基于Hill估计的VaR计算

©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:(1979-),,,,.HillVaR(,314001):Hill,Hill2002-01-042008-09-18,:,:;;;Hill:O176Value-at-RiskbasedonHillEstimatorAnExampleofSubprimeLendingCrisisXIAOJing-hong(SchoolofMathematicsandInformationEngineering,JiaxingUniversity,Jiaxing,Zhejiang314001)Abstract:Thispapermakesatheoreticalanalysisofthetailformofextremevaluedistribution,Hillestimator,riskvalueanalysis,etc.,andcalculatestheriskvalueoftheSSECompositeIndex,theDowJonesindex,andtheHangSengIndexduringtheperiodof2002-01-042008-09-18byusingtheHillEstimatoroftheExtremeValueTheory.IthasmadeacomparisonandanalysisofthemarketrisksfacedbydifferentnationsandholdsthattheoutbreakoftheSubprimeLendingCrisisintheUnitedStateshasbroughttheglobalfinancialmarketsenormousrisks,anditsim2pactonChinaisespeciallytremendous.Keywords:SubprimeLendingCrisis;ValueatRisk(VaR);ExtremeValueTheory;HillEstimator:A1:1008-6781(2009)05-0059-04(subprimelendingcrisis),.VaR(ValueatRisk),,,VaR,,,,,VaR,VaR,[1]:,Hill,Hill,Hill9521520099Vol.21No.52009.9JournalofJiaxingUniversity©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[2]Fisher-Tippett,L(x),x,:F(x)=1-L(x)x-x,L(x)L(x)=a(1+bx-),F(x):F(x)=1-ax-(1+bx-)(1)ab;:f(x)=ax--1+ab(+)x---1Dacarong(1)2.HillHillm:[3]1^=(m)=1mmj=1[lnx(j)-lnx(m)](2),x(m)Hill,,Hill,x(m)mx(m),,Hall1990,x(m)1/^,[4]m,Hall:E(m)-1E-b(+)a-mn/(3)Var(m)-11m2(4):E(m)-12b(+)a-(mn)/2+1m22(5):Hillm,m,m,m3.p1p2,p21-1/np1,n,ptxpxt,:F(Z1)=p1,F(Z2)=p2(6)1-1/np1,Z1max(x1,,x2),,y1,(1)(3),:1-p21-p1=(Z1Z2)1+b(Z2)-1+b(Z1)-1=1+b(Z2)-1+b(Z1)-,1,1,=06215©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:Z1=Z21-p21-p11/Z2=xk+1,:1-k/n1-p2p1,:xp1=Z1=X(k+1)n-kn(1-p1)1/^(7)Stt,rt,:rt=ln(St/St-1),,xt=-rt,xtx^p,VaR-x^p1.yahoo,2002142008918,1700,19972001,116(%)(%)-0120408041299579010932116628011226123107171801068211039401076643613353490103181133880103933441882867010104111642-0134807051027172010270110981-0111391091628697-0101701141841,60,,,3,21(2)kHill,,11Hill1,k,Hill,,;,(k)=0;2002,,,,,,Hill3.1,k=200,,(200),95%99%VaR,216:HillVaR©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(%)81388411035179851391415935106699%VaR(%)1615676182110144710104061871810802,95%VaR5%,,,,,,VaR,Hill,,,2,:,,;,,,,VaR,-VaRVaR:[1].[M].:,2000:377-380.[2]DanielssonJ.Usingabootstrapmethodtochoosethesamplefractionintailindexestimation[J].Journalofmultivariateanalysis,2001,76(2):226-248.[3]HillB.ASimpleGeneralApproachtoInferenceAbouttheTailofaDistribution[J].TheAnnalsofMathematicsStatistics,1975(3):1163-1174.[4]HallP.Usingthebootstraptoestimatemeansquareerrorandselectsmoothingparametersinnon-parametricproblems[J].JournalofMultivariateAnalysis,1990,32:177-203.[5],.Hill[J].,2004(21):305-309.()(17)[7].[M].:,2002:506.[8],.:[J].,2001(3):177-186,208.[9].:3[M]..(1894).[10].[M]..:,1990:1.[11].[M]:.:,2003:387.[12].:7[M].:,1965:749.[13].:[M]..:,.[14].:2[M]...[15].:27[M]...()26215