.25.

For calculating the weighted net JTD, the risk weights of securitisation exposures are defined by the tranche instead of the credit quality. The risk weight for securitisations (non-CTP) is applied as follows:

1. The default risk weights for securitisation exposures are based on the corresponding risk weights for banking book instruments as set out in CRE40 to CRE44, with the following modification: the maturity component in the banking book securitisation framework is set to zero (ie a one-year maturity is assumed) to avoid double-counting of risks in the maturity adjustment (of the banking book approach) since migration risk in the trading book will be captured in the credit spread capital requirement.
2. Following the corresponding treatment in the banking book, the hierarchy of approaches in determining the risk weights should be applied at the underlying pool level.
3. The capital requirement under the standardised approach for an individual cash securitisation position can be capped at the fair value of the transaction.

No hedging is recognised between different buckets. Therefore, the total DRC requirement for securitisations (non-CTP) must be calculated as a simple sum of the bucket-level capital requirements.

For the computation of gross JTD on securitisations (CTP), the same approach must be followed as for default risk-securitisations (non-CTP) as described in MAR22.27.

The gross JTD for non-securitisations (CTP) (ie single-name and index hedges) positions is defined as their market value.

Nth-to-default products should be treated as tranched products with attachment and detachment points defined below, where “Total names” is the total number of names in the underlying basket or pool:

1. Attachment point = (N – 1) / Total names
2. Detachment point = N / Total names

Exposures that are otherwise identical except for maturity may be offset. The same concept of long and short positions from a perspective of loss or gain in the event of a default as set out in MAR22.10 and offsetting rules for non-securitisations including scaling down positions of less than one year as set out in MAR22.15 to MAR22.18 apply to JTD risk positions for securitisations (non-CTP).

1. For index products, for the exact same index family (eg CDX.NA.IG), series (eg series 18) and tranche (eg 0–3%), securitisation exposures should be offset (netted) across maturities (subject to the offsetting allowance as described above).
2. Long and short exposures that are perfect replications through decomposition may be offset as follows. When the offsetting involves decomposing single name equivalent exposures, decomposition using a valuation model would be allowed in certain cases as follows. Such decomposition is the sensitivity of the security’s value to the default of the underlying single name obligor. Decomposition with a valuation model is defined as follows: a single name equivalent constituent of a securitisation (eg tranched position) is the difference between the unconditional value of the securitisation and the conditional value of the securitisation assuming that the single name defaults, with zero recovery, where the value is determined by a valuation model. In such cases, the decomposition into single-name equivalent exposures must account for the effect of marginal defaults of the single names in the securitisation, where in particular the sum of the decomposed single name amounts must be consistent with the undecomposed value of the securitisation. Further, such decomposition is restricted to vanilla securitisations (eg vanilla CDOs, index tranches or bespokes); while the decomposition of exotic securitisations (eg CDO squared) is prohibited.
3. Moreover, for long and short positions in index tranches, and indices (non-tranched), if the exposures are to the exact same series of the index, then offsetting is allowed by replication and decomposition. For instance, a long securitisation exposure in a 10–15% tranche vs combined short securitisation exposures in 10–12% and 12–15% tranches on the same index/series can be offset against each other. Similarly, long securitisation exposures in the various tranches that, when combined perfectly, replicate a position in the index series (non-tranched) can be offset against a short securitisation exposure in the index series if all the positions are to the exact same index and series (eg CDX.NA.IG series 18). Long and short positions in indices and single-name constituents in the index may also be offset by decomposition. For instance, single-name long securitisation exposures that perfectly replicate an index may be offset against a short securitisation exposure in the index. When a perfect replication is not possible, then offsetting is not allowed except as indicated in the next sentence. Where the long and short securitisation exposures are otherwise equivalent except for a residual component, the net amount must show the residual exposure. For instance, a long securitisation exposure in an index of 125 names, and short securitisation exposures of the appropriate replicating amounts in 124 of the names, would result in a net long securitisation exposure in the missing 125th name of the index.
4. Different tranches of the same index or series may not be offset (netted), different series of the same index may not be offset, and different index families may not be offset.

For default risk of securitisations (CTP), each index is defined as a bucket of its own. A non-exhaustive list of indices include: CDX North America IG, iTraxx Europe IG, CDX HY, iTraxx XO, LCDX (loan index), iTraxx LevX (loan index), Asia Corp, Latin America Corp, Other Regions Corp, Major Sovereign (G7 and Western Europe) and Other Sovereign.

