单个期货合约市场风险VaR-GARCH评估模型及其应用研究

4612OO61JournalofDalianUniversityofTechnologyVol.46No.1Jan.2OO6:1OOO-86O8(2OO6DO1-O127-O8:2OO4-12-19;:2OO5-12-O3.:(7O571O1OD;(GT2OO41O;ZZ2OO5O5D;(2OO4C1ZC227D.:(1955-DE-mail:[e-mail]-GARCH12321(1.116O24;2.116O24;3.116O23D:VGR(GARCHDVGR-GARCH.GARCH~VGR;VGRX2VGR;.:;;;(VGRD;(GARCHD:F83O.9:A[1]...VGRVGR:...VGR[2~4].[5]VGR.~..[6~8].David[9](VGRD(ARCHDVGR.VGR[1O~11].VGR(GARCHDGARCH-M~EGARCHVGR-GARCH.GARCH[3]~.VGR-GARCH.1VaR-GARCH1.1VaRVOR,,.6,[12]Prob(RRmin)=1-6(1);R;Rmin.u,PO,P=PO(1+R).6,Pmin=PO(1+Rmin),;VOR=E(P)-Pmin=-PO(Rmin-u)(2)VOR,Rmin.f(R),1-6=Rmin-Of(R)dR(3),,R~(u,o2).,c=(R-u)/o,cO~1(O,1),c~(O,1).-a=(Rmin-u)/o,1-6=Rmin-Of(R)dR=-a-O(c)dc(4)(c).,a,-a=(Rmin-u)/o(2),VOR=POao()VOR,.VOR;VOR;VOR~.,.1.2GARCHBOllerSlev[13]1986GARCH,.BOllerSlevGARCH,,ARCHEngel[14]2OO3.GARCHARCH,ARCH(G)[1];yt=It7+Et(6)EtIMt-1~(u,o2t)(7)Et=tot(8)o2t;o2t=aO+Gz=1azE2t-zaOO,azO(z=1,2,,G)(9);yt;It;7;Et;o2t;ot;(u,o2t)O~o2t;t,E(t)=O,var(t)=1;Mt-1t-1;aO;az.ARCH,,.ARCH(G).G,,G,.,,ARCH(G)p,GARCH(p,G).GARCH(p,G)o2t[13];o2t=aO+Gz=1azE2t-z+pJ=1BJo2t-J(1O)azO,BJO(z=1,2,,G;J=1,2,,p)az~BJ.GARCH(p,G)(o2tot),GARCH-,~.yt=/o2t+It7+Et(11)/.GARCH(p,G)~,,.821462VaR-GARCH2.1VaR-GARCH,.,,,.VOR,,VOR.VOR.~,~GARCH.,,.,.,.,VOR-GARCHGARCH,,VOR,VOR.1.1VOR-GARCHFig.1TheoryofsinglefuturescontractriskassessmentbasedonVOR-GARCH2.2VaR-GARCH2.2.1.,,.~,,(VI).,.,.I(1I),1I=PI-PI-1PI-1=PIPI-1-1(12),PII;PI-1I-1.2.2.2VaR-GARCHGARCH,~.,GARCH62I,(10).(10)62I6I,,6I=O0-zgz=1Oz2I-z-zpj=1j62I-j(13)6I(5)6,I-19211,VOR-GARCHPt-1(5)P0,,tVaRt.VaR-GARC~;VaRt=Pt-1a6t=Pt-1aa0+z=1azE2t-z+j=1Bj62t~-j(14);aC,.2.3(1)62t,t-1,,t30,62t.(10),GARC~,t62t.(2)6tt62t6t.(3)a95%,a=1.65.(4)tVaRt(14)VaRt.(5)tVaRt,(1),GARC~,VaRt,VaRt.(5),VaRt,.VaRt,(14),6t.T,62t,(T-1)62t/62tT-1X2,6t[16];6t(T-1)/X21+C~26t6t(T-1)/X21-C~2(15)X21+C2X21-C2C,X2.(15)Pt-1a,VaRtPt-1a6t(T-1)/X21+C~2VaRtPt-1a6t(T-1)/X21-C~2(16)(15)(16),VaRt.VaRt,VaRt9,,(1),VaRt.2.4VaR-GARC~..,...,.,,..,[17].,.,.VaR,[17].,SPANTIMS,,,,[17].,,,..,.03146,VGR-GARCHVGRt.,,,.VGRt.VGRtt,VGRt;VGRtt,VGRt;VGRtt,.Ct=Pt-1X%(17)MGlt=min(VGRt,Ct)(18):%t;Ctt;MGltt.,,.33.104082003-11-28~2004-07-23155[18],(12),1.104081)Tab.1Al0408futurescontractsettlementpriceandfluctuationtPt/Vt/lt2003-11-28157202003-12-01160002800.017812003-12-0215820-180-0.01130SSSS2004-07-2314990-200.001332:1)[19].ADF,.2,0.05,ADF-4.711611-2.8807,.,0408.20408ADFTab.2ADFtestoffuturesAl0408fluctuationseriesADF1)1%5%10%-4.711611-3.4749-2.8807-2.5769:1)Mackinnon13:-0.274,1311:VGR-GARCH0;4.044,3.0408.3(:155)Tab.3Fluctuationstatistics(155samples)-0.0001300.038-0.0400.011-0.2744.0443.30408VaR0408,,0408.VGR-GARCH(13)(14)0408.2003-12-01~2004-01-12302004-01-1331VGR31[18].040831VGR31:(1)(10),EvieWs3.1GARCH30,95%:O2t=0.0000125+0.13313E2t+0.823833O2t-1(19)(0.00023)(0.02567)(0.04151),0.05,,.