FRTB: The Canadian perspective, Part 2: Standardized approach · The standardized approach capital requirement under FRTB is the aggregation of three components: the risk charges

The Canadian perspective

Part 2: Standardized approach

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FRTB

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Capital adequacy requirements (CAR)

Current marketrisk rule

Approach

Key features

Risk categories

Standardized approach (SA)

Internal modelsapproach (IMA)

IR EQ IR FX EQ CM CR

Specific risk Generalmarket risk

VaR &stressed VaR

Incremental risk charge

A comparison between FRTB and CARIn Part 2 of our series on FRTB: the Canadian Perspective, we highlight key differences and similarities between FRTB and the Capital Adequacy Requirements (CAR) guidelines that have been adopted by Canadian banks. The new capital requirements under FRTB are a marked change from those in the Basel 2.5 and CAR guidelines; however, both regulatory documents offer banks

a choice between a standardized approach (SA) and an internal models approach (IMA). The FRTB standardized approach is generally more sophisticated than its predecessor, and is based on three components: risk charges under the sensitivities-based method, default risk charge, and residual risk add-on.

The capital charges for market risk are predefined by OSFI based on historical losses for each product type, and typically based on a weighted sum, where

the weights are prescribed for each risk category and instrument type in Chapter 9 of the CAR guidelines.

The total capital requirement is the aggregated specific risk charge and general market risk charge for the applicable risk categories.

The standardized approach capital requirement under CAR considers five risk categories:

Interest rate position risk

Equities risk

Foreign exchange position risk

Commodities risk

Options risk.

1

2

3

4

5

Capital adequacy requirements

© 2017 KPMG LLP, a Canadian limited liability partnership and a member firm of the KPMG network of independent member firms affiliated with KPMG International Cooperative (“KPMG International”), a Swiss entity. All rights reserved.

FRTB 2

The standardized approach capital requirement under FRTB is the aggregation of three components: the risk charges under the sensitivities-based method, the default risk charge, and the residual risk add-on. The sensitivities based risk charge is further divided among seven risk classes defined in the FRTB:

General Interest Rate Risk (GIRR)

Credit Spread Risk (CSR): non-securitization

CSR: securitization Correlation Trading Portfolio (CTP)

CSR: securitization non-CTP

Foreign Exchange (FX) Risk

Equity Risk

Commodity Risk.

The hierarchy of this approach is visualized below.

1

2

3

4

5

6

7

Fundamental review of the trading bookFRTB’s standardized approach aligns more closely to the current internal models approach under CAR, incorporating concepts such as sensitivities that were previously mainly used by banks using IMA approach.

Fundamental review of the trading book(FRTB)

New market risk rule

Approach

Key features

Risk classes

Sensitivites

Standardized approach (SA)

Internal modelsapproach (IMA)

non-sec, sec CTP, sec non-CTP

Stressed capital add-on

Default risk charge

Global expectedshortfall

Residual risk add-on

Sensitivities based risk charge

Default riskcharge

IR, FX, EQ, CM, CSR (non-sec), CSR (sec-CTP), CSR (sec non-CTP)

Delta Vega Curvature

It is important to note that under FRTB, the standardized approach calculation will need to be computed, regardless if the desk in question is subject to IMA or not. For IMA banks, the capital charge under the standardized approach will be used to

construct a “floor” on the IMA capital charge. While the details of how this floor is calculated remains to be seen, it will be used to set the binding constraint for the minimum amount of capital that needs to be held.


3The Canadian Perspective

Key changes from current CAR to FRTB – Sensitivities Based Measures

(new): Different from the specific and general risk calculation in CAR, the FRTB guidelines introduce three sensitivities-based measures: Delta, Vega and Curvature. These sensitivities must be calculated for each of the seven risk classes under FRTB, but were not included for use in this way in the CAR framework. Both Vega and Curvature are new concepts from CAR, and Delta was only previously used as a multiplier for specific risk charge of options. The capital calculations are specific to each measure and the capital requirement under the sensitivities based measures is obtained by aggregating all three measures. To calculate sensitivities the bank must have a price for each kind of derivative in its portfolio.

– Default Risk Charge: Default Risk Charge was introduced to capture the jump-to-default (JTD) risk based on the credit risk treatment in the banking book. The motivation behind this new addition is to reduce the possible discrepancy in capital requirements for similar risk exposures across the banking book and the trading book.

