Incremental Risk Capital (IRC) and Comprehensive …

1 Group Risk ManagementRisk IM Incremental Risk Capital (IRC) and Comprehensive Risk measure (CRM):Modelling Challenges in a Bank-wide SystemJean-Baptiste BrunacBNP Paribas Risk Methodology and AnalyticsEIFR February 2012 GRM Risk IM22 Outline New Capital charges on trading books: Overview IRC and CRM: Definition IRC: Calculation Modelling default and migration Selected examples CRM: Calculation Additional risk factors for credit correlation products Modelling choices Selected examples Backtesting feasibility Industry and regulator views Conclusion and outlookGRM Risk IM33 New Capital charges on trading books.

2 Overview (I) With internal models missing major market (and credit) risks during the recent financial crisis, the Basel Committee has suggested new Capital charges for trading books Targeted shortcomings Differences in the underlying liquidity of trading book positions 99%/one-day or ten-day Value-at-Risk (VaR): No adequate reflection of large default losses that occur less frequently as well as the potential for large cumulative price movements over several weeks or months The proposed framework has evolved since 2007, accompanied and driven by extensive Quantitative Impact Studies (QIS)

3 EBA draft guidelines on IRC were published in November 2011 Focus of this talk are those new charges based on internal models, which require validation by home regulators and are to be introduced together with other requirements ( , designated stress tests)GRM Risk IM44 Current market risk Capital formula:* VaRis the standard Value-at-Risk measure , based on 99% 10-day loss mcis a model-based multiplier, mc 3 bis an additional factor, depending on VaR backtesting excesses, 0 b 1 Coming soon:* Stressed VaRis VaR calibrated to financial crisis data, , 2007-2008; mc/s 3 IRCis an Incremental charge for default and migration risks for non-securitised products (at least weekly computation) CRMis an Incremental charge for correlation trading portfolios (at least weekly computation) Flooris calculated as times Capital charge for specific risk according to the modified standardised measurement method for the correlation book ( banking-book charge ).

4 = 8% SCis standardised charge on securitisation exposures (not covered by CRM), comparable to the banking bookCapital = (mCapital = (mcc+ b) + b) VaRVaR+ + VaRVaR(specific) (specific) Capital = (mCapital = (mcc+ b) + b) VaRVaR+ (+ (mms s + b)+ b) Stressed Stressed VaRVaR+ IRC + max {CRM, Floor} + SC+ IRC + max {CRM, Floor} + SC* Ignoring the averaging over quarters Capital charges on trading books: Overview (II)GRM Risk IM55 Incremental Risk Capital (IRC) Products: flow products bonds and CDS (if not part of CRM, as defined below).

5 May include listed equities Simulated risks : credit rating migrations and default Comprehensive Risk measure (CRM) Although initially considered part of securitisation positions, correlation trading portfolio are carved out of standardised charge and subject to CRM and floor (the CRM cannot be lower than 8% of the standard charge) Products: correlation instruments and their hedges (including CDS), but without re-securitisation positions ( , CDO2) or LSS Simulated risks : Default and migration (as in IRC) and all price risks (multiple defaults, credit spread volatility, volatility of implied correlations, basis risks , recovery rate) Risk measure Both are based on loss quantile at 1-year Capital horizon This contrasts with VaR and stressed VaR, which are much more short-term Rebalancing may be taken into account via shorter liquidity horizons coupled with a constant level of risk concept For CRM, the modelling of dynamic hedging and its cost are allowed IRC and CRM.

6 DefinitionGRM Risk IM66 The IRC charge must capture default and migration risk Range of modellingchoices, for example: Rating-based simulation (usually through asset values/returns) Direct simulation of spreads with migration/default barriers Granularityof simulation ( , in the case of bonds) Guarantor/obligor Issuer Parameterisationchoices, for instance: Historical vs. market-implied default (and migration) probabilities Granularity of factors to capture asset and/or credit spread dependence Different possibilities regarding trade revaluation: As of today or in the future; recognition of cash flows or not Full revaluation or approximation On-the-fly (for each scenario) vs.

7 Pre-computation Interpretationof the constant level of riskconcept: Simplifying assumption to rebalance frequently or rollover the positions (at the liquidity horizon) in a manner that maintains the initial level of riskIRC: Modelling default and migration (I)GRM Risk IM702004006008001,0001,200 AaaAa1Aa2Aa3A1A2A3 Baa1 Baa2 Baa3Ba1Ba2Ba3B1B2B3 Caa1 Caa2 Caa3 Rating (Moody's)Median credit spread (bps)7 Example of a concrete approach: Rating-based simulationfor each obligor ( , CDS entity/bond guarantor) Marginal default probabilitiesbased on historical transition matrices ( through-the-cycle ).

8 Differentiation between sovereigns and corporates Dependence between obligorsvia multi-factor asset return model Conversion of rating moves to credit spread movesvia mapping tablesIRC: Modelling default and migration (II)Aaa-1 notch+1 Asset ReturnsFinal ratingSpread multiplier to apply onpar spreadSpread-to-Rating mappingZxGRM Risk IM Trade revaluation As of today , , no ageing of deals Full revaluation where possible, since approximation via sensitivities, for example, not well suited for large credit spread moves Pre-calculation of PVs possible, given the limited number of target ratings Full revaluation where possible Par bond approximation for the rest:S spread; r risk free rate; C bond coupon.

9 R recovery rate. Constant level of riskconcept: Full reset of a deal at the liquidity horizon, to the original maturity and credit qualityName Rating Country IndustryDefaultRating 2 Rating Rating 11 Rating 12 Rating 13 .. Rating 17 Rating 18X11818312,874,6701,297,3451,050, ,04164,92352, ,3430X2315-11,049,593 233, ,498,730 -2,536,780 -2,587,099 ..-2,772,410 -2,812,323 X3121713-47,859,017 -1,089,469 -581,677 ..-3,363 0-6,095 ..-34,720 -41,041 X4171657-1,693,898 -3,346,523 -2,693,739 ..-173,423 -139,470 -108,230.

10 023,470X512113441,781,103-320,845 -407,236 ..-6,595 09, ,37253,216()()()[]() + + + =rRSTrRSCrSPV1/1/exp11100 IRC: Modelling default and migration (III)GRM Risk IM99 IRC: Modelling default and migration (IV) Illustration of IRC simulation with liquidity horizon of 6 months and Capital horizon of 1 year (assumed current obligor rating: Aa2): Usually high number of simulations required (1m+) to achieve stable resultsP&L 6 months due tomigration eventP&L 6 months due todefault P&L 1 yearRebalancing0 Asset returnsP&L6 months6 6 months due tomigration eventP&L 6 months due todefault P&L 1 yearRebalancing0 Asset returnsP&L6 months6 Risk IM1010 Credit derivatives flow trading is usually less impacted by IRC since positions are hedged in terms of credit risk For example, positions on risky bonds will be hedged by buying protection on the obligor Though the overall default risk is reduced, on a large portfolio.