2015基于COPULA的沪深300股指期货与现货间相关性模型_李战江

36120151JournalofInnerMongoliaAgriculturalUniversityNaturalScienceEditionVol．36No．1Jan．2015COPULA300*123*11．0100192．6111303．010018。300。Copula。Copula。300CopulaF830．9A1009－3575201501－0159－04THECOＲＲELATIONMODELOFHS300STOCKLNDEXFUTUＲESANDLTSSPOTBASEDONCOPULALIZhanjiang1ZHANGHao2SUJinmei3*XIUChangbai11．CollegeofEconomicsandManagementInnerMongoliaAgriculturalUniversityHuhhot010019China2．SchoolofStatisticsSouthwesternUniversityofFinanceandEconomicsChengdu611130China3．CollegeofScienceInnerMongoliaAgriculturalUniversityHuhhot010018ChinaAbstractThecorrelationbetweenstockindexfuturesandspotisveryimportanttothefinancialsystem．ThispaperusesempiricalresearchtoanalyzetherelevancebetweenHS300indexfuturesandspotfillstheblanksusingrealtransactionaldata．Therearetwofeaturesinthisthesis．FirstlyThepaperusestheCopulafunctionbasedonthemethodofnonparametrickerneldensityestimationtoeliminatethetraditionalmethod＇sdefectsaccuratelymeasurescorrelationbetweenstockindexfuturesandspot．SecondlythispaperselectstheoptimalCopulafunctioneffectivelyanalysesthetaildependenceinextremecondition．KeywordsStockindexfuturesHS300correlationCopula、。20104161。①。20082、VECM*2014－05－21“”2013MS0121*[e-mail]201530020083GrangerGeorge20104APAＲCH20115。②。2010620117Ｒoll20078VAＲ。。、。Copula300。。2Gum-bel、Clayton、FrankArchimedeanCopula。Kendallτ、Kolmogorov－SmirJanCopula。300QXsQsXfQxgXyFQxFXyCopulaCSklar9Hxy=C．FQxFXy。2．1t。Copula9。KQ·、KX·hQ、hXsQsXu、v9u=F∧QS'Q=∫S'Q－∞f∧Qxdx=∫S'Q－∞1ThQ∑Ti=1KQx－S'Qh()Qdx1v=F∧XS'X=∫S'X－∞g∧Xydx=∫S'X－∞1ThX∑Ti=1KXy－S'Qh()Xdy22．2CopulaCopula、10。ArchimedeanCopulaClayton、Gumbel、Frank9CCuv=maxu－α+v－α－1－1/α03CGuv=exp－－lnuα+－lnvα1/α4CFuv=－1/α·ln1+e－αn－1e－αv－1e－α－15αCopula9α=argmax∑Ti=1lnu∧tv∧tα62．3CopulaKendallτCopulaK－SCopulaτCopula2．3．1Kolmogorov－SmirJanCopulaCopulaCuv01K－S11。PCopulaCopula。2．3．2KendallτKendallττCopula。Pearsonτ11τ=4∫10∫10cuvdcuv－172．40611COPULA300、ClaytonCopulaλLGumbelCopulaλU12－13λL=2－1/α8λU=2－21/α933．1300300201041620111111383。。13。13。“”。11－21Tab．1Sampledata1SQ2SX3u4v5CC6CG7CF13415．63356．30．93470．92380．93070．94510．941323197．43176．40．73670．74040．72780．73600．7364……………………1923030．43026．50．52280．54040．52700．52770．5320……………………3822707．02699．60．12530．12740．11150．10630．10753832699．22695．00．11820．12310．10060．09520．096011http//．cffex．com．cn/12http//．csin-dex．com．cn/2Tab．2StatisticalpropertiesofthesampleK－SPJ－BPsQ8．00890．0813－0．01372．36060．04340．0380sX8．00210．0782－0．11822．21640．01650．01103．2300SQ、SXsQ=lnSQ、sX=lnSX。2。2J－BK－Snormal。95%。3．3Gaussinmatlabu、v13～4。3．4Copulau、v345Clayton、Gum-bel、FrankCopulaCC、CG、CF15～7。6Copu-laα21。CopulaK－SP32Frank＞Gumbel＞Clayton＞0．0595%CopulaCopula。3CopulaTab．3CopulafunctionparametersCopula1α2K－SP3τClayton30．46030．94830．9384Gumbel20．31190．98110．9508Frank98．37180．99630．9600K－SPCopulaKendallττ0．9607。CopulaFrank1612015GumbelClayton。GumbelClaytonGumbelCopula10λU=0．9653。3．5300FrankCopula。GumbelCopulaClaytonCopu-la。4Copula300。。、。1XiaoxueLiuCuipingDong．TheEmpiricalStudyontheIn-tradayInteractionＲelationshipbetweenStockIndexFuturesandStockIndexJ．CommunicationsinComputerandIn-formationScience2011210407－413．2．300J．2008104321－325．3．J．20086146－148．4GeorgeAKValisiosIS．Spillovereffectsoffuturescon-tractsinitiationonthecashmarketaregimeshiftapproachJ．ＲeviewofQuantitativeFinanceandAccounting201034195－143．5．J．2011251115－120．6．D．2010．7．J．201138555－60．8ＲichardＲollEduardoSchwartz．LiquidityandtheLawofOnePriceTheCaseoftheFutures－CashBasisJ．TheJournalofFinance200752201－2234．9．CopulaD．2008．10．J．2002941－49．11．CopulaM．2008．12．copulaJ．2009829－31．13．CopulaJ．．2013343170－173．261