Gross JTD is the essential part in the default risk capital charge calculation. It is calculated as a

function of the Loss Given Default (LGD), notional amount and the cumulative profit and/or loss already realized on the position. The formulas for calculating gross JTD are subject to specific risk classes.

– Residual Risk Add-On: The Residual Risk Add-On is introduced by FRTB to capture any other risks beyond the main risk factors already captured in the sensitivities-based method and the Default Risk Charge. The Residual Risk Add-On is to be calculated for all instruments individually and in addition to the other components of the capital requirements under the standardized approach. The calculation is done by summing the gross notional amounts of the individual instruments. This sum is then multiplied by a residual risk weight to determine the residual risk add-on. The magnitude of residual risk weight is dependent on the type of underlying assets. Instruments with exotic underlying assets are given a much higher (100 x higher) residual risk weight.

– Consideration of Correlations: In order to capture the risk from correlation in periods of financial stress, which previously had not been considered as part of the standardized approach, the Basel committee has set up three

different scenarios, representing low, medium and high correlation environments. Under each scenario, different correlation parameters are set and three risk charge figures are calculated using these correlation inputs. The ultimate portfolio level risk capital charge under FRTB is chosen as the maximum of the three scenario-related portfolio level capital charges.

– Standardized Approach for the Correlation Trading Portfolio: Under the CAR framework, banks can choose to model the Correlation Trading Portfolio (CTP) risk using the standardized approach or the internal models approach. However, under FRTB, the CTP risk must be captured using the standardized approach. This is due to regulatory concerns around the ability of internal models to adequately capture the CTP’s risks. This classification is expected to lead to much larger capital requirements. Based on a sample of 44 bank portfolios, the BCBS has estimated that weighted-mean capital charges of securitizations (excluding CTP instruments) would increase by 22 percent relative to Basel 2.5, whereas CTP securitizations would lead to an increase of 70 percent.1

1 Banking Tech, (2016), Fundamental Review of the Trading Book: impact on capital requirements and risk architecture


FRTB 4

Example: Cross-Currency Swap capital requirement calculation

1 year cross currency swap

Risk weighted positions

Total general market risk

Total capital requirement

Total specific market risk

Risk weights Risk factors

Basis riskcharge

Net positioncharge

Yield curverisk charge

For this example, it is assumed that the maturity T is 1yr: at time T we buy C1 of currency 1 and sell C2 in currency 2. Also assume the counterparty has a BBB rating.

General riskIRR (Basis Risk Charge)

The IRR charge for basis risk is given by the maximum of long and short positions at each maturity band (measured in the reporting currency) multiplied by that bands risk weight and the basis charge (10%). Since there is only 1 maturity period in our example this is given by.

Forthisexample,itisassumedthatthematurityTis1yr:attime𝑇𝑇webuy𝐶𝐶!ofcurrency1andsell𝐶𝐶!incurrency2.AlsoassumethecounterpartyhasaBBBrating.

GeneralRisk

IRR(BasisRiskCharge)

TheIRRchargeforbasisriskisgivenbythemaximumoflongandshortpositionsateachmaturityband(measuredinthereportingcurrency)multipliedbythatbandsriskweightandthebasischarge(10%).Sincethereisonly1maturityperiodinourexamplethisisgivenby.

𝐼𝐼𝐼𝐼𝐼𝐼!"#$# = 𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶!𝐹𝐹𝐹𝐹!,𝐶𝐶!𝐹𝐹𝐹𝐹! ∗ 𝑅𝑅𝑅𝑅!!!" ∗ 10%

Where𝑅𝑅𝑅𝑅!!!"istheriskweightforapositionwithmaturitybetween6and12months.𝑅𝑅𝑅𝑅!!!"isgivenintheCARguidelinesas0.70%.

IRR(YieldCurveCharge)

Theyieldcurvechargeisgivenbythenetoffsettingpositionmultipliedbythezoneyieldcharge:

𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶!𝐹𝐹𝐹𝐹!,𝐶𝐶!𝐹𝐹𝐹𝐹! ∗ 𝑅𝑅𝑅𝑅!!!" ∗ 𝑍𝑍𝑍𝑍𝑍𝑍𝑍𝑍 1 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎

TheZone1(maturities12monthsorless)yieldchargeisgivenby40%intheCARguidelines.

