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Formulas Risk Management
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Name: – ID:Chapter 7: How traders manage their risks[pic 1][pic 2][pic 3]ΔP: Change PF valueΔS: Change variable valueΔσ: Change in volatility Δr: Change interest rate[pic 4][pic 5]Delta-neutral Portfolio[pic 6]Chapter 8: Interest rate riskParallel yield curve shiftsOne interest-dependent instrumentDuration [pic 7][pic 8]ci: cash flow at tiy: yieldDollar duration [pic 9]Δy: Change yieldKey relationship[pic 10]Modified duration [pic 11][pic 12]m: compounding frequencyConvexity[pic 13][pic 14]Dollar duration[pic 15]Portfolio interest-dependent instrumentsSmall parallel shift[pic 16]Duration[pic 17][pic 18]Xi: PV ith assetP: PV all assetsDollar duration[pic 19][pic 20][pic 21]Nonparallel yield curve shifts[pic 22]Chapter 9: VaR[pic 23][pic 24]Impact of autocorrelation [pic 25]VaR conversion[pic 26] [pic 27]Incremental VaR: VaR = ∑iVaR [pic 28]xi = invested ith subportfolioAggregating VaRs[pic 29]Backtesting[pic 30][pic 31][pic 32]Kupiec’s Two-Tailed Test[pic 33][pic 34]n: Trialsm: # of exceptionsp: prob of exceptionChapter 10: VolatilitySimplified variance[pic 35]Power Law[pic 36][pic 37]K,a: constantsARCH model[pic 38][pic 39]a: weight observation iVolatility weighting schemesEMWA[pic 40]GARCH (1,1)[pic 41][pic 42][pic 43]VL: Long-run variance rate: Weight VL[pic 44]Ljung-Box statistic[pic 45][pic 46]m: # of observationsck: autocorrelation for a lag of kK: # of lagsVolatility forecast GARCH (1,1)[pic 47]Volatility term structures[pic 48][pic 49]V(0): σ2nImpact of volatility changes[pic 50]Chapter 11: Correlations and Copulas

Correlation two variables[pic 51]V1: Variable 1V2: Variable 2CovarianceCov(V1,V2) = E(V1V2)-E(V1)E(V2)Monitoring correlations between 2 variables: Xi=(Xi-Xi-1)/Xi-1        Yi=(Yi-Yi-1)/Yi-1 [pic 52] [pic 53] [pic 54]EMWA [pic 55]Garch(1,1) [pic 56]Variance-Covariance Matrix[pic 57]Bivariate Normal DistributionV1, V2 normal with mean: [pic 58] [pic 59]Multivariate Normal DistributionGenerating random sample:  [pic 60] [pic 61] [pic 62]Factor ModelsOne factor: [pic 63]Multifactor: [pic 64][pic 65]Factor Copula Model[pic 66][pic 67]Vasicek’s Model [pic 68] [pic 69] [pic 70] [pic 71] [pic 72]Q: Probability Default Time TX: Confidence Level (0.999)Possible loss: Investment * WCDR*(1-recovery rate)Chapter 12: Basel I, II and Solvency IICook ratio[pic 73]Derivatives[pic 74]NettingWithout netting[pic 75]With netting[pic 76]Net replacement ratio (NRR)[pic 77]Credit equivalent amount [pic 78]1996 Amendment[pic 79]Total capital = (credit risk RWA + Market risk RWA) *0.08Basel IITotal capital required = 0.08*(credit risk RWA + market risk RWA + operational risk RWA)