How To Write A Credit Risk Book

CRM validation

Jérôme BRUN, Head of model validation (market risk)

June 2011

 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

Today Target (Q4 2011)

“Specific risk surcharge” =

VaR x [1+]

VaR x [3+]

(including “general risk” and “specific risk”) Credit and equity

trades

VaR x [3+]

(including “general risk” and “specific risk”) Trades not generating specific risk Stressed VaR x [3+] CRM Trades not generating

specific risk _{Equity trades Correlation}

trading portfolio (CDO + CDS) Other credit (bonds and CDSs on corporate and sovereign issuers) IRC

Credit and equity trades “Securitisation” (= all tranches except correl) Standardised approach (RBA, SFA, deduction)

IRC vs. CRM – general principles

 P&L impact of rating migration and default

 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”

 Perimeter

 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:

IRC vs. CRM – implementation

 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

IRC & CRM – implementation

 IRC/CRM market scenarios

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

RBA Rated securitisation ? Unrated securitisation ?  SFA  Tranparency  deduction STANDARD Single-name CDS

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)

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

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

Summary of measures based on fractile

Perimeter Captured risk Model

Capital

horizon Fractile Multiplier

Pro-cyclical

VaR

(shocks over past year) 10 days 99% 5 Yes

SVaR

(shocks over worst year) 10 days 99% 5 No

IRC

& Default Correlated migrations 1 year 99.9% 1 No

Validation – an example of governance

 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)

Validation – the challenge

 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

Validation – the perimeter

 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

 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

Validation – the price risks to keep

 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

 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 ?

Validation – the 99.9% fractile

 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 1000th 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

Next steps

 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