IRR(NetPositionCharge)

1yearcrosscurrencyswap

Where RW6 –12 is the risk weight for a position with maturity between 6 and 12 months. RW6 –12 is given in the CAR guidelines as 0.70%.

IRR (Yield Curve Charge)

The yield curve charge is given by the net offsetting position multiplied by the zone yield charge:

Forthisexample,itisassumedthatthematurityTis1yr:attime𝑇𝑇webuy𝐶𝐶!ofcurrency1andsell𝐶𝐶!incurrency2.AlsoassumethecounterpartyhasaBBBrating.

GeneralRisk

IRR(BasisRiskCharge)

TheIRRchargeforbasisriskisgivenbythemaximumoflongandshortpositionsateachmaturityband(measuredinthereportingcurrency)multipliedbythatbandsriskweightandthebasischarge(10%).Sincethereisonly1maturityperiodinourexamplethisisgivenby.

𝐼𝐼𝐼𝐼𝐼𝐼!"#$# = 𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶!𝐹𝐹𝐹𝐹!,𝐶𝐶!𝐹𝐹𝐹𝐹! ∗ 𝑅𝑅𝑅𝑅!!!" ∗ 10%

Where𝑅𝑅𝑅𝑅!!!"istheriskweightforapositionwithmaturitybetween6and12months.𝑅𝑅𝑅𝑅!!!"isgivenintheCARguidelinesas0.70%.

IRR(YieldCurveCharge)

Theyieldcurvechargeisgivenbythenetoffsettingpositionmultipliedbythezoneyieldcharge:

𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶!𝐹𝐹𝐹𝐹!,𝐶𝐶!𝐹𝐹𝐹𝐹! ∗ 𝑅𝑅𝑅𝑅!!!" ∗ 𝑍𝑍𝑍𝑍𝑍𝑍𝑍𝑍 1 𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦𝑦 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎

TheZone1(maturities12monthsorless)yieldchargeisgivenby40%intheCARguidelines.

IRR(NetPositionCharge)

1yearcrosscurrencyswap

The Zone 1 (maturities 12 months or less) yield charge is given by 40% in the CAR guidelines.

Example of capital requirements calculation To illustrate the difference between the capital requirements under CAR vs. FRTB, here below is an example of a cross-currency swap calculation under both regimes.



IRR (Net Position Charge)

Net position charge is applied to unmatched positions. However, since the timing of the swap payments is the same, there is no unmatched positions, resulting in no net position charge.

Foreign exchange position risk

Foreign Exchange risk is given by 8% of the larger of the total long and total short positions of each currency. In the case of a single cross-currency swap this is given by:

Netpositionchargeisappliedtounmatchedpositions.However,sincethetimingoftheswappaymentsisthesame,thereisnounmatchedpositions,resultinginnonetpositioncharge.

ForeignExchangePositionRisk

ForeignExchangeriskisgivenby8%ofthelargerofthetotallongandtotalshortpositionsofeachcurrency.Inthecaseofasinglecross-currencyswapthisisgivenby:

𝐹𝐹𝐹𝐹 𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = max 𝐶𝐶!𝐹𝐹𝐹𝐹!,𝐶𝐶!𝐹𝐹𝐹𝐹! ∗ 8%

SpecificRisk

Sincecross-currencyswapsarenotbasedonanunderlyinginstrument,nospecificriskcapitalchargeisrequired.

Total

Thetotalcapitalchargeisthesimplesumofthesecharges:

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐶𝐶ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 𝐼𝐼𝐼𝐼𝐼𝐼!"#$# + 𝐼𝐼𝐼𝐼𝐼𝐼!"#$% !"#$% + 𝐹𝐹𝐹𝐹 𝑐𝑐ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎

= 𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶!𝐹𝐹𝐹𝐹!,𝐶𝐶!𝐹𝐹𝐹𝐹! ∗ 0.7% ∗ 10% +𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶!𝐹𝐹𝐹𝐹!,𝐶𝐶!𝐹𝐹𝐹𝐹! ∗ 0.7% ∗ 40%+max 𝐶𝐶!𝐹𝐹𝐹𝐹!,𝐶𝐶!𝐹𝐹𝐹𝐹! ∗ 8%

= 𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶!𝐹𝐹𝐹𝐹!,𝐶𝐶!𝐹𝐹𝐹𝐹! ∗ 8.07% +𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶!𝐹𝐹𝐹𝐹!,𝐶𝐶!𝐹𝐹𝐹𝐹! ∗ 0.28%

Example:Cross-CurrencySwapcapitalrequirementcalculation

Specific risk

Since cross-currency swaps are not based on an underlying instrument, no specific risk capital charge is required.

