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1、Keywords:Stochasticcontrol;pairstrading;cointegration;ConstantElas-ticityofVariance;statisticalarbitrage1OptimalPairsTradingwithTime-VaryingVolatilityThomasNanfengLi,AgnèsTourinyJanuary6,2016AbstractWeproposeapairstradingmodelthatincorporatesatime-varyingvolatilityoftheConstantElasticityofVar
2、iancetype.Ourapproachisbasedonstochasticcontroltechniques;givenafixedtimehorizonandaportfoliooftwocointegratedassets,wedefinethetradingstrategiesastheportfolioweightsmaximizingtheexpectedpowerutilityfromterminalwealth.WecomputetheoptimalpairsstrategiesbyusingaFiniteDifferencemethod.Finally,weillu
3、strateourresultsbyconduct-ingtestsonhistoricalmarketdataatdailyfrequency.TheparametersareestimatedbytheGeneralizedMethodofMoments.NewYorkUniversityTandonSchoolofEngineering.DepartmentofMathematics.6MetrotechCenter,Brooklyn,NY11201.nl747@nyu.eduyCorrespondingauthor:NewYorkUniversityTandonSchoo
4、lofEngineering.Depart-mentofFinanceandRiskEngineering.SixMetrotechCenter,Brooklyn,NY11201,USA;(646)997-3889.atourin@nyu.edu21IntroductionThisarticleextendsthepairstradingmodelproposedinTourinandYan(2013)toincorporatetime-varyingvolatility.IncontrasttoTourinandYan(2013),weareunabletoderiveafull
5、yexplicitsolutionfortheoptimalpairstradingstrategies,evenforafullyspecifiedlocalvolatilitymodel.However,byusingstochasticcontroltechniques,weshowthatthisproblemcanbereducedtoadegeneratetwo-dimensionallinearPartialDifferentialEquation(PDEinshort)andcanthereforeeasilybesolvednumericallybyusinganim
6、plicitFiniteDifferencescheme.WerefertothebookbyFlemingandSoner(1993)andPham(2009)foranintroductiontostochasticcontrolanditsapplicationsinFinance,andtoTouzi(2013)forapresentationofFiniteDifferenceschemesforfinancialapplications.ThevolatilitymodelwechooseisoftheConstantElasticityofVariancetype,intr
7、oducedinCox(1975),CoxandRoss(1976),whichcapturesthenegativelinkbetweenvolatilityandstockpriceobservedonfinancialdata,forarelativelymodestcomputationalcost.Althoughthesolutioncanbeeasilycomputedforboththepowerandtheexponentialutilityfunct