Bespoke securitisation exposures should be allocated to the index bucket of the index they are a bespoke tranche of. For instance, the bespoke tranche 5% - 8% of a given index should be allocated to the bucket of that index.

The default risk weights for securitisations applied to tranches are based on the corresponding risk weights for the banking book instruments, which is defined in a separate Basel Committee publication - Revisions to the Securitisations framework of 2014, 2016 and 2018, with the following modification: the maturity component in the banking book securitisation framework is set to zero, ie a one-year maturity is assumed to avoid double-counting of risks in the maturity adjustment (of the banking book approach) since migration risk in the trading book will be captured in the credit spread capital requirement.

For the non-tranched products, the same risk weights for non-securitisations as set out in MAR22.24 apply. For the tranched products, banks must derive the risk weight using the banking book treatment as set out in MAR22.42.

Within a bucket (ie for each index) at an index level, the capital requirement for default risk of securitisations (CTP) is determined in a similar approach to that for non-securitisations.

1. The hedge benefit ratio (HBR), as defined in MAR22.23, is modified and applied to net short positions in that bucket as in the formula below, where the subscript ctp for the term HBR_ctp indicates that the HBR is determined using the combined long and short positions across all indices in the CTP (ie not only the long and short positions of the bucket by itself). The summation of risk-weighted amounts in the formula spans all exposures relating to the index (ie index tranche, bespoke, non-tranche index or single name).
2. A deviation from the approach for non-securitisations is that no floor at zero applies at the bucket level, and consequently, the DRC requirement at the index level ( ) can be negative.

The total DRC requirement for securitisations (CTP) is calculated by aggregating bucket level capital amounts as follows. For instance, if the DRC requirement for the index CDX North America IG is +100 and the DRC requirement for the index Major Sovereign (G7 and Western Europe) is -100, the total DRC requirement for the CTP is .²⁸

The residual risk add-on (RRAO) is to be calculated for all instruments bearing residual risk separately in addition to other components of the capital requirement under the standardised approach.

Instruments with an exotic underlying and instruments bearing other residual risks are subject to the RRAO.

Instruments with an exotic underlying are trading book instruments with an underlying exposure that is not within the scope of delta, vega or curvature risk treatment in any risk class under the sensitivities-based method or default risk capital (DRC) requirements in the standardised approach.²⁹

Instruments bearing other residual risks are those that meet criteria (1) and (2) below:

1. Instruments subject to vega or curvature risk capital requirements in the trading book and with pay-offs that cannot be written or perfectly replicated as a finite linear combination of vanilla options with a single underlying equity price, commodity price, exchange rate, bond price, credit default swap price or interest rate swap; or
2. Instruments which fall under the definition of the correlation trading portfolio (CTP) in MAR20.5, except for those instruments that are recognised in the market risk framework as eligible hedges of risks within the CTP.

A non-exhaustive list of other residual risks types and instruments that may fall within the criteria set out in MAR23.4 include:

1. Gap risk: risk of a significant change in vega parameters in options due to small movements in the underlying, which results in hedge slippage. Relevant instruments subject to gap risk include all path dependent options, such as barrier options, and Asian options as well as all digital options.
2. Correlation risk: risk of a change in a correlation parameter necessary for determining the value of an instrument with multiple underlyings. Relevant instruments subject to correlation risk include all basket options, best-of-options, spread options, basis options, Bermudan options and quanto options.
3. Behavioural risk: risk of a change in exercise/prepayment outcomes such as those that arise in fixed rate mortgage products where retail clients may make decisions motivated by factors other than pure financial gain (such as demographical features and/or and other social factors). A callable bond may only be seen as possibly having behavioural risk if the right to call lies with a retail client.

When an instrument is subject to one or more of the following risk types, this by itself will not cause the instrument to be subject to the RRAO:

1. Risk from a cheapest-to-deliver option;
2. Smile risk: the risk of a change in an implied volatility parameter necessary for determining the value of an instrument with optionality relative to the implied volatility of other instruments optionality with the same underlying and maturity, but different moneyness;
3. Correlation risk arising from multi-underlying European or American plain vanilla options, and from any options that can be written as a linear combination of such options. This exemption applies in particular to the relevant index options;
4. Dividend risk arising from a derivative instrument whose underlying does not consist solely of dividend payments; and
5. Index instruments and multi-underlying options of which treatment for delta, vega or curvature risk are set out in MAR21.31 and MAR21.32. These are subject to the RRAO if they fall within the definitions set out in this chapter. For funds that are subject to the treatment specified in MAR21.36(3) (ie treated as an unrated “other sector” equity), banks shall assume the fund is exposed to exotic underlying exposures, and to other residual risks, to the maximum possible extent allowed under the fund’s mandate.

