CRM validation Jérôme BRUN, Head of model validation (market risk) June 2011
Introduction and agenda 1 3 amendments on the trading book to be implemented in 2011 Incremental Risk Charge (IRC) & Comprehensive Risks Measure (CRM): capture P&L impact of rating migration and default on credit excluding securitisation Standardised approach on securitisation perimeter (inspired by banking book) Stressed VaR: value-at-risk on stressed scenarios VaR, SVaR, IRC and CRM are all fractiles of P&L distributions. As such, they require: A perimeter of deals Scenarios for the risk factors Repricing of the deals in the perimeter in each scenario Computation of the fractile of the P&L distribution just built Agenda IRC vs. CRM Focus on the standardized approach used to compute the CRM floor Validation of CRM
Reminder on the perimeter of the new charges 2 Today Target (Q4 2011) Trades not generating specific risk Credit and equity trades Trades not Credit and equity trades generating specific risk Equity trades Correlation Securitisation (= all tranches except correl) trading portfolio (CDO + CDS) Other credit (bonds and CDSs on corporate and sovereign issuers) Specific risk surcharge = VaR x [1+] Standardised approach (RBA, SFA, deduction) CRM IRC VaR x [3+] (including general risk and specific risk ) VaR x [3+] (including general risk and specific risk ) Stressed VaR x [3+] Add up the boxes to get the capital required for market risk
IRC vs. CRM general principles 3 P&L impact of rating migration and default Perimeter 1-year capital horizon 99,9% confidence level 3-month minimum liquidity horizon Can rebalance positions at every liquidity horizon with Constant level of risk assumption CRM Correlation trading portfolio: CDOs on liquid corporate portfolios not CDO² and LSS CDSs used to hedge the CDOs IRC Other credit (excluding securitisation) Risks covered IRC & CRM: migration and default CRM: specific price risks (spread, recovery and correlation volatility) CRM impact subject to floor 8% of standardized approach IRC inconsistent with VaR: 99.9% Vs. 99%, 1 year Vs. 10 days
IRC vs. CRM implementation 4 Start with simulations of correlated migrations on all issuers in book Large number of scenarios required (99.9% = every 1000 scenarios) need up to 1 million simulations! In each scenario, get migration for each issuer Scenario #1 : Peugeot: A AA, Renault: AA AA, Ford: BB C Scenario #2 : Peugeot: A A, Renault: AA AAA, Ford: BB A Etc. For IRC, in each scenario: All issuers are subject to either of: Downgrade / Upgrade Can be translated into spread move ( S), assuming a fixed spread per rating class E.g. AAA = 20bps, AA = 40bps, A = 90bps, BBB = 140 bps, etc. Default Compute P&L impact of resulting market moves on the IRC perimeter Need to reprice full perimeter 1 million times CRM specificities (for CDOs): All market moves (incl. volatility of spread of rating classes, of recovery, of credit correlation) are added to spread moves resulting from migrations These market moves must account for correlation between credit and market Regulator requires to use 2 nd order sensitivities for pricing
IRC & CRM implementation 5 IRC/CRM market scenarios Market spread shocks are based on cohort spread dynamics (average spread per rating class)
6 Standardised approach for the CRM floor For all (re-)securitisations, capital charge = 100% of Standardised approach Transitory measure (till Q4 2013) capital = Max(capital on longs; capital on shorts) CRM floor also based on standardised approach - but a fraction of it! capital = 8% * Max(capital on longs; capital on shorts) Capital charge = Exposure x Risk Weight capped at Max Loss Rated securitisation? Unrated securitisation? Single-name CDS RBA SFA Tranparency deduction STANDARD
