Levy Option Pricing Models Theory And Application(Matsuda)

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1、LévyOptionPricingModels:TheoryandApplicationbyKazuhisaMatsudaAdissertationsubmittedtotheGraduateFacultyinEconomicsInpartialfulfillmentoftherequirementsforthedegreeofDoctorofPhilosophy,TheCityUniversityofNewYork2006UMINumber:3213170UMIMicroform3213170Copyright2006byProQu

2、estInformationandLearningCompany.Allrightsreserved.ThismicroformeditionisprotectedagainstunauthorizedcopyingunderTitle17,UnitedStatesCode.ProQuestInformationandLearningCompany300NorthZeebRoadP.O.Box1346AnnArbor,MI48106-1346iiThismanuscripthasbeenreadandacceptedfortheGra

3、duateFacultyinEconomicsinsatisfactionofthedissertationrequirementsforthedegreeofDoctorofPhilosophy.April42006SalihN.NeftciDateChairofExaminingCommitteeApril42006ThomB.ThurstonDateExecutiveOfficerProfessorSalihN.NeftciProfessorThomB.ThurstonDistinguishedProfessorMichaelG

4、rossmanSupervisoryCommitteeTHECITYUNIVERSITYOFNEWYORKiiiAbstractLévyOptionPricingModels:TheoryandApplicationbyKazuhisaMatsudaAdviser:ProfessorSalihN.NeftciThegoalofthisdissertationistoprovideboththeunderlyingtheoryandapplicationsofLévyoptionpricingmodelswhichhavebeendev

5、elopedrecently.Thedissertationiscomposedoffivemainparts.PartIcoversthemathematicaltheoryofLévyprocesseswhichconstituteawideclassofstochasticprocesseswhosesamplepathscanbecontinuous,mostlycontinuouswithoccasionaldiscontinuities,andpurelydiscontinuous.EachLévyprocessisdef

6、inedandcharacterizedusingtheoremssuchastheLévy-ItôdecompositionandtheLévy-Khinchinrepresentation.TheyalsoarecharacterizedintermsoftheirinfinitedivisibilitiesandtheLévymeasures.Part2providestheintroductiontoFouriertransformanditsapplicationtotheoptionpricing.Fouriertrans

7、formoptionpricingmethodhasbecomethemainstreampricingmethodbecauseofitsgeneralityinthesensethatitonlyrequiresthecharacteristicfunctionofthelogterminalassetprice.Part3describesthemathematicsoftheLévyoptionpricingmodels.TheclassicBlack-Scholes(BS)modelischaracterizedastheo

8、nlycontinuousLévymodel.TheivclassicMertonjump-diffusion(MJD)modelischaracterizedasthenon-GaussianLévymodelinwh