In cases where a transaction exactly matches with a third-party transaction (ie a back-to-back transaction), the instruments used in both transactions must be excluded from the RRAO capital requirement. Any instrument that is listed and/or eligible for central clearing must be excluded from the RRAO for other residual risks as defined in MAR23.4. Any instrument that is listed and/or eligible for central clearing with an exotic underlying must be included in the RRAO.

The residual risk add-on must be calculated in addition to any other capital requirements within the standardised approach. The residual risk add-on is to be calculated as follows.

1. The scope of instruments that are subject to the RRAO must not have an impact in terms of increasing or decreasing the scope of risk factors subject to the delta, vega, curvature or DRC treatments in the standardised approach.
2. The RRAO is the simple sum of gross notional amounts of the instruments bearing residual risks, multiplied by a risk weight.
   1. The risk weight for instruments with an exotic underlying specified in MAR23.3 is 1.0%.
   2. The risk weight for instruments bearing other residual risks specified in MAR23.4 is 0.1%.³⁰

The use of internal models for the purposes of determining market risk capital requirements is conditional upon the explicit approval of the bank’s supervisory authority.

The supervisory authority will only approve a bank's use of internal models to determine market risk capital requirements if, at a minimum:

1. the supervisory authority is satisfied that the bank's risk management system is conceptually sound and is implemented with integrity;
2. the bank has, in the supervisory authority's view, a sufficient number of staff skilled in the use of sophisticated models not only in the trading area but also in the risk control, audit and, if necessary, back office areas;
3. the bank's trading desk risk management model has, in the supervisory authority's judgement, a proven track record of reasonable accuracy in measuring risk;
4. the bank regularly conducts stress tests along the lines set out in MAR30.19 to MAR30.23; and
5. the positions included in the bank's internal trading desk risk management models for determining minimum market risk capital requirements are held in trading desks that have been approved for the use of those models and that have passed the required tests described in MAR30.17.

Supervisory authorities may insist on a period of initial monitoring and live testing of a bank’s internal trading desk risk management model before it is used for the purposes of determining the bank’s market risk capital requirements.

The scope of trading portfolios that are eligible to use internal models to determine market risk capital requirements is determined based on a three-prong approach as follows:

1. The bank must satisfy its supervisory authority that both the bank’s organisational infrastructure (including the definition and structure of trading desks) and its bank-wide internal risk management model meet qualitative evaluation criteria, as set out in MAR30.5 to MAR30.16.
2. The bank must nominate individual trading desks, as defined in MAR12.1 to MAR12.6, for which the bank seeks model approval in order to use the internal models approach (IMA).
   1. The bank must nominate trading desks that it intends to be in-scope for model approval and trading desks that are out-of-scope for the use of the IMA. The bank must specify in writing the basis for these nominations.
   2. The bank must not nominate trading desks to be out-of-scope for model approval due to capital requirements for a particular trading desk determined using the standardised approach being lower than those determined using the IMA.
   3. The bank must use the standardised approach to determine the market risk capital requirements for trading desks that are out-of-scope for model approval. The positions in these out-of-scope trading desks are to be combined with all other positions that are subject to the standardised approach in order to determine the bank’s standardised approach capital requirements.
   4. Trading desks that the bank does not nominate for model approval at the time of model approval will be ineligible to use the IMA for a period of at least one year from the date of the latest internal model approval.
3. The bank must receive supervisory approval to use the IMA on individual trading desks. Following the identification of eligible trading desks, this step determines which trading desks will be in-scope to use the IMA and which risk factors within in-scope trading desks are eligible to be included in the bank’s internal expected shortfall (ES) models to determine market risk capital requirements as set out in MAR33.
   1. Each trading desk must satisfy profit and loss (P&L) attribution (PLA) tests on an ongoing basis to be eligible to use the IMA to determine market risk capital requirements. In order to conduct the PLA test, the bank must identify the set of risk factors to be used to determine its market risk capital requirements.
   2. Each trading desk also must satisfy backtesting requirements on an ongoing basis to be eligible to use the IMA to determine market risk capital requirements as set out in MAR32.4 to MAR32.19.
   3. Banks must conduct PLA tests and backtesting on a quarterly basis to update the eligibility and trading desk classification in PLA for trading desks in-scope to use the IMA.
   4. The market risk capital requirements for risk factors that satisfy the risk factor eligibility test as set out in MAR31.12 to MAR31.24 must be determined using ES models as specified in MAR33.1 to MAR33.15.
   5. The market risk capital requirements for risk factors that do not satisfy the risk factor eligibility test must be determined using stressed expected shortfall (SES) models as specified in MAR33.16 to MAR33.17.