7 Standardised approach Focus on the components Exposure: not always equal to the maximum MtM loss on the asset Cf. guidelines QIS 4.1 (differ from those of QIS4) MtM for a note/bond For a swap/cds format, MTM of associated bond Ntl + CDS MTM for CDS long risk Ntl - CDS MTM for CDS short risk Exposure <> maximum loss for a swap short risk! Risk-weight of a tranche Essentially driven by external rating, when available (RBA = Ratings-Based Approach) Around 1% when AAA, but falls to 100% when <BB- Otherwise, use Supervisory Formula Approach (SFA), based on ratings within underlying portfolio Usually SFA uses only internal ratings a more liberal use could be possible (blend internal/external ratings) Not much arbitrage between RBA and SFA (when data is available to compute both) For rated single-name exposures (contributing to CRM floor), risk-weight similar to tranches The Max loss is computed from the worst case scenario Worst case? When long risk All credits default with 0 recovery When short risk All credits become risk-free As a consequence: For a bond or a CDS long risk, the Exposure is already equal to the Max loss cap has no impact For a CDS short risk, Max loss = MtM + PV of risk-free spread payments (~ MtM when contract spread is small) the cap may be useful for large risk-weights (in particular for deductions)
8 Standardised approach Netting Limited netting : for a long/short, charge is driven by M = Max (Charge(long), Charge(short) ) 1. Identical exposures 0% * M 2. format mismatch (bond vs. CDS) 20% * M 3. maturity and/or currency mismatch 100% * M In all other cases, the charge of the long/short is the sum: Charge(long) + Charge(short) Open questions coupon mismatch? credit index = sum of its components? Sum of tranches = portfolio? Floor computation 1. Compute individual charges for all assets 2. Do the netting as above for all long/shorts in the portfolio, the resulting capital is called netted capital. 3. Add up capital for all (non-netted) long assets and all netted capital get L = total long charge 4. Add up capital for all (non-netted) short assets and all netted capital get S = total short charge 5. The floor is 8% of the max of L and S
9 Standardised approach Example of a NBT NBT of CDOs bond referencing some CDO tranche CDS buying protection on the same tranche Common notional = 100 MtM assumptions: Bond = 80%, CDS = 20% Exposures vs. Max Loss Bond Exposure = Max Loss = 80 CDS Exposure = 80, Max Loss = 20 (neglect PV of spread payments) Tranche rating = BB- risk-weight = 52% Resulting charges: Bond charge = 80 * 52% (capped @ 80) = 41.6 CDS charge = 80 * 52% (capped @ 20) = 20 cap is hit Max charge = bond charge = 41.6 Given there is a format mismatch, the charge of the package is 20% * MaxCharge = 8.3
Summary of measures based on fractile Perimeter Captured risk Model Capital horizon Fractile Multiplier Procyclical VaR Trading book Market risks Historical or Monte-Carlo (shocks over past year) 10 days 99% 5 Yes SVaR Trading book Market risks Historical or Monte-Carlo (shocks over worst year) 10 days 99% 5 No IRC Vanilla credit book Rating migration & Default Correlated migrations 1 year 99.9% 1 No CRM Exotic credit books Rating migration & Default & Market risks Correlated migrations & Dynamics for credit market parameters 1 year 99.9% 1 No 10
Validation an example of governance 11 Risk department does modelling + implementation With FO support (trading, quants, IT ) Initial modelling choices are validated by expert committees quants experts assessing compliance with regulatory expectations Audits Internal audit Regulator audit Permanent governance Regular calibrations (Q/W/S/Y) Regular expert committees (S/Y)
Validation the challenge 12 Rumour has it that CRM Internal Model < CRM floor for most large correlation dealers In this case the validation only allows to charge 8% of the standardised approach rather than 100% i.e. get a validation of the internal model only to have the right to override it by the std approach Is the floor computation part of the validation? Standardised approach applied to CRM perimeter requires clarifications Netting rules are designed for traditional securitization ABS hedged by CDS on that very ABS no ambiguity Ford bond with maturity 5 Oct 2013 hedged by standard CDS with maturity 20 Sep 2013? Series of CDSs on Ford with different maturities, coupons, and currencies? Delta hedge of CDO tranche with single-name CDSs? Use of SFA methodology traditionally relies on internal ratings Makes sense on banking book, as all credits are also clients and therefore they are internally rating On the trading book the credits traded are not necessarily clients of the bank A strict application on SFA penalizes external ratings but there might be a tolerance, among others to be consistent with computation of CRM IM Exposure is not the maximum loss for a CDS short risk It is actually the maximum gain. But this makes sense when netting with the opposite CDS.