(10)31O231=0.0000425.(2)O31.(13),O23131O31=0.00651920.(3),95%,a=1.65.(4)VGR31.04083017060,(14),31VGR31=170601.650.00651920=183.508961.(5)VGR31.T=30,95%,X2X21+95%2=45.921X21-95%2=16.114,(16):170601.650.00651920~(30-1)/45.921VGR^31170601.65~0.00651920(30-1)/16.114(20)[145.831,246.181],VGR31=183.508961,.040831VGR31.,312004-01-13VGR31183.508961,31.VGRt,t-1(t=32,33,~,156)tVGRt.2004-01-14~2004-07-26VGRt4.4VGRtTab.4VGRtcalculatingtabletO2tOt95%VGRt2004-01-130.00004250.00651920183.5089612004-01-140.00004620.00679706190.7506022004-01-150.00004650.00681909189.798483EEEE2004-07-260.00003270.00571839141.1953752004-01-13~2004-07-26VGRt1Vt,0408,3.3VGRtFig.3VGRtandabsolutefluctuationtrend23146,VORt,.,3:VORt(3).,,VORt;,VORt.,VORt;,VORt.VORt.3.40408VOR-GARC~0408VORt0408.040831VOR31,31.0408313%.(17),040831C31=170603%=511.8.(18),040831MOr31=min(VOR31,C31)=min(183.508961,511.8)=183.508961.31,.4GARC~,,VOR,VOR-GARC~.(1),.GARC~,VOR-GARC~.0408~.(2)~,VOR,GARC~~,.(3)VORX2,VOR.(4).VORt,,.:[1]C.[M].:,2000:75-77.[2],.Var[EB/OL].:[2004-05-19].[3]MARKR,RAYMONDM,LEUT~OLDM.Marketriskandthecattlefeedingmargin:anapplicationofvalue-at-risk[J].Agribusiness,2001,l7(3):333-353.[4]FALLONW.Calculatingvalue-at-risk[R].Philadelphia:UniversityofPennsylvania,1996.[5],,,.[J].(),2001,7(4):325-327.[6]BLACKJ,TONKSI.Timeseriesvolatilityofcommodityfuturesprices[J].TheJFuturesMarkets,2000,20(2):127-144.[7]BOLLERSLEVT.Modelingthecoherenceinshort-runnominalexchangerates:AmultivariategeneralizedARC~approach[J].ReVofEconomandStatist,1990,72:498-505.[8]DIMITRIOSDT,WANGTao.Realizedvolatilityinthefuturesmarkets[J].JEmpiricalFinanc,2003(10):321-353.[9]DAVIDJ,SEMPERC,MOYACLEMENTEI.ValueatriskcalculationthroughARC~factormethodology:Proposalandcomparativeanalysis[J].EuroJofoperRes,2003,l50(3):516-528.3311:VOR-GARC~[10]GAOA~WANGG~K.MOdelingnOnlineardynamicsOfdailyfuturespricechanges[J].theJofFuturesMarkets199919(3D:325-352.[11]ALFREDLSC~EIC~ERMSC~ITTEKOPFC.GARC~vsstOchasticvOlatility:OptiOnpricingandriskmanagement[J].JofBankingSFinance200226:323-345.[12].[M].:2001:137-145.[13]BOLLERSL