Total

The total capital charge is the simple sum of these charges:





SpecificRisk


Total










SpecificRisk


Total










SpecificRisk


Total










SpecificRisk


Total






Example: Cross-Currency Swap capital requirement calculation

1 year cross-currency swap

Delta GIRR

WeightedDelta GIRR

Correlationwithin buckets

Risk weights

Correlationbetweem buckets

Delta GIRRrisk position

Total capital requirement

Delta FXrisk position

Delta GIRRrisk charge

Delta FXrisk charge

WeightedDelta FX

Delta FX

Defaultrisk charge


FRTB 6

Assume our portfolio consists of the same cross-currency swap as in the previous example. The capital charge is the sum of the Delta charge, DRC and Residual risk charge. This example will focus on the first 2 charges.

Delta

The price of a Cross-Currency Swap is given by:

Assumeourportfolioconsistsofthesamecross-currencyswapasinthepreviousexample.ThecapitalchargeisthesumoftheDeltacharge,DRCandResidualriskcharge.Thisexamplewillfocusonthefirst2charges.

Delta

ThepriceofaCross-CurrencySwapisgivenby:

𝑉𝑉 = 𝐶𝐶! ∙ 𝐹𝐹𝐹𝐹! ∙ exp −𝑟𝑟! 𝑇𝑇 ∙ 𝑇𝑇 − 𝐶𝐶! ∙ 𝐹𝐹𝐹𝐹! ∙ exp −𝑟𝑟! 𝑇𝑇 ∙ 𝑇𝑇

Thefirststepistoidentifytheriskfactors:Generalinterestrate:𝑟𝑟! 𝑇𝑇 and𝑟𝑟! 𝑇𝑇 andforeignexchange:rates𝐹𝐹𝐹𝐹!and𝐹𝐹𝐹𝐹!.Thenwecalculatethesensitivitiestoeachriskfactor:

𝑠𝑠!"! = 𝐶𝐶! ∙ exp −𝑟𝑟! 𝑇𝑇 ∙ 𝑇𝑇 = 𝑑𝑑!

𝑠𝑠!"! = −𝐶𝐶! ∙ exp −𝑟𝑟! 𝑇𝑇 ∙ 𝑇𝑇 = 𝑑𝑑!

1yearcross-currencyswap

DeltaFX

WeightedDeltaFX

DeltaFXRiskposition

DeltaFXRiskcharge

DefaultRiskCharge

The first step is to identify the risk factors: General interest rate: r1(T ) and r2(T ) and foreign exchange: rates FX1 and FX2. Then we calculate the sensitivities to each risk factor:


Delta







DeltaFX

WeightedDeltaFX

DeltaFXRiskposition

DeltaFXRiskcharge

DefaultRiskCharge


Delta







DeltaFX

WeightedDeltaFX

DeltaFXRiskposition

DeltaFXRiskcharge

DefaultRiskCharge

𝑠𝑠!! = 𝐶𝐶! ∙ 𝐹𝐹𝐹𝐹! ∙ exp −𝑟𝑟! 𝑇𝑇 ∙ 𝑇𝑇 ∙ −𝑇𝑇 = 𝑇𝑇 ∙ 𝐹𝐹𝐹𝐹! ∙ 𝑑𝑑!

𝑠𝑠!! = −𝐶𝐶! ∙ 𝐹𝐹𝐹𝐹! ∙ exp −𝑟𝑟! 𝑇𝑇 ∙ 𝑇𝑇 ∙ −𝑇𝑇 = 𝑇𝑇 ∙ 𝐹𝐹𝐹𝐹! ∙ 𝑑𝑑!