Validation the perimeter 13 Liquidity test Basel : All reference entities in the underlying portfolio should be liquid but the US draft only requires All or substantially all Liquid = a 2-way CDS market exists and a trade can be executed within the day In practice, very few names are illiquid Strict application of Basel would exclude many trades 100% of standardized approach + hedge remains as open position in CRM Test allows to exclude CLOs where most reference entities are illiquid Exclusion of LSS, options on tranches and CDO² How about their hedge? The hedge of these excluded products is also excluded from the CRM perimeter In practice, these products are risk-managed along with vanilla CDOs (mismatch between the regulatory correlation trading portfolio and the real-life correlation desk ) In these conditions, how to identify the hedge of the excluded products? Keeping the hedge in CRM perimeter creates an open position, an thus a CRM explosion! Options on tranches do not exist What about the callability features, e.g. callable CDO? Should we exclude a transaction based on its booking or based on its confirmation, when these differ? Conservative bookings may be aggressive from a capital viewpoint
Validation the scenarios 14 Scenarios combine migrations + defaults (as in IRC) and market moves (as in VaR) Consistency with IRC migration/default engine: nice to have, or mandatory? Spread moves result from the joint effect of migrations & market moves specific to CRM Cf. before: may use cohort spreads as tool to ensure consistent approach Given the fractile (99.9%) and horizon (1y), cannot use historical scenarios Would require thousands of years of history Therefore need to specify dynamics on the market parameters to generate scenarios Choice of dynamics for a given price risk Historical dynamics (as opposed to risk-neutral used when pricing) Balance between realism, robustness, stability and conservatism Examples : Spread drift, Spread vol When a parameter is not observable on the market Parameter calibration done at expert level Or specific capital add-on
Validation the price risks to keep 15 Credit the usual suspects Credit spreads: observable, standard dynamics (lognormal) Credit correlations: daily historical series for the base correlation. Non-trivial dynamics as bounded Recovery rates: distinguish between: Pricing recoveries : not observable. Noise around current market recovery? Default recoveries : observed on the recent IG defaults. Split between soft and hard defaults U-shaped distribution Credit - the different basis Bond vs. CDS : irrelevant Index vs. CDS : observable, but unusual dynamics (strong mean-reversion with jumps) Bespoke vs. index = to be accounted for when pricing a bespoke tranche Non-credit FX, rates: not explicitly asked, and very liquid, so the CRM horizon is irrelevant. Should hedge cost be included, since we claim to benefit fully from dynamic hedging? Huge correlation matrix Not all correlations matter Credit/market correlation? Actually this is the correlation between the factors driving the migrations/defaults and those driving the market moves Correl among Credit correl often estimated from equiity returns. Fine
Validation the valuation 16 Computational burden More than 100 000+ simulations 1000 tranches 1s to 5s per tranche with usual pricers 1000 CPUs More than a week of computation time How to reduce computational burden? Optimized pricers focus on CDS curve bootstrapping and computation of bespoke correlation Taylor expansion Cross gammas Pre-computed prices large multi-dimensional arrays + an interpolation methodology Challenge is to demonstrate that pricing is accurate enough Actually it is not so much the pricing in itself but more the difference of prices (P&L) We want a fast pricing that remains accurate enough in stressed conditions (99.9% scenarios) What is a right level of accuracy? Well-defined when pricing for accounting reasons (as close as possible to fair value ) Here the impact of pricing inaccuracy should be compared to the uncertainty around the definition of a 99.9% scenario What about CDSs? Full repricing feasible May require duplication of FO code in dedicated chain
Validation the 99.9% fractile 17 Number of scenarios required 1,000,000 scenarios require 10 times more CPU than 100,000 scenarios why bother if number is overridden anyway by the floor? Only ensure that CRM IM + large confidence interval remains < CRM floor Computation of the fractile Contribution of different desks require good convergence vital for IRC, but CRM involves essentially one desk Stability increased when computing contribution from average over scenarii around 99.9.% scenario Example: 1,000,000 scenarios, ranked by increasing P&L. CRM is by definition the P&L on the 1000 th scenario. Look for unique X > 1000 such that the CRM is also the average of the P&Ls on the first X scenarii Backtesting At less severe fractiles and/or shorter horizons? Or just make sure the few observed realisations are < CRM? Stress testing Of the CRM perimeter Pre-defined stress tests : apply all observed market moves on stressed periods defined by the regulator Ad hoc Of the CRM measure itself: recompute CRM on a stressed perimeter
Next steps 18 Fundamental review of the trading book Joint work between regulators and industry Long-term In the interim, will have to cope with CRM floor make it your friend E.g. same ratings and LGD for CRM IM and SFA in CRM floor Benchmarking was an anti-floor weapon Floor was supposed to give extra comfort with a simple methodology Benchmarking of CRM on stylised portfolios was an alternative suggestion from the industry Even though the floor is here to stay, benchmarking can still help get validation As long as floor remains, no incentive to optimize CRM model this would increase validation risk for a constant level of capital Constant level of risk Dynamic hedging