金融市场风险测量模型-VaR（PDF10）

VaR,,(,,300072):VaR,VaRVaR;VaR,,;VaR.:;;VaR;:F830.9:A:100025781(2000)0120067209ThemodelofmarketriskmeasurementVaRWANGChun-feng,WANHai-hui,ZHANGWei(InstituteofSystemsEngineering,TianjinUniversity,Tianjin300072)Abstract:Inthispaper,VaR,themainstreammodelofmarketriskmeasurementisintroduced.Thebackground,conception,andthecomputingmethodsofVaRaresurveyedindetail.Atlast,wediscusstheproblemsinVaRandproposethedirectionsofresearchinthefuture.Keywords:marketrisk;riskmeasurement;VaR;stresstest1VaR20,,,.[1]..,.70,,,70,:(1):()(co2movement);(2)15120003JOURNALOFSYSTEMSENGINEERINGVol.15No.1Mar.2000:1998212214;:1999201228.:95(79790130).:(19662),(),,,,.©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.:70(Black2Scholes)(),,;(3):.,.,,,.,:19841996,;J.P.MorganBankersTrustChemicalBankChaseManhattan[2].,,()().,.(),delta(duration)B,(convexity),(underlying),gamma,[3].,,VaR(ValueatRisk).80VaR,VaR.:VaR.VaR,VaR,J.P.MorganRiskMetrics[2,4].VaR,,VaR.,VaRö.BankerTrustRAROC(riskadjustedreturnofcapital)ROC(returnofcapital),(RAROC=ROCöVaR).VaR;VaR,,;VaR.2VaRVaR(ValueatRisk),,.VaR,1.(),,.,.VaR.86151©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.1VaR,VaR,.prob($P-VAR)=1-A$P$t,VaRA.,J.P.Morgan1994,199495%VaR1500.,95%,199424,1500.VaR,.3VaR3.1VaRVaR,.,,.101,102.101(),102.,.VaR,101100,102,102100,.,,,(),VaR(marketfactors)..,VaR:,();();(,Mart2to2Market);,VaR.:;().1),,(sensitivity).,;,Black2Scholes,;2)9620003:VaR©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,;2MonteCarloMonteCarlo;3-(),.,VaR,:MonteCarlo.3.2,,VaR,,.:,;N,(N);(N),;,VaR.3.3N,,,.,.,.3.3.1delta-[5]Garbade,(delta),.,.P(t,xn1),t,xn.P21P(t,x),Pt=5P(t,x)5t,gn1=5P(t,x)5x1,5P(t,x)5x2,,5P(t,x)5xn,.X21xrNn(0,1r),rit=(xi,t+$t-xit)öxit,i=1,2,,n;$xtxt+$t-xt,$xtNn(0,xt1rxt),xt1rxt=1.X21,(HOM).VaR,,VaR$P.,P(t,x)=P(t0,x0)+Pt(t-t0)+g(x-x0)+R2=P(t0,x0)+Pt$t+g$x+R2P(t0,x0)t0,R2.P21R2=0,$P($t,$x)P(t,x)-P(t0,x0)=Pt$t+g$x1$P1$P($t,$x),$P1,$P1N(Pt$t,g1g)VaRProb$P1-Pt$tg1g-VaR-Pt$tg1g=1-AProbZ-VaR-Pt$tg1g=1-AZ(A)A,Z(A)=-VaR-Pt$tg1gVaR=-Pt$t-Z(A)g1g,delta2theta(P)delta(g),VaR.3.3.2delta2[2]delta2RiskMetrics,J.P.Morgan.delta207151©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,P21;,.(WTN)2rt,2rt.X22:2rtRij(t)=k=0Xk(ri(t-k)-Lri)(rj(t-k)-Lrj)Xk=Kk(1-K),0K1$xtNn(0,xt2rtxt),xt2rtxt=2t.,Rij(t).X21,1öN,N;X22,Xk.,Xk1,.,.Rij(t),R2t=KR2t-1+(1-K)(xt-xt-1)2=KR2t-1+(1-K)u2t-1GARCH(1,1)R2t=A+BR2t-1+Cu2t-1,.WTNA=0,B=K,C=1-K,GARCH(1,1).,WTNIGARCH.VaRdelta2,2.3.3.3delta2GARCH[6],delta2GARCH,,GARCH.ARCH,.ARCHEngle[7],,HsiehEGARCH[6]:rt=L+GtGtû8t-1N(0,ht)lnht=A+Blnht-1+UûGt-1ûht-1-(2öP)1ö2+CGt-1ht-18t-1t-1,ABUC.ht.UC,htGt-1.(Black1976[8]),.U0,C=0,ûGt-1û(2öP)1ö2,ht,;E(ûGt-1û)=(2öP)1ö2.U=0,C0,Gt-10,ht,.,delta2GARCHdelta2delta22.GARCHt3t.3.3.4gamma2[9]Wilson,,P21P22;,X21.,.P22P(t,x)txPt=5P5t,Ptt=52P5t2,g=5P5x,Ptx=52P5t5x,Hnn=(Hij),Hij=52P5xi5xj,.WilsonVaR,VaR:max$x-$P(t,$x)s.t.F($x)AX21P22max$x-(Pt$t+g$x+12$xH$x)s.t.$x-1$xJ,Wilson.,1720003:VaRWilsonPtxPtt,$t$x$t$t,Black2Scholes.©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,.Wilson,.3.3.5gamma2GARCH[10]Fallongamma2GARCH.,GARCH,P22,X23:rtrt=L+ututû7t-1N(0,3rt)rt,L,utn,3rtnn,7t-1t-1,3rt=VtRVt,R,Qij;Vt,vii(t),vii(t)=A0i+A1iu2i,t-1+Bivii(t-1),i=1,2,,nvij(t)=Qijvii(t)vjj(t)i,j=1,2,,nijX23,$xtNn(0,3t),3t=xt3rtxt.VaRgamma2,,2.3.3.6VaR[4]VaR,VaR,VaR.,,VaR.VaR,VaR.VaR,,,VaR.VaRVaR,VaR:VaR,;.VaR,VaR.,,.VaRdelta[4].,,VaR.VaRVaRdelta,VaR.VaRdelta,.VaRdelta90,VaR;90,VaR.VaRdelta,VaR..:,;.,,,.,,GARCH.,:(1),.(riskmapping),.(2),,.(3).,,.(4)VaR.,VaR.3.4MonteCarlo[2]MonteCarlo,27151©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,.:,;(),();MonteCarlo,;,VaR.MonteCarloVaR,::,,,,.J.P.MorganRiskMetrics,VaR15,10-14,,.,;(2)MonteCarlo.,,,;.,MonteCarlo.(1)MonteCarlo,JamshudianZhuscenarioMonteCarlo[11].MonteCarlo,scenario,,,Sakura(SGC)SakuraPrime;(2)MonteCarlo,MarkovChainMonteCarlo(MCMC),,Gibbs,,(),MCMC.MonteCarlo,,,VaR.1VaRMonteCarlo,,,,3.5VaR,?.,3720003:VaR,MCMC2VaR,()©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,delta,,,RiskMetrics;,MonteCarlo.delta,,gammavegathetarhodelta.1.4VaRVaR,VaR,:4.1,.(MonteCarlo),,delta,delta.,P=P(R,R,K,S,r),P,R,R,K,S,r.S,P0,dP5P5RûP0dS+1252P5R2ûP0(dS)2+5P5RûP0dR+5P5SûP0dS+5P5rûP0drdpDdS+12#(dS)2++dR+(dS+PdrDdelta,;#gamma,delta;+vega,;(theta,,;Prho,.delta,gammatheta.gammathetavegarho,,.4.2,.,,.,,(),.VaR.,(t)(GARCH).t,.tn,n,,n,t,.4.3VaR,.VaR,.,J.P.Morgan95%125VaR;,99%10VaR.10,99%.VaR,.47151.©1995-2004TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,.T,:VaR,TTVaR...VART=TVARdaily,,2.4.4VaR..VaR.,(BIS)[12].,.,BISVaR.VaR,,J.P.MorganRiskMetrics.4.5,VaR,VaRVaR,,;VaR,,,(1987),VaR.,,VaR,(Stresstest)VaR[13].5VaR,VaR[12].,VaR().:[1]FreemanA.Asurveyofinternationalbanking[M].TheEconomist,1993,137[2]MorganGuarantyTrust.RiskMetrics-TechnicalDocument[M].3rded.NewYork:MorganGuarantyTrust,1995[3]SmithsonC,MintonL.ValueatRisk[J].Risk,Jan.1996,9(1):2527[4]GarmanMB.MakingVaRproactive[R].Researchreport,FEA,1996[5]GarbadeK.Assessingriskandcapitaladequacyfortreasurysecurities[R