Weightedsensitivitiesareobtainedastheproductofriskweightandsensitivity:

𝑊𝑊𝑊𝑊!! = 𝑅𝑅𝑅𝑅!! ∙ 𝑠𝑠!!;𝑊𝑊𝑊𝑊!! = 𝑅𝑅𝑅𝑅!! ∙ 𝑠𝑠!!;𝑊𝑊𝑊𝑊!"! = 𝑅𝑅𝑅𝑅!"! ∙ 𝑠𝑠!"!;𝑊𝑊𝑊𝑊!"! = 𝑅𝑅𝑅𝑅!"! ∙ 𝑠𝑠!"!

TheriskweightsforFXandInterestratesareprovidedintheFRTBstandard:

𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!" = 30%

𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅! = 2.25%

Nextwecalculatethetotaldeltausingbucketcorrelations.Thereare4buckets:eachcurrencies’interestrateandFX.Allriskfactorsbelongtoeachownbucket;sonoinside-bucketaggregationandinside-bucketcorrelationisirrelevant.Crossbucketcorrelationiscalculatedusingcrossbucketcorrelations:γ.FullDeltariskchargeacrossIRandFXriskclassesiscomputedvia:

𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 = 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷!" + 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷!"

= 𝑊𝑊𝑊𝑊!!! +𝑊𝑊𝑊𝑊!!! + 2 ∙ 𝛾𝛾!" ∙𝑊𝑊𝑊𝑊!! ∙𝑊𝑊𝑊𝑊!! + 𝑊𝑊𝑊𝑊!"!! +𝑊𝑊𝑊𝑊!"!

! + 2 ∙ 𝛾𝛾!" ∙𝑊𝑊𝑊𝑊!"! ∙𝑊𝑊𝑊𝑊!"!

Thestandardidentifiescrossbucketcorrelationsforeachassetclass:𝛾𝛾!" = 50%;𝛾𝛾!" = 60%.

DefaultRiskCharge

Jump-to-Default(JTD)chargeingeneralis:






𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!" = 30%

𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅! = 2.25%




! + 2 ∙ 𝛾𝛾!" ∙𝑊𝑊𝑊𝑊!"! ∙𝑊𝑊𝑊𝑊!"!


DefaultRiskCharge


Weighted sensitivities are obtained as the product of risk weight and sensitivity:






𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!" = 30%

𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅! = 2.25%




! + 2 ∙ 𝛾𝛾!" ∙𝑊𝑊𝑊𝑊!"! ∙𝑊𝑊𝑊𝑊!"!


DefaultRiskCharge







𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!" = 30%

𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅! = 2.25%




! + 2 ∙ 𝛾𝛾!" ∙𝑊𝑊𝑊𝑊!"! ∙𝑊𝑊𝑊𝑊!"!


DefaultRiskCharge


The risk weights for FX and Interest rates are provided in the FRTB standard:






𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!" = 30%

𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅! = 2.25%




! + 2 ∙ 𝛾𝛾!" ∙𝑊𝑊𝑊𝑊!"! ∙𝑊𝑊𝑊𝑊!"!


DefaultRiskCharge







𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!" = 30%

𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅! = 2.25%




! + 2 ∙ 𝛾𝛾!" ∙𝑊𝑊𝑊𝑊!"! ∙𝑊𝑊𝑊𝑊!"!


DefaultRiskCharge


Next we calculate the total delta using bucket correlations. There are 4 buckets: each currencies’ interest rate and FX. All risk factors belong to each own bucket; so no inside-bucket aggregation and inside-bucket correlation is irrelevant. Cross bucket correlation is calculated using cross bucket correlations: g. Full Delta risk charge across IR and FX risk classes is computed via:






𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!"! = 𝑅𝑅𝑅𝑅!" = 30%

𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅!! = 𝑅𝑅𝑅𝑅! = 2.25%




! + 2 ∙ 𝛾𝛾!" ∙𝑊𝑊𝑊𝑊!"! ∙𝑊𝑊𝑊𝑊!"!


DefaultRiskCharge


The standard identifies cross bucket correlations for each asset class: gIR = 50%; gFX = 60%.



Default risk charge

Jump-to-Default (JTD) charge in general is:

𝐽𝐽𝐽𝐽𝐽𝐽 long = max 𝐿𝐿𝐿𝐿𝐿𝐿 ∙ Notional+ 𝑃𝑃&𝐿𝐿, 0

𝐽𝐽𝐽𝐽𝐽𝐽 short = min 𝐿𝐿𝐿𝐿𝐿𝐿 ∙ Notional+ 𝑃𝑃&𝐿𝐿, 0

and“whenthepriceoftheinstrumentisnotlinkedtotherecoveryrateofdefaulter,thereshouldbenomultiplicationofthenotionalbytheLGD.”ThiscaseisexactlyrelatedtoIR/FXderivative,sotheaboveequationsreduceto:

𝐽𝐽𝐽𝐽𝐽𝐽 long = max 𝑉𝑉, 0 ; 𝐽𝐽𝐽𝐽𝐽𝐽 short = min 𝑉𝑉, 0

Formaturityof1yearthereisnoexposureoffsetfor 𝐽𝐽𝐽𝐽𝐽𝐽.Hedgingrelationshipwithrespecttoshort:

𝑊𝑊𝑊𝑊𝑊𝑊 =𝐽𝐽𝐽𝐽𝐽𝐽!"#$

𝐽𝐽𝐽𝐽𝐽𝐽!"#$ + 𝐽𝐽𝐽𝐽𝐽𝐽!!!"#

When𝑉𝑉 > 0itgives:𝐽𝐽𝐽𝐽𝐽𝐽!"#$ = 𝑉𝑉,𝐽𝐽𝐽𝐽𝐽𝐽!!!"# = 0,𝑊𝑊𝑊𝑊𝑊𝑊 = 1.

For𝑉𝑉 < 0itwillbe:𝐽𝐽𝐽𝐽𝐽𝐽!"#$ = 0,𝐽𝐽𝐽𝐽𝐽𝐽!!!"# = 𝑉𝑉,𝑊𝑊𝑊𝑊𝑊𝑊 = 0.

Defaultriskchargeforabucket:

𝐷𝐷𝐷𝐷𝐷𝐷! = 𝑅𝑅𝑅𝑅!"# ∙max 𝐽𝐽𝐽𝐽𝐽𝐽!"#$ −𝑊𝑊𝑊𝑊𝑊𝑊 ∙ 𝐽𝐽𝐽𝐽𝐽𝐽!!!"# , 0

or

𝐷𝐷𝐷𝐷𝐷𝐷! =𝑅𝑅𝑅𝑅!"# ∙ 𝑉𝑉, 𝑉𝑉 > 0

0, 𝑉𝑉 ≤ 0 = max 𝑅𝑅𝑅𝑅!"# ∙ 𝑉𝑉, 0 = 𝑅𝑅𝑅𝑅!"# ∙max 𝑉𝑉, 0

Itisonlyonebuckethere,so𝐷𝐷𝐷𝐷𝐷𝐷 = 𝐷𝐷𝐷𝐷𝐷𝐷!.

and “when the price of the instrument is not linked to the recovery rate of defaulter, there should be no multiplication of the notional by the LGD.” This case is exactly related to IR/FX derivative, so the above equations reduce to:












or




For maturity of 1 year there is no exposure offset for JTD. Hedging relationship with respect to short:












or




When V > 0 it gives: JTDlong = V, JTDshort = 0, WtS = 1.

For V < 0 it will be: JTDlong = 0, JTDshort = V, WtS = 0.

Default risk charge for a bucket:












or




or












or




It is only one bucket here, so DRC = DRCb.

Residual risk add-on

This trade is not a subject of Vega or Curvature risk and is not a Correlated Trade Portfolio. There is no residual risk connected to it.


FRTB 8

Total

Capital Charge = Delta + DRC

ResidualRiskAdd-On

ThistradeisnotasubjectofVegaorCurvatureriskandisnotaCorrelatedTradePortfolio.Thereisnoresidualriskconnectedtoit.

Total

𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶ℎ𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 + 𝐷𝐷𝐷𝐷𝐷𝐷

= 𝑊𝑊𝑊𝑊!!! +𝑊𝑊𝑊𝑊!!! + 2 ∙ 𝛾𝛾!" ∙𝑊𝑊𝑊𝑊!! ∙𝑊𝑊𝑊𝑊!!

+ 𝑊𝑊𝑊𝑊!"!! +𝑊𝑊𝑊𝑊!"!

! + 2 ∙ 𝛾𝛾!" ∙𝑊𝑊𝑊𝑊!"! ∙𝑊𝑊𝑊𝑊!"! + 𝑅𝑅𝑅𝑅!"# ∙max 𝑉𝑉, 0

= 𝑅𝑅𝑅𝑅! ∙ 𝑇𝑇 ∙ 𝑑𝑑!! ∙ 𝐹𝐹𝐹𝐹!! + 𝑑𝑑!! ∙ 𝐹𝐹𝐹𝐹!! + 2 ∙ 𝛾𝛾!" ∙ 𝑑𝑑! ∙ 𝑑𝑑! ∙ 𝐹𝐹𝐹𝐹! ∙ 𝐹𝐹𝐹𝐹!

+𝑅𝑅𝑅𝑅!" ∙ 𝑑𝑑!! + 𝑑𝑑!! + 2 ∙ 𝛾𝛾!" ∙ 𝑑𝑑! ∙ 𝑑𝑑! + 𝑅𝑅𝑅𝑅!"# ∙max 𝑉𝑉, 0

= 0.0225 ∙ 𝑑𝑑!! ∙ 𝐹𝐹𝐹𝐹!! + 𝑑𝑑!! ∙ 𝐹𝐹𝐹𝐹!! + 𝑑𝑑! ∙ 𝑑𝑑! ∙ 𝐹𝐹𝐹𝐹! ∙ 𝐹𝐹𝐹𝐹!

+0.3 ∙ 𝑑𝑑!! + 𝑑𝑑!! + 1.2 ∙ 𝑑𝑑! ∙ 𝑑𝑑! + 0.06 ∙max 𝑑𝑑! ∙ 𝐹𝐹𝐹𝐹! − 𝑑𝑑! ∙ 𝐹𝐹𝐹𝐹!, 0

WhatcanbanksleveragefromCARforFRTB?

CARInternalModelsforFRTBStandardizedApproach

BankscurrentlyusinginternalmodelsmayleveragetheirexistingmodelsandsystemsfortheFRTBStandardizedApproach(whichwillbeamandatorycalculation).Specifically,banksmayadapttheirframeworksforcalculatingthesensitivities-basedriskmeasures.BothpricingandriskinternalmodelsmayhaveDelta,VegaandCurvatureelements,especiallyinthecaseofderivativeinstruments,andthesesensitivitiesmaybeextendedtotheFRTBstandardizedapproach.Additionally,thenewFRTBJTDriskisafunctionofnotionalamount,marketvalueoftheinstrumentsandprescribedLGD.Banksmodelingincrementalriskcharge(IRC)underIMAhaveincorporatedLGDintheexpectedlosscalculation.TheexistingmodelsandsystemsrelatingtoLGD,usedinIMAdevelopment,canbemodifiedtoimplementdefaultriskcharge.

ResidualRiskAdd-On


Total












ResidualRiskAdd-On


Total












What can banks leverage from CAR for FRTB?CAR Internal models for FRTB standardized approach

Banks currently using internal models may leverage their existing models and systems for the FRTB Standardized Approach (which will be a mandatory calculation). Specifically, banks may adapt their frameworks for calculating the sensitivities-based risk measures. Both pricing and risk internal models may have Delta, Vega and Curvature elements, especially in the case of derivative instruments, and these sensitivities may be extended to the FRTB standardized approach. Additionally, the new FRTB JTD risk is a function of notional amount, market value of the instruments and prescribed LGD. Banks modeling incremental risk charge (IRC) under IMA have incorporated LGD in the expected loss calculation. The existing models and systems relating to LGD, used in IMA development, can be modified to implement default risk charge.



In our final installment of the series, we will focus on the comparison in the Internal Models approach.

Coming up next…..

ConclusionThe BCBS, through their Fundamental Review of the Trading Book has proposed an overhaul of the standardized approach for market capital calculation purposes which is, in general, more complex than the existing Canadian standards under CAR. The

new standardized approach must be calculated institution wide, and must be used for capitalization for all trading desks that do not gain IMA approval, as well as for all instruments in the correlation trading portfolio.


FRTB 10



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Contact usJohn ArmstrongNational Industry Leader,Financial ServicesT: 416-777-3009 E: [email protected]

Jennifer Liu Senior Manager, Financial Risk ManagementT: 416-777-3056 E: [email protected]

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Documents

FRTB: The Canadian perspective, Part 2: Standardized approach · The standardized approach capital requirement under FRTB is the aggregation of three components: the risk charges