FRM二级公式表（培训资料）.docx

MarketRiskMeasurementandManagementParametricVaRNormalVaRVaR-(z)VaR=(z)×RTJensen'sInequalityEkl+r)lE(l+r)InterestRateTermStructureModel1LognormalVaRVaR=1-CU-z#dr=dwdw=vdtVaR=(1-el#)×PtTModel2HybridApproachAge-WeightedSimulationMethodi1(l)=5dr=dt+dwHo-LeeModeld=(t)dt+dwVasicekModeldr=(r)dt+dwVolatility-WeightedSimulationMethod.i-*三11jtriModel3dr=(t)dt+etdwCox-Ingersoll-Ross(CIR)ModelEmpiricalPropertiesofCorrelationMeanreversionispresentifthereisanegativedr=k(-r)dt+Vrdwrelationshipbetweenthechangeofavariable,St-St,andthevariableSt-.St=a(UsSt-)÷St-Model4dr=ardt+rdwTheSalomonBrothersModeldln(r)=a(t)dt+dwTheBlack-KarasinskiModeldln(r)=k(t)ln(t)ln(r)dt+(t)dwCreditRiskMeasurementandManagementExpectedLoss(EL)EL=PD×(1-RR)×EAD=PD×LGD×EADEquity=VN(d)Ke-rN(d)i7Debt=KeTTJPUt=VN(-dJ+KeTTN(d2)In(S/Ke-r) fDefault Correlation12 -口1n2p =_ qI 1(l -1) 2(l-2)Binomial Trees of PDCumulative Default ProbabilityUnexpectedLoss(CreditVaR)UL=CreditVaR=WCL-ELMood,sKMVModelDefault=ST÷50%×LTzif<1.5Default=ST+(0.7-0.3×STLT)LTzifotherwiseDefiNamestMarginalDefaultProbabilityPD,'rg=PDCUmUlatedPDcumulatedKt+ktForwardProbabilityp11Forw=Deft+kDeftNamessurvvedtExponentialDistributionCumulativeDefaultTimeDistributionP(t*<t)=F(t)=1e-tConditionalDefaultProbabilityP(t*>t)=1-F(t)=e-tSurvival RateSR黑裁=11 - PDIj 11 - PDmulatedAverage Default RateI 1 PDcumulatedI =(I- ADR > 1 PDCFmUlatedl=e-ADRxtSingleFactorModel=隔+12jKi-肘P=111-%i=l,2InferCreditRiskfromCorporateBondPricesRisk-NeutralProbabilityofDefault$1S1×PD×RR÷S1×(1-PD)"1+YTM(1+Rf)1lYTM-RfnPD=EGnIYTM=YTM-Rf*PDxLGDMertonModelConcentrationriskNlCxP×(l-P)N-X=：p×(l-P)N-xNX!(NX)!CreditValueAdjustmentmCVA=LGDIEE(t)×PD(t,t)i=iIiCVA=EPE×Spreadg3ex08 一匕 EScored PerformanceNettingFactorEE(netting)n+n(n-l)Nettingfactor=EE(nonetting)nOperationalandIntegratedRiskManagementTheBaseloperationalriskchargeBasicIndicatorApproachORCbia=×GI(=15%)TheStandardizedApproachORCTSA=t|XGIWAdvancedMeasurementApproachORCama=UL(1year,99.9%confidence)Risk-AdjustedReturnonCapital(RAROC)Risk-AdjustedReturnRAROC=EconomicCapital(EC)Risk-AdjustedreturnRAR=Revenues+ReturnonEC-Expenses-ELAdjustedRAROC(ARAROC)AdjustedRAROC=RAROC-(Rw-rf)BaselAccordBaselIRisk-WeightedAssetsRiskWeight(%)AssetCategory0Cash,GoldBullion,ClaimsonOECD20ClaimsonOECDBanksandOECDPublicSectorEntities50UninsuredResidentialMortgageLoans100AllOtherClaims1996AmendmentMarketRiskChargeMaxVaRt-,mc×VaRavg÷SRCwhere:VaRt-'previousday'sVaRVaRavg：averagevalue-at-riskoverthelast60daysm:multiplicativefactor(3)SF:specificriskchargeBaselIlPillarPillar1:MinimumCapitalRequirementTotalCapitalRWAcredit+MRCMarketX12.5+ORCp×12.5Pillar2:SupervisoryReviewProcessPillar3:MarketDisciplineCreditRisk-InternalRatingsBasedApproachWCL99.9%,i-yearHEFADJXLGDXVCDRjNRR=mmx(EU%,°)空11三M0)creditequivalentamountN=maxVi,0+(0.4+0.6XNRR)i=lN1.aLOperationalRisk-BasicIndicatorApproachBlA=0.15X必也JqOperationalRisk-StandardizedApproachBusinessLineBetaFactorCorporateFinance18%TradingandSales18%RetailBanking12%CommercialBanking15%PaymentandSettlement18%AgencyServices15%AssetManagement12%RetailBrokerage12%Ksa=11max11(Gh-8×-s),O/3years1-3OperationalRisk-AdvancedMeasurementApproach99.9%,1yearVaRBasel2.5StressedValueatRisk(SVaR)MaxVaRt-,Mc×VaRavg+MaXlSVaRt-,MSXSVaRavgIncrementalRiskCapital(IRC)One-year99.9%VaRforlossesfromcreditsensitiveproductsinthetradingbookBaselIIIMinimumCapitalRequirementTier1equitycapital4.5%TotalTier1capital6%Totalcapital8%CapitalConservationBuffer(CCB)AfterCCBadjustment:Tier1equitycapital7%TotalTier1capital8.5%Totalcapital10.5%CountercyclicalBufferRecommended:0-2.5%StandardizedApproachORC=BIC-ILMILM=Ln(exp(l)-1+()08)RiskManagementandInvestmentManagementpMarketTimingAbilityNoMarketTimingrp-rf=a+b(rM-rf)MarketTiming(HenrikssonandMerton)rprf=a+b(mf)+c(m11)D+eMarketTiming(TreynorandMazuy)rp-rf=a+b(rM-rf)+c(m一rf)2+ePortfolioVaRDiversifiedVaRVaRp=IVaR,+VaR¾+2pVaRIVaR2MarginalVaROVaRpMVaRA=OVaIncrementalVaRIncrementalVaRAMVaRA×WAComponentVaRCVaRA=MVaRAXVAPortfolioRiskManagementGlobalMinimumPortfolioMVaRi=MVaRjOptimalPortfolioPositionireturnriskfreerateM%R；Positionjreturnriskfreerate=MV三;RiskBudgetingWeightofportfoliomanagedbymanageriIR,×(PortfoliozStrackingerrorvolatility)IRPX(ManagerrStrackingerrorVrlatiIitylSurplusExpectedsurplus=A×(1÷Ra)L×(1÷Rl)surpiu三=IA2衣+L2匕2AJgSurplusatrisk=z×surp)usLiquidityandTreasuryRiskMeasurementandManagementLiquidity一AdjustedVaRCostofliquidation1.C=£0.5XoqXSi(normalmarket)(offerprice-bidprice)spreadofferprice+bidpriceWhere:=asset(orportfolio)valueiSi=bid-offerspreadinnormalmarketfortheithfinancialinstrument1.C=E°5X%(j+入)(stressmarket).givestherequiredconfidencelevelforthespread.andarethemeanandstandarddeviationforthebid-offerspreadfortheithfinancialinstrument.1.iquidity-AdjustedVaR1.VaR=VaR+，0.5XaiXSj(normalmarket)1.VaR=VaR+E0.5×oq(j+i)(stressmarket)1.iquidityRegulation1.iquidityCoverageRatio(LCR)HighQualityLiquidAssetsyNetCashoutflowsin30days-TotalNetCashOutflowsNetcashoutflows=outflowsoverthenext30days-min(inflows,75%ofoutflows)NetStableFundingRatio(NSFR)AmountofStableFunding：；EFl%RequiredAmountofStableFundingMarginCostMarginalCostMarginalCost=Changeintotalcost=Newinterestrate×Totalfundsraisedatnewrate-Oldinterestrate×TotalfundsraisedatoldrateChangeintotalcostMarginalCostRate=AWr三：TAdditionalfundsraisedManagingNondepositLiabilitiesEffectivecostrateondepositandnondepositEffectivecostrate=(Currentinterestcostonamountsborrowed+Noninterestcostsincurredtoaccessthesefunds)/(Netinvestablefundsraisedfromthiscource)Asset-LiabilityManagementandDurationTechniquesNetinterestmarginNIMInterestincomefromloansandinvestmentInterestexpenseondepositsandotherborrowedfudsTotalearningassetssourcesoffunds