Stressed VaR - EIFR

1 Stressed VaRPascal Gibart EIFR 7 Feb 2012 Stressed VaR EIFR Feb 20122 Contents03 Regulatory context08 sVaR in practice17 sVaR and risk management28 Conclusion29 ReferencesStressed VaR EIFR Feb 20123 Regulatory FrameworkStressed VaR EIFR Feb 20124 Regulatory FrameworkMotivationlosses during the 2008 crisis were higher than the minimum capital requirement for many banksreduce the procyclicality of the minimum capital requirementexample for EUR/USD FX exposureVolatility 2*VaRVaR+SVaRV low8%16%28%V neutral12%24%32%V high20%40%40%Stdev0,120,06 Stressed VaR EIFR Feb 20125 Regulatory FrameworkDescription in BCBS158 article 718 (July 2009) Current portfolio Stressed market conditions to be calibrated at least once a year 99 percentile over a 10 day period Calculated at least weekly Same back-testing penalty as the VaR Added to the capital requirement with a specific multiplier avgstavgctmmcsVaR,sVaRmaxVaR,VaRmax11 Stressed VaR EIFR Feb 20126 Regulatory FrameworkQuantitative Impact (BCBS163 Oct 2009)sVaR is roughtly times the VaR in a normal period (2006)there is no specific reduction in the netting effect for the sVar compared to VaRthese macro results vary greatly across institutions and will obviously vary as well depending on the present regime If we move to a low volatility regime the ratio will rise If we go back to a Stressed environment the ratio will decreaseStressed VaR EIFR Feb 20127 Regulatory FrameworkConsultation paper on Stressed VaR (30 Nov 2011)

2 Length of the period is 12 months even if VaR period is longerno scenario weightingdetermination of the Stressed period: Judgment based approach Formulaic approachSpecial care to proxies because they will always staySpecial care to sensitivity based approachesUse testStressed VaR EIFR Feb 20128sVar in practiceStressed VaR EIFR Feb 20129sVaR in practiceGlobally a far lower challenge than the other additional market risk measures introduced recently (IRC and CRM)The natural choice is to build on the existing VaR frameworkthe calibration period is differentfrequency of calculation can be different as well the main challenge is to reconstruct appropriate historical data over long periodsAs a result, it is difficult to go too far back (1987?) particularly for large banks that have positions in complex derivatives for which there was no market at the timeStressed VaR EIFR Feb 201210sVaR in practiceGoing forward it will be more difficult to reconstruct historical data for risk factor that did not exist (or were not liquid) in the pasthow do you generate prices for Carbon emission before 2005?

3 What about CDO correlation structure before 2005 ?what proxy do you use for a new stock?Some data during the 2008 crisis are of poor qualitysome shocks result from very illiquid markets and arbitrage can be created depending on the initial data structureStressed VaR EIFR Feb 201211sVaR in practiceChoosing the stress period is time consumingneed to run VaR on longer and longer periods as time goes byIdeally should be reviewed whenever there is a significant change in the structure of the portfolio (what is a significant change?)Do we use the stock of trades for a set of dates or just one?In the end it seems that most bank will end up with more or less the same period, which will always include September to November 2008A consultancy, Lepus, organized a survey of 23 banks and all of them included September to November 2008 in their sVaR periodStressed VaR EIFR Feb 201212sVaR in practice: US Equity VolatilityStressed VaR EIFR Feb 201213sVaR in practice: European Equity VolatilityStressed VaR EIFR Feb 201214sVaR in practice: EURUSD 1m ATM volatilityStressed VaR EIFR Feb 201215sVaR in practice: USDJPY 1m ATM volatilityStressed VaR EIFR Feb 201216sVaR in practice: USD Swaption 5y5yStressed VaR EIFR Feb 201217sVaR as a Risk Management toolStressed VaR EIFR Feb 201218sVar for Risk ManagementRisk factors can be divided between.

4 The liquid ones that can be hedged easily in all circumstancesthe illiquid ones that can not be hedged at allthe less liquid ones that can not be hedged in Stressed periodthe liquid risk can be managed by a VaR limitwhen volatility is low the trader can have significant positionswhen volatility is high the trader must reduce exposures the illiquid risk factors are managed by a global sensitivitya maximum sensitivity is set in order to cap the risk for an extreme movementStressed VaR EIFR Feb 201219sVar for Risk ManagementThe sVaR has limited appeal for linear portfoliosImagine an Equity Index exposure When volatility is 15% the 10 day VaR is roughly *15%*sqrt(25)=7% When the volatility is 30% the sVaR is simply doubled! There is no additional information from a risk point of limits depending on the sVaR has limited appealIf risk factors are not very liquid, in a Stressed period it will be even worse.

5 A 10 day VaR or sVaR will be a bad predictor of future losses anyway! Stressed VaR EIFR Feb 201220sVar for Risk ManagementThe sVaR is more interesting for non-linear portfoliossVaR produces large moves in risk factors and hence exhibits non linear behavior of the P&L of complex portfoliosIn that respect, it is very similar to historical stress scenarios which are already part of the Internal Model frameworkExample of a Long Term FX portfoliomajor risk factors are FX spot FX volatility Interest rate spreadin the following graphs the 3 factors are moved togetherStressed VaR EIFR Feb 201221sVar for Risk ManagementLong Term FX PortfolioFX up- FX Vol up- Spread up050 000100 000150 000200 000250 000300 000350 000400 000450 000500 00000,20,40,60,811st derivativeMtMStressed VaR EIFR Feb 201222sVar for Risk ManagementLong Term FX PortfolioFX up- FX Vol down-Spread down-200 000-150 000-100 000-50 000050 000100 000150 00000,10,20,30,40,50,60,70,80.

6 911st derivativeMtMStressed VaR EIFR Feb 201223sVar for Risk ManagementEven when each underlying risk factor is liquid, hedging the multi factor dynamic is not easy and gaps appear Correlation risk or cross gamma risk High order derivative riskAs a result, complex portfolios will generate high stress scenarios (or sVaR) valuesStressed VaR EIFR Feb 201224sVar for Risk ManagementStylized example Consider a simple OTM option in a Black Scholes frameworkIt is hedged with an ATM option European Call European CallVega RatioC1 - ratio C2 Value0,3889 Value5,6449 0,323 (1,436) Delta0,066 Delta0,535 (0,107) Gamma0,0091 Gamma0,022 0,002 Vega9,099 Vega28,138 - Vanna1,058 Vanna0,141 1,013 Volga112,580 Volga(0,882) 112,866 Strike125,00 Strike100,00 Maturity03-ao t-12 Maturity03-ao t-12 Today02-f vr-12 Today02-f vr-12 Spot100 Spot100 Volatility20%Volatility20%Rate0,00%Rate0 ,00%Dividends0,00%Dividends0,00% Stressed VaR EIFR Feb 201225sVar for Risk ManagementStylized example We generate 5000 simulations with low volatility.

7 Index volatility=20% Volatility of volatility=30% Correlation=-50% 10 day shocksand then high volatility Index volatility=40% Volatility of volatility=60% Stressed VaR EIFR Feb 201226sVar for Risk ManagementsVaR=12*VaRDistribution of P&L for each VaR scenario-6-5-4-3-2-1012 Low VolHigh VolP&LLow VolHigh VolAverage0,008 (0,070) Stdev0,053 0,389 0,010,175 0,568 0,99(0,147) (1,770) Stressed VaR EIFR Feb 201227sVar for Risk ManagementExotic portfolio tend to be accumulated during low volatility periods In low volatility environment, the VaR coming from the unhedged risk is small When volatility rises in Stressed periods, the VaR rises and even if traders hedge tightly the major risks, cross risks will become an issueMonitor sVaR at inception in order to make sure that the VaR in future stress periods can still be managed efficiently by the traders Stressed VaR EIFR Feb 201228 ConclusionsVaR is a natural extension of the current VaR frameworkManaging proxies in the long run may prove difficultFor most banks, the sVaR period includes the 3 months periodstarting with the Lehman collapse (15 Sep 2008) ending the Citigroup bail out (23 Nov 2008)

8 In terms of risk management, sVaR is useless for linear portfoliosMonitoring sVaR for non linear portfolios will limit sizes to manageable levelsStressed VaR EIFR Feb 201229 ReferencesRevisions to the Basel II market risk framework, Jul 2009, of the trading book quantitative impact study, Oct 2009, Consultation Paper on the Draft Guidelines on Stressed Value At Risk (CP48) Nov 2011, A-BS-2011-166r-(CP48-on-GL- Stressed -VaR) Stressed VaR December 2011