Lewis Model Revisited: Option Pricing with Levy Processes

dc.authoridBeyazit, Mehmet Fuat/0000-0003-3031-7132
dc.contributor.authorBeyazit, Mehmet Fuat
dc.contributor.authorEroglu, Kemal Ilgar
dc.date.accessioned2024-07-18T20:42:28Z
dc.date.available2024-07-18T20:42:28Z
dc.date.issued2021
dc.departmentİstanbul Bilgi Üniversitesien_US
dc.description.abstractThis paper aims to discuss the mathematical details in Lewis' model by considering the analyticity and integrability conditions of characteristic functions and payoff functions of contingent claims. In his seminal paper, Lewis shows that it is much easier to compute the option value in the Fourier space than computing in terminal security price space. He computes the option value as an integral in the Fourier space, the integrand being some elementary functions and the characteristic functions of a wide range of Levy processes. The model also illustrates how the residue calculus leads to several variations of option formulas through the contour integrals. In this paper, we provide with, to a reasonable extent, some rigor into the mathematical background of Lewis' model and validate his results for particular Levy processes. We also simply give the analyticity conditions for the characteristic function of the Carr-Geman-Madan-Yor model and a simple derivation of the characteristic function of Kou's double exponential model.en_US
dc.identifier.doi10.1007/s40840-020-01025-3
dc.identifier.endpage1668en_US
dc.identifier.issn0126-6705
dc.identifier.issn2180-4206
dc.identifier.issue3en_US
dc.identifier.scopus2-s2.0-85