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Granger120058911200698FuturesIndustryAssociationFIA1/3200420052001FIAJOSEPHStockindexfutures2005option197422.1perfectmarket1234567r89T10marktomarket112.2'tF'tCttCtF).)((),)((''tTdrFCtTdrCFtttt−−+=−−+=rdtT−.)(,)(21'1111'1'1'tttftcttttctftCCCCCCCCεβαεβα+−++=+−−+=−−−−−−cβfβcαfαt1εt2ε23⎥⎦⎤⎢⎣⎡+⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡−−+⎥⎦⎤⎢⎣⎡=⎥⎦⎤⎢⎣⎡−−ttttffcccfttCCCC211'1'11εεββββααcβfβ'tCtCcβfβ3ttCC−'4tttttCCCC31'1')(εδα+−+=−−−.4cfααα−=,fcββδ−−=1t3ε=t1ε-t2εcβ=fβ=0δ=1δ=0δ=1ttCC−'ttCC−'Garbade&Silber1983ttCF−ttCC−'GSGarbade&Silber’smodelttttttCCCFCF−+−=−'',5a15a,ttttCCtTdrCF−+−−=−'))((.5b1'111)1)((−−−−−++−−=−ttttCCtTdrCF.5c5b5c3tttttCFCF31'110)(εββ+−+=−−−.5d)1)(())((0+−−−−−+=tTdrtTdrδαβδβ=1.12δ=1ttCC−'33GARCH3.1GARCHBollerslevet.al.,1992Engle(1982)(AutoregressiveConditionalHeteroskedasticmodel--ARCH)Bollerslev(1986)ARCHGARCHGeneralizedAutoregressiveConditionalHeteroskedasticitymodel--GARCH3.1.1ARCHARCHtyβtxβtx1−ΩtARCH.),,,,,(),,(~211βεαεεεβtttqttttttttxyhhhxNy−==Ω−−−−Λ(6a)thqttt−−−εεε,,,21Λ),,,,(21αεεεqtttthh−−−=Λαβεtttxy−=th),,,,,,,,(121αεεεptttqttttxxxhh−−−−−=ΛΛ(6b)thq210itqiith−=∑+=εαα(6c).,,2,1,0,00qiiΛ=≥αα3.1.2GARCH1986BollerslevARCHGARCHGARCH(p,q).,)()(),,0(~2012101βεβεααβεααtttttitpiiitqiittttxyhLLhhhNy−=++=++=Ω−=−=−∑∑(7).,,2,1,0,,,2,1,0,0,0,00piqiqpiiΛΛ=≥=≥≥βααp=0GARCH(p,q)ARCH(q)p=q=0,tεpqBox&Jenkins(1976)2tε3.2EGARCH3.2.1EGARCHGARCH1991NelsonGARCHexponentialGARCHmodelEGARCH)1991Sentana(1991)1990EngleGARCHquadraticGARCHmodelQGARCH)1994ZakoianTGARCHthresholdGARCH--TGARCH)GARCHGARCH)(110itititqiiitpiitEInhInh−−−=−=−+++=∑∑εγεγθεαβα,(8).,,2,1,,,,2,1,,,,,0,00piqiqpiiΛΛ==≥βαγθαiiβαα,,0GARCHEGARCH3.2.2EGARCHEGARCHBivariateErrorCorrectionEGARCHModelTse1999RamaprasadBhar2001EGARCHRamaprasadBhartFtSCo-integration“1”“2”),(′=tttSFPVectorErrorCorrectionModel--VECMtitkiiitkiittScFbzaF11111111εα+∆+∆++=∆−=−=−∑∑,9titkiiitkiittScFbzaS21212122εα+∆+∆++=∆−=−=−∑∑.10∆L−=∆1LkttkttxxLxLx−−==,1111−−−−=tttSFzerrorcorrectionterm),0(~121tttttHN−Ω⎟⎟⎠⎞⎜⎜⎝⎛=εεε,11a⎟⎟⎠⎞⎜⎜⎝⎛≡22212121tttttttHσσρσσρσσ,11b()()()()()2,1,21,1,21,2221,11102=++++=−−−−ieInInzfzfIntiitiititiiitθσγααασ.122,1,)()(1,1,1,1,=+−=−−−−izzEzzftiitititiiδ.132,1,,==izitittiσε.1411unauto-correlatedresidualst1εt2εVECM9101−Ωt1−tmaximizingthelog-likelihoodfunction1114{}∑=Θ=ΘTttlInL1)()(,15[][]2/)2(1'2/1211)2()2/(2/)2()(vtttttHvHvvvl+−−−⎥⎦⎤⎢⎣⎡−±−ΠΓ+Γ=Θεε.16νBollerslev,1987121γvolatilityspillover2γ1iα2iαthemarket-specificvolatilityclustering/autocorrelationsiθasymmetricvolatilitycoefficient41RamaprasadBhar2001RamaprasadBhar910kGARCHkpqtitqiiitpiittScFbzaF11111111εα+∆+∆++=∆−=−=−∑∑,17titqiiitpiittScFbzaS21212122εα+∆+∆++=∆−=−=−∑∑.18MATLABMathematicaforWindowsSASSPSSEconometricViewsTSW55.15.1.1lead-lagHerbst1987S&P500MMICheung&Ng1991S&P50015~30Grunbichler1994DAX15~20Fleming1996S&P500198811991351998PizziS&P50036205.1.2Stoll&Whaley1990S&P5005.25.31987101925%TheBradyCommissionReportCascadeTheoryGrossman198819871198710Furbush198919871014201014S&P50050%101920Hasbrouck1996HoganKroner&Sultan1997EGARCHHarris1990Neal199266.1RamaprasadBhar20016.26.36.4[1][M]20056[2][J]200236121317~1319[3][J]200512[4]..[M]199912[5]Sutcliffe,CharlesM.S.StockIndexFutures:TheoriesandInternationalEvidence(2rded.)[M].InternationalThomsonBusinessPress,1997.[6]Garbade,K.&Silber,W.Pricemovementsandpricediscoveryinfuturesandcashmarkets[J].ReviewofEconomicsandStatistics,1983,289-297.[7]Tse,Y.PricediscoveryandvolatilityspilloversintheDJIAindexandfuturesmarkets[J].JournalofFuturesMarkets,1999,19:911–930.[8]RamaprasadBhar.ReturnandvolatilitydynamicsinthespotandfuturesmarketsinAustralia:AninterventionanalysisinabivariateEGARCH-Xframework[J].JournalofFuturesMarkets,2001,??219:??833-850.[9]Maddala,G.S.&C.R.Rao.StatisticalMethodsinFinance[M].ElsevierScienceB.V.,1996.[10]Fleming,J.,Ostdiek,B.,&Whaley,R.E.Tradingcostsandtherelativeratesofpricediscoveryinstock,futures,andoptionmarkets[J].JournalofFuturesMarkets,1996,16:353-387.[11]Pizzi,M.A.,Economopoulos,A.J.,&O'NeillH.M.Anexaminationoftherelationshipbetweenstockindexcashandfuturesmarkets:aco-integrationapproach[J].JournalofFuturesMarket,1998,183:297-305.[12]Stoll,H.R.&Whaley,R.E.Thedynamicsofstockindexandstockindexfuturesreturns[J].JournalofFinancialandQuantitativeAnalysis,1990,25:441468.[13]HoganK.C.Jr.,Kroner,K.F.&Sultan,J.Programtrading,non-programtrading,andmarketvolatility[J].JournalofFuturesMarkets,1997,177:733-756.[14]WalterEnders.AppliedEconometricTimeSeries[M].JohnWiley&Sons,Inc.1995.[15]Maddala,G.S.&C.R.Rao.StatisticalMethodsinFinance[M].ElsevierScienceB.V.,1996.[16]Bollerslv,T.Generalizedautoregressiveconditionalheteroskedasticity[J].JournalofEconometrics,1986,31:307-327.[17]Engle,R.F.ARCHSelectedReadings[M].NewYork:OxfordUniversityPress,1995.[18]Engle,R.F.&Granger,C.W.J.(1987).Co-integrationanderrorcorrection:Representationestimationandtesting[J].Econometrica,1987,55:251276.11963.04-