In order to use the IMA to determine market risk capital requirements, the bank must have market risk management systems that are conceptually sound and implemented with integrity. Accordingly, the bank must meet the qualitative criteria set out below on an ongoing basis. Supervisors will assess that the bank has met the criteria before the bank is permitted to use the IMA.

The bank must have an independent risk control unit that is responsible for the design and implementation of the bank’s market risk management system. The risk control unit should produce and analyse daily reports on the output of the trading desk’s risk management model, including an evaluation of the relationship between measures of risk exposure and trading limits. This risk control unit must be independent of business trading units and should report directly to senior management of the bank.

The bank’s risk control unit must conduct regular backtesting and PLA assessments at the trading desk level. The bank must also conduct regular backtesting of its bank-wide internal models used for determining market risk capital requirements.

A distinct unit of the bank that is separate from the unit that designs and implements the internal models must conduct the initial and ongoing validation of all internal models used to determine market risk capital requirements. The model validation unit must validate all internal models used for purposes of the IMA on at least an annual basis.

The board of directors and senior management of the bank must be actively involved in the risk control process and must devote appropriate resources to risk control as an essential aspect of the business. In this regard, the daily reports prepared by the independent risk control unit must be reviewed by a level of management with sufficient seniority and authority to enforce both reductions of positions taken by individual traders and reductions in the bank’s overall risk exposure.

Internal models used to determine market risk capital requirements are likely to differ from those used by a bank in its day-to-day internal risk management functions. Nevertheless, the core design elements of both the market risk capital requirement model and the internal risk management model should be the same.

1. Valuation models that are a feature of both models should be similar. These valuation models must be an integral part of the internal identification, measurement, management and internal reporting of price risks within the bank’s trading desks.
2. Internal risk management models should, at a minimum, be used to assess the risk of the positions that are subject to market risk capital requirements, although they may assess a broader set of positions.
3. The construction of a trading desk risk management model must be based on the methodologies used in the bank’s internal risk management model with regard to risk factor identification, parameter estimation and proxy concepts and deviate only if this is appropriate due to regulatory requirements. A bank’s market risk capital requirement model and its internal risk management model should address an identical set of risk factors.

A routine and rigorous programme of stress testing is required. The results of stress testing must be:

1. reviewed at least monthly by senior management;
2. used in the bank’s internal assessment of capital adequacy; and
3. reflected in the policies and limits set by the bank’s management and its board of directors.

Where stress tests reveal particular vulnerability to a given set of circumstances, the bank must take prompt action to mitigate those risks appropriately (eg by hedging against that outcome, reducing the size of the bank’s exposures or increasing capital).

The bank must maintain a protocol for compliance with a documented set of internal manuals, policies, controls and procedures concerning the operation of the internal market risk management model. The bank’s risk management model must be well documented. Such documentation may include a comprehensive risk management manual that describes the basic principles of the risk management model and that provides a detailed explanation of the empirical techniques used to measure market risk.

The bank must receive approval from its supervisory authority prior to implementing any significant changes to its internal models used to determine market risk capital requirements.

The bank’s internal models for determining market risk capital requirements must address the full set of positions that are in the scope of application of the model. All models’ measurements of risk must be based on a sound theoretical basis, calculated correctly, and reported accurately.

The bank’s internal audit and validation functions or external auditor must conduct an independent review of the market risk measurement system on at least an annual basis. The scope of the independent review must include both the activities of the business trading units and the activities of the independent risk control unit. The independent review must be sufficiently detailed to determine which trading desks are impacted by any failings. At a minimum, the scope of the independent review must include the following:

1. the organisation of the risk control unit;
2. the adequacy of the documentation of the risk management model and process;
3. the accuracy and appropriateness of market risk management models (including any significant changes);
4. the verification of the consistency, timeliness and reliability of data sources used to run internal models, including the independence of such data sources;
5. the approval process for risk pricing models and valuation systems used by the bank’s front- and back-office personnel;
6. the scope of market risks reflected in the trading desk risk management models;
7. the integrity of the management information system;
8. the accuracy and completeness of position data;
9. the accuracy and appropriateness of volatility and correlation assumptions;
10. the accuracy of valuation and risk transformation calculations;
11. the verification of trading desk risk management model accuracy through frequent backtesting and PLA assessments; and
12. the general alignment between the model to determine market risk capital requirements and the model the bank uses in its day-to-day internal management functions.