IRC / stressed VaR : feedback from on-site examination EIFR seminar, 7 February 2012 Mary-Cécile Duchon, Isabelle Thomazeau CCRM/DCP/SGACP-IG 1
Contents 1. IRC 2. Stressed VaR 2
IRC definition Incremental Risk Charge (IRC): Add-on to the VaR calculation for capital requirements, to capture the default and migration risks of the trading book (except for correlation books) confidence interval of 99,9% over a capital horizon of 1 year
IRC definition Assumption: constant level of risk over the one-year capital horizon, or one-year constant position If constant level of risk: initial level of risk to be maintained ; risk indicator to be defined Liquidity horizon : set according to the time required to sell the position or to hedge all material relevant price risks in stressed market, with a floor of 3 months Calculated at least weekly: = Max (last IRC calculation, average on the 12 last weeks)
IRC modelling and ACP on-site examination questionnings a. Migration and default simulation: which transition matrices? b. Correlation structure: which correlations? c. Conversion of migration into spread shocks d. P&L computation and losses calculation at a 99.9% quantile
1.a. Migration and default simulation Ratings dynamic : use of normal distribution discomposed into a systemic component (F being more or less complex) and an idiosyncratic component : X i = ρf + 2 1 ρ ε Rating modification : migration or default happen over a given horizon when X i reaches a threshold : use of transition matrices to determine this threshold. i Generally derived from the Merton s model with use of assets (KMV) or equities returns (CreditMetrics). Sometimes use of latent factors.
1.a. Migration and default simulation Ratings Internal (especially if used in banking book) External (same information as markets) Transition matrices Internal External : S&P, Moody s Representativity of the agency sample Period longer than an ecomomic cycle (how many economic cycles?) Number of matrices to use : An unique matrix for the whole portfolio Differentiated matrices: sovereign, corporate, financials,
1.a. Migration and default simulation
1.a. Migration and default simulation Issues about the matrices corrections : «Rating withdrawals», Use of specific algorithms or similar method aiming at «regularizing», Manual methods, Frequency of updates of the transition matrices
1.b. Correlation structure Number of factors in the simulation Can vary greatly, but 1 factor is not acceptable Correlations between these factors Which Copula to use : Gaussian copula or not? When KMV or other external model/data is in use, how to audit the process and the inputs on the «black boxes»?
1.b. Correlation structure Estimation of correlations: Different approaches and problems : Equity data: sovereign issue Credit Spread: historical length Ratings dynamics: difficulties in the interpretation Conservative estimation of the values : What is a conservatism level and how to define it? Representativity of the calibration sample Frequency of update
1.c. Conversion into spread shocks Migrations to be translated into credit spread variations Mapping between ratings and spreads For each rating : definition of the spreads term structure Calibration Frequency Representativity Use of market spreads, average spreads, One or several spread-rating matrix : corporate, sovereign, Integration of the bond/cds basis. Backtesting is an issue : how to extract only the credit effect when looking at the spread variation over a oneyear horizon?
1.d. P&L computation and losses calculation at a 99.9% quantile Computation of the losses : use of a P&L function. Valuations: Full revaluation with use of new market parameters and valuation functions Use of simplified models Use of P&L valuations by greeks with shocks on market parameters What LGD to use : market, IRBA, stochastic? Convergence of the simulations
2. Stressed VaR Selection process for the stressed period : Criteria for this choice Justification Data availability, missing values Impact or a modification of the time window on the Stressed VaR amount Adequacy with the portfolio
2. Stressed VaR
2. Stressed VaR
2. Stressed VaR
2. Stressed VaR
2. Stressed VaR Justification of the SQRT(10) coefficient when computing 1-day VaRs Checking that no discrepancies with the VaR methodology in terms of P&L calculation Update of the stressed window