FRTB Accelerator User & Developer Guide 2.1.0

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Measures - starting point

In a Nutshell...

This page lists (for SA and IMA separately)the key set of measures and hierarchies you can use to break down the Capital Charge by organisational structure and methodology.

For further information on these entities, see:

References to BCBS 352 (Paragraph number and page number) are provided below where appropriate.

For details on specific levels, see the FRTB Cube documentation.

 

ClosedSA and IMA Dimensions, Hierarchies and Levels
ClosedKey SA Measures
Headline Measure Acronym Full Measure Name
SA CRC SA Capital Charge (no filtering by desk)

 

Component measures of the SA Capital Charge

Acronym Full Name BCBS 352 Specification Reference
  SBM CC Sensitivities Based Method Capital Charge

BCBS 352 Paragraph 55 - no filtering by desk:

For each scenario (High, Medium, Low), the bank must determine a scenario-related risk charge at the portfolio level as the simple sum of the risk charges at risk class level for that scenario. The ultimate portfolio level risk capital charge is the largest of the three scenario-related portfolio level risk capital charges.
  SA DRC SA Default Risk Charge

BCBS 352 Paragraph 134 to 137 - no filtering by desk:

Paragraph 134:

The approach for the standardised default risk capital charge comprises a multi-step procedure.

  • The first step is to determine JTD loss amounts for each instrument that is subject to default risk.
  • The second step is to offset the JTD amounts of long and short exposures with respect to the same obligor (where permissible) to produce net long and net short amounts in distinct obligors.
  • In the third step, the net short exposures are discounted by a hedge benefit ratio.
  • As a final step, default risk weights are applied to arrive at the capital charge.

The procedure is specified in the material below. In the procedure, offsetting refers to the netting of exposures to the same obligor (where a short exposure may be subtracted in full from a long exposure), while 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).

Paragraph 135:

The default risk charge for non-securitisations and securitisations is independent of the other capital charges in the Standardised Approach for Market Risk; in particular it is independent of the CSR capital charge.

Paragraph 136:

For the correlation trading portfolio (CTP), the capital charge includes the default risk for securitisation exposures and for non-securitisation hedges. These hedges are to be removed from the default risk non-securitisation calculations. There must be no diversification benefit between the default risk charge for non-securitisations, default risk charge for securitisations (non-correlation trading portfolio) and default risk charge for the securitisation correlation trading portfolio.  

Paragraph 137:

In line with criteria set out in other parts of the Capital Accord, at national discretion, claims on sovereigns, public sector entities and multilateral development banks may be subject to a zero default risk weight. 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. 
  RRAO Residual Risk Add On

BCBS 352 Paragraph 58 - no filtering by desk:

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

(a) The residual risk add-on must be calculated in addition to any other capital requirements within the standardised approach.

(b) The scope of instruments that are subject to the residual risk add-on must not have an impact in terms of increasing or decreasing the scope of risk factors subject to the delta, vega, curvature or default risk capital treatments in the standardised approach.

(c) The residual risk add-on is the simple sum of gross notional amounts of the instruments bearing residual risks, multiplied by a risk weight of 1.0% for instruments with an exotic underlying and a risk weight of 0.1% for instruments bearing other residual risks.

(d) 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 charges in the standardised approach.

(e) Instruments bearing other residual risks are those that meet criteria (i) and (ii) below:

(i) Instruments subject to vega or curvature risk capital charges 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, CDS price or interest rate swap.
(ii) Instruments which fall under the definition of the Correlation Trading Portfolio (CTP) in BCBS 352 Paragraph 61, except for those instruments which are recognised in the Market Risk Framework as eligible hedges of risks within the CTP.


(f) In cases where a transaction exactly matches with a third-party transaction (i.e. a back-to-back transaction), the instruments used in both transactions must be excluded from the residual risk add-on charge. Any instrument that is listed and/or eligible for central clearing must be excluded from the residual risk add-on. 

(g) A non-exhaustive list of other residual risks types and instruments that may fall within the criteria set out in paragraphs 58(e) include:

  • 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.
  • Correlation risk: risk of a change in a correlation parameter necessary for determination of 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.
  • 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.

(h) 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 residual risk add-on:

(i) Risk from a cheapest-to-deliver option.
(ii) Smile risk – the risk of a change in an implied volatility parameter necessary for determination of 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.
(iii) Correlation risk arising from multi-underlying European or American plain vanilla options where all underlyings have sensitivities for delta risk of the same sign, 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.
(iv) Dividend risk arising from a derivative instrument whose underlying does not consist solely of dividend payments. 



 

ClosedKey IMA Measures
Component measures of the IMA Capital Charge
  Acronym Full Name BCBS 352 Specification Reference
  CA-IMA IMA Capital Charge filtered by approved desks

CA from BCBS 352 Paragraph 181(j)

Each bank must meet, on a daily basis, a capital requirement CA expressed as the higher of:

Its previous day’s aggregate capital charge for market risk

An average of the daily capital measures in the preceding 60 business days according to the parameters specified in Paragraphs 187 to 194 for the following formula:

 

and Paragraph 189:

The aggregate capital charge for modellable risk factors (IMCC) is based on the weighted average of the constrained and unconstrained expected shortfall charges. 

 

The stress period used in the risk class-level ESR,S,i should be the same as that used to calculate the portfolio-wide ESR,S.  ρ is the relative weight assigned to the firm’s internal model. The value of ρ is 0.5. For regulatory capital purposes, the aggregated charge associated with approved desks (CA) is equal the maximum of the most recent observation and a weighted average of the previous 60 days scaled by a multiplier (mc). 

 

where SES is the aggregate regulatory capital measure for K risk factors in model-eligible desks that are non-modellable.

 

The multiplication factor mc will be 1.5 or set by individual supervisory authorities on the basis of their assessment of the quality of the bank’s risk management system, subject to an absolute minimum of 1.5. Banks must add to this factor a “plus” directly related to the ex-post performance of the model, thereby introducing a built-in positive incentive to maintain the predictive quality of the model. The plus will range from 0 to 0.5 based on the outcome of the backtesting of the bank’s daily VaR at the 99th percentile based on current observations on the full set of risk factors (VaRFC). If the backtesting results are satisfactory and the bank meets all of the qualitative standards set out in paragraph 180, the plus factor could be zero. Appendix B presents in detail the approach to be applied for backtesting and the plus factor. Banks must develop the capability to perform backtests using both hypothetical (i.e. using changes in portfolio value that would occur were end-of-day positions to remain unchanged) and actual trading (excluding fees and commissions) outcomes. The multiplication factor will be based upon the maximum of the exceptions generated by the two backtesting results. 

  CA-IMA Spot Spot version of CA-IMA (IMCC + SES) filtered by approved desks IMCC + SES filtered by approved desks
  IMADRC IMA Default Risk Charge filtered by approved desks 

DRC from BCBS 352 Paragraph 191

The additional regulatory capital charge for modellable risk positions subject to default risk is DRC as described in Paragraph 186:

Banks must have a separate internal model to measure the default risk of trading book positions. The general criteria in Paragraphs 176 to 179 and the qualitative standards in Paragraph 180 also apply to the default risk model.
  CU-SA SA Capital Charge filtered by unapproved desks

CU from BCBS 352 Paragraph 193 filtered by unapproved desks:

The regulatory capital charge associated with risks from model-ineligible (i.e. unapproved) desks (CU) is to be calculated by aggregating all such risks and applying the standardised charge.
  PLA Tests The mean of the unexplained P&L divided by the standard deviation of the hypothetical P&L

From BCBS 352 Paragraph 183(b):

P&L attribution requirements are based on two metrics: mean unexplained daily P&L (i.e. risk theoretical P&L minus hypothetical P&L) over the standard deviation of hypothetical daily P&L and the ratio of variances of unexplained daily P&L and hypothetical daily P&L. These ratios are calculated monthly and reported prior to the end of the following month. If the first ratio is outside of the range of -10% to +10% or if the second ratio were in excess of 20% then the desk experiences a breach. If the desk experiences four or more breaches within the prior 12 months then it must be capitalised under the standardised approach. The desk must remain on the standardised approach until it can pass the monthly P&L attribution requirement and provided it has satisfied its backtesting exceptions requirements over the prior 12 months. Trading desks that do not satisfy the minimum backtesting and P&L attribution requirements are ineligible for capitalisation using the internal models approach. Risk exposures within these ineligible desks must be included with the out-of-scope desks and capitalised according to the standardised methodology on a portfolio basis. 
  The variance of the unexplained P&L divided by the variance of the hypothetical P&L
  Backtesting The number of exceptions at the 97.5% confidence level

From BCBS 352 Paragraph 183(b):

Backtesting requirements are based on comparing each desk’s 1-day static value-at-risk measure (calibrated to the most recent 12 months’ data, equally weighted) at both the 97.5th percentile and the 99th percentile, using at least one year of current observations of the desk’s one-day P&L. If any given desk experiences either more than 12 exceptions at the 99th percentile or 30 exceptions at the 97.5th percentile in the most recent 12-month period, all of its positions must be capitalised using the standardised approach. Positions must continue to be capitalised using the standardised method until the desk no longer exceeds the above thresholds over the prior 12 months.
  The number of exceptions at the 99% confidence level
  The dates of the exceptions at the 97.5% confidence level
  The dates of the exceptions at the 99% confidence level
ClosedCombined Measures
Acronym Full Name BCBS 352 Specification Reference
CCC Combined Capital Charge

BCBS 352 Paragraph 194 (Page 65)

The combined capital charge for market risk (CCC) is equal to the aggregate capital requirement for eligible trading desks plus the standardised capital charge for risks from unapproved trading desks (CU).

ACC = CA + DRC + CU

CCC Spot Spot version of Combined Capital Charge - no history BCBS 352 Paragraph 55 - no filtering by desk
ClosedViewing measure chains with DoctorPivot

DoctorPivot is a tool specifically designed to produce visual representations of the relationships and links between measures. For any measure you select (from any given cube), DoctorPivot calculates and displays all the chains of measures that are derived from this measure, together with the names and Javadoc classes of the PostProcessors that generate the more advanced measures from the selected measure.

For more information, see DoctorPivot - viewing measures and postprocessors.

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