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:1003-207(2003)01-0022-06VaR-APARCH,(,510405):,,,APARCHVaR,GARCH,,APARCHVaR,GARHC:;APARCH;GARCH;;:F830.59;F830.91:A:2001-07-23:(1974-),(),,,,:11VaR(ValueatRisk),[10],,-VaR,,,VaR,XF,VaRq:VaRq=F-1(1-q),qVaR,VaR,VaR,,,,,,,VaRVaR-APARCH,VaR,GARCH,VaR22.1,,[9],,,,[7,9],,,,,,BLACK[2],,,QQ1997122002322,11120032ChineseJournalofManagementScienceVol.11,No.1Feb.,2003©1995-2003TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.1QQ1,QQ2.2APARCH,Engle(1982)(ARCH)[6],,ARCH,,,1986,BollerslevARCH,ARCH,ARCHGARCH[3]ARCH,GARCH:GARCHARCH,,{Xt},,GARCH(p,q),:Xt=t+tZt(1)2t=0+qi=1i(Xt-1-t-1)2+pj=1j2t-j(2)(1)(2),p0,q0,00,i0(i=1,2,,q),j0(j=1,2,,p)Zt01,Fz(Z),GARCH,Ding,GrangerEngle(1993)GARCH[5],APARCH(theAsymmetricPowerARCH),APARCH(p,q):t=0+qi=1i(|t-i|-it-i)+pj=1jt-j(3),00,0,j0(j=1,,p),i0-1i1(i=1,,q)APARCHGARCH,,i2.3VaRVaR,VaR:VaRtp=t+tzq(4),zq{Zt}q,{Zt}VaRAPARCHGarch,,garchZt2.4,APARCH,,,,,t(GED),,tt,,t,,t,t,t,t321:VaR-APARCH©1995-2003TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.GEDJPMorganRiskMetrics,GED:f(zt)=exp(-|zt/|/2)2(1+-1)(-1),=(2-(2/)(1/)/(3/))1/2,()gammav,,v=2,GED,v2,,v2,GED2GED(v=1.27),,v2,GED2GED3Beder(1995)[1]Hendricks(1996)[11]VaR,VaR3.1VaR,,,,:,VaR()[8]LR,VaR,VaRVaR,,VaR,VaR,(1),VaR,(0),VaR,T,N,p(=N/T),p(=1-)p=p,VaRppKupiec:LR=-2ln[(1-p)T-N(p)N]+2ln[(1-p)T-NpN],LR1295%3.84,,LRuc3.84,,,:3.2(AverageCapitalEmployed)VaR=1TTt=1VaRt+1,,VaR3.3(StandardDeviationofCapitalEmployed)STD(VaR)=1TTt=1(VaRt+1-VaR)2,VaR,,4,Xt,:Xt=log(Pt)-log(Pt-1):1997122002322,20023252002927,APARCHGARHCVaR,4.1,VaR422003©1995-2003TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.,,,A2PARCH,,tGED,1,,,,Jarquebera5.9915,,:1XtMeanSEskewnesskurtosisJarquebera0.00070.0168-0.46188.89191.6688e+003,1,(ACF),,,112Engle(LM)ARCH,p0.0001APARCH(1,1)GARCH(1,1),Xt=t+t,t3MatLab1-2095%,232APARCH(1,1)GARCH(1,1)Model0111DFGARCH(1,1)-N0.00000.16210.8291---GARCH(1,1)-T0.00000.27980.6945--4.2000GARCH(1,1)-G0.00000.25630.7099--1.1706APARCH(1,1)-N0.00120.15890.81980.04270.9047-APARCH(1,1)-T0.00240.12760.83670.07140.69264.8075APARCH(1,1)-G0.00000.01520.86420.06163.39891.16232,,10,4.2VaRVaR,APARCHGARCH:tVaR34:521:VaR-APARCH©1995-2003TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.3GARCH(1,1)95%confidentlevel99%confidentlevelSampleDistribPFMeanStdLRPFMeanStdLRPartlGED0.05510.02730.01500.66760.00960.04420.02420.0221T0.02000.03590.019230.4820.00320.06230.03347.9702Normal0.05590.02790.01660.88830.01840.03930.02347.1045Part2GED0.03850.02340.01000.394500.03780.0162-T0.01540.03090.01314.447400.05360.0227-Normal0.03850.02340.00950.39450.00770.03290.01330.07604APARCH(1,1)95%confidentlevel99%confidentlevelSampleDistribPFMeanStdLRPFMeanStdLRPart1GED0.05590.02590.01150.88830.01120.04200.01860.1702T0.02720.03240.013316.3750.00480.05450.02254.2474Normal0.04870.02630.01080.04340.01760.03700.01525.9162Part2DED0.05380.02010.00550.03950.00770.03260.00890.0760T0.04620.02180.00610.041500.03670.0103-Normal0.05380.02050.00600.03950.02310.02890.00841.6400*PF,Mean,Std,LR:LR:(1)LR,GEDGARCHAPARCH(2)APARCH(1,1)GARCH(1,1)(3)APARCH(1,1)GARCH(1,1)(4),APARCH(1,1)GARCH(1,1),,GED5,,VaR,:SSE,,APARCHGARCHVaR,,:GED,APARCHVaR,GARHC,VaR,(95%),,,(1-95%=5%)VaRVaR,(95%),VaR(5%),,ES,VaR,:[1]Beder,T.S.VAR:SeductivebutDangerous[J],FinancialAnalystsJournal,(1995),September-October,1995,12-24.[2]Black,F.StudiesofStockMarketVolatilityClanges[C].ProcedingsoftheAmericanStatisticalAssociation.BusinessandEconomicStatisticsSection,1976,177-181.[3]Bollerslev,T.A,GeneralizedAutoregressiveConditionalHeteroskedasticity[J].JournalofEconometrics,1986,31:307-27.[4]Christoffersen,P.(1998),EvaluatingIntervalForecasts[J],InternationalEconomicReview,1998,39:841-862.[5]Ding,Z.,C.W.J.Granger,andR.F.Engle,ALongMemo2ryPropertyofStockMarketReturnsandaNewModel[J].JournalofEmpiricalFinance,1993,1:83-106.[6]Engle,R.Autoregressiveconditionalheteroscedasticitywith622003©1995-2003TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.estimatesoftheVarianceofUKinflation[J],Econometri2ca,1982,50:987-1008.[7]Fama,E.TheBehaviourofStockMarketPrices[J].JournalofBusiness,1965,38:34-105.[8]Kupiec,PaulH.Techniquesforverifyingtheaccuracyofriskmeasurementmodels[J].JournalofDerivatives,1995,3(2):73-84.[9]Mandelbrot,B.TheVariationofCertainSpeculativePrices[J],JournalofBusiness,1963,36:304-419.[10]PhilippeJorion.ValueatRisk[M],2ndedition,McGraw-Hill,20011VaR-APARCHModelforRiskMeasuresofStockMarketCHENXue-hua,YANGHui-yao(InstituteofQuantitativeEconomicsGuangzhouUniversity,Guangzhou510405,China)Abstract:PreliminarydataanalysisshowsthatthereturnratesdistributionofSSEisfat-tailedanddoesntobeynormaldistributionandthereisleverageeffectinShanghaiStockmarket.Inthispaper,weproposeanA2PARCHmodelwiththreedifferentdistributionsassumptiontoestimateconditionalVaR.ThismodelisthencomparedwiththeGARCHmodelunderthecorrespondingthreedistributionsassumption.Usingback-testingofhistoricaldailyreturnseriesweshowthattheAPARCHmodelyieldsstatisticallyvalidVaRmeasuresandgivesbetterone-dayaheadestimatesthattheGARCHmodel.Keywords:ValueatRisk;APARCHModel;GARCHmodel;fat