Fundamental Review of the Trading Book

Agenda» Overview FRTB» Structure of SA vs. IMA» SA add-on vs. IMA non-modellable risk factors» Curvature risk of digital options» Recognition of hedging and diversification» Global selection of correlation scenarios» Calibrating F risk: IMA vs. SA» Model approval at desk level d-fine d-fine All rights All rights reserved reserved 1

Overview FRTB 1 New trading book definition 2 New standardised approach for market risks 3 New requirements for internal market risk models» Boundary between trading book and banking book» Definition of trading desks» Internal risk transfers» Sensitivity-based Method» Default Risk» Residual Risk Add-On» Liquidity adjusted Expected Shortfall» Default Risk Charge» Non-modellable risk factors All banks Banks with trading book and/or F risks and/or commodity risks Internal model banks d-fine d-fine All rights All rights reserved reserved 2

Add-on components Default risk charge Five market risk classes Structure of SA vs. IMA SA-TB Standardised Approach IMA Internal Model Approach 1» Standard formulae» Delta, Curvature and Vega components» Prescribed risk weights and correlations» Liquidity-adjusted expected shortfall» Integrated modelling» Actual market data time series 2» Exposure based on nominal and PV» Prescribed weights, LGDs» 2-factor VaR: default simulation model» Observed PDs, LGDs 3» Captures residual risk» Gross nominal exposure to certain derivatives» Captures non-modellable risk factors» Scenario analysis without correlation to modellable risk Manifest effort by BCBS to align structures. Detailed analysis reveals several significant divergences, however. d-fine d-fine All rights All rights reserved reserved 3

SA add-on vs. IMA non-modellable risk factors SA add-on» Surcharge based on notional exposure» In addition to SA capital charge (in most cases) IMA non-modellable risk factors» Scenario analysis for certain risk factors» Instead of inclusion in the model» Need to clarify scope of definition» Non-standard pay-off i.e. digital options, Bermudans, etc.» Exotic underlying i.e. dividends, weather, etc.?» Lack of observed market prices esp. credit derivatives, residual risk (bonds)» Derived market data depending on definitions: implied volatilites, correlations, etc. Huge difference in scope and definition. Challenges to make approaches comparable and risk sensitive. d-fine d-fine All rights All rights reserved reserved 4

Curvature risk of digital options SA charge per risk class is a sum of delta, curvature and vega components» Such decomposition into additive components is not always possible» Add on of 0,1% in addition to SA charge Numerical example: 30-day digital gold call option: spot $1180, strike $1200, implied vol 15%» Curvature Charge CVR = $1,04 3 times option value» IMA: full revaluation approach respects max loss condition ES < $1 3 2,5 2 1,5 1 0,5 0 0,000 1100 1200 1300 1400 1500 SA too conservative for curvature risk of digital options. 0,009 0,008 0,007 0,006 0,005 0,004 0,003 0,002 0,001 Payoff Tangent Option price CVR Option delta Strike d-fine d-fine All rights All rights reserved reserved 5

GIRR Capital Charge Recognition of hedging and diversification SA» Three additive components per risk class (delta, curvature and vega)» Calculate charges using prescribed correlations» Scale correlations 75% and 125% (capped at 1)» Repeat calculation» Choose correlations scenario with highest capital charge IMA» Fully integrated modelling of liquidity-adjusted ES with correlations across risk types» Calculate capital charge per risk class without correlation to other risk classes» Determine capital charge as linear combination of correlated and uncorrelated results 250% 200% 150% 100% 50% Bank #1 Bank #2 Bank #3 Difficulties:» scaling by 75% grossly overstates basis risk» Splitting delta, curvature and vega significantly restricts hedging ( see slide on curvature risk) 0% low medium =100% high Recognition of hedging and diversification differs significantly between SA and IMA. d-fine d-fine All rights All rights reserved reserved 6

Capital Charges Global selection of correlation scenarios Correlation scenario to be chosen across risk classes for relevant portfolio [ new in final paper!]» Contribution of risk class to trading book charge in general not equal to stand-alone charge for risk class» Contribution of different risk classes to trading book charge can shift discontinuously Numerical example: Well-hedged IR portfolio & well diversified EQ portfolio» Assume favourable correlation scenario attracts 80% CC of adverse scenario» Keep total risk charge across portfolios (roughly) constant 1.800 1.600 1.400 1.200 1.000 800 600 400 200 - Total risk charge IR Desk EQ Desk 800 850 900 950 1.000 1.050 1.100 1.150 1.200 IR Charge (high correlation) Attribution of capital charges presents operational challenges. d-fine d-fine All rights All rights reserved reserved 7

Calibrating F risk: IMA vs. SA 45% 40% 35% IMA Factor 1,5 IMA Factor 2 SA Reporting Currency: EUR 30% 25% 15% 10% 5% 0% AUD CAD CHF GBP JPY MN NOK RUB SEK SGD USD AUD CAD CHF GBP JPY MN NOK RUB SEK SGD USD 80% GBP 60% 40% GBP 40% 60% GBP 80% GBP 60% CAD, MN 40% GBP, 10% CAD, 10% JPY, 5% CHF, 5% NOK, 5% AUD, 5% RUB 50% JPY, 30% AUD, SGD 60% GBP, CHF, 10% NOK, 10% SEK 100% 100% GBP, - AUD, - 100% 100% CHF JPY long short diversified hedged 100% - 100% CAD Figures calculated by Andreas Ahrens of NORD/LB. Reproduced with his kind permission. d-fine d-fine All rights All rights reserved reserved 8

Model approval at desk level If some desks use SA and other IMA:» Total charge depends on delineation of desks» Internal deals between desks influence total charge Desk #1 Risk transfers within the trading book :» Generally allowed to delineate desks» Only limited by documented trading strategy. Desk #5 Desk #2 If a desk loses IMA approval:» Resulting capital charge depends on many factors unrelated to that desk» Incentive to transfer risk to other desks arises Desk #4 Desk #3 Complex optimisation problems and potential cliff effects abound. d-fine d-fine All rights All rights reserved reserved 9

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