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1、JournalofEconomicDynamics&Control28(2004)727–754www.elsevier.com/locate/econbaseOptionvaluationwithco-integratedassetpricesJin-ChuanDuana;∗,StanleyR.PliskabaJosephL.Rotman,SchoolofManagement,UniversityofToronto,105St.GeorgeStreet,Toronto,ONM5S3E6,CanadabDepartmentofFinance,UniversityofIlli
2、noisatChicago,USAAccepted4February2003AbstractThispaperinvestigatestheoreticalandpracticalaspectsofoptionsthatarebasedupontwoormoreassetswhichareco-integrated.Forthispurpose,anew,discrete-timemodelofassetpricesisdeveloped,amodelfeaturingboththeco-integrationpropertyaswellasstochasticvolati
3、lities.UsingaGARCH,equilibrium-basedoptionpricingapproach,itisshownthatwhenvolatilitiesaredeterministictheoptionpricesdonotdependontheco-integrationparameters,exceptforthemis-speci6catione7ectastothemannerinwhichthevolatilitiesareestimated.However,withstochasticvolatilitiestheoptionpricese
4、xplicitlydependupontheco-integrationparameters.Inordertounderstandtheseresultsbetter,thispaperalsoexaminesacontinuous-time,di7usionlimitoftheassetpricesystemandempiricallystudiestheco-integratione7ectusingspreadoptionsbasedupontheS&P500andtheNASDAQ100.Thesenumericalresultssuggestthatconsid
5、erationofco-integrationcansubstantiallyalterthevalue,deltaandvegaofaspreadoption.?2003ElsevierB.V.Allrightsreserved.JELclassi*cation:G13;C3Keywords:Co-integration;Optionvaluation;GARCH;Di7usionlimit;Spreadoptions1.IntroductionManyoptions,suchasspread,maximum,minimum,andbasketoptions,arede6
6、nedintermsoftwoormoreunderlyingpriceprocesses.Typically(e.g.,seeStulz,1982;Pearson,1995)theunderlyingpricesystemismodeledasamultivariategeometricBrownianmotionwhosevolatilitymatrixisconstant,inwhichcasetheoptionval-uationproblemisstraightforward.However,suchamodelisunrealisticforcertaincir
7、cumstances.Forexample,Mbanefo(1997)pointedoutthatthecorrelationbetween∗Correspondingauthor.Tel.:+1-416-946-5653;fax:+1-416-971-3048.E-mailaddress:jcduan@rotman.utoronto.ca(J.-C.Duan).0165-1889/03/$-seefrontmatter?2003ElsevierB.V.Allrightsreserved.doi:10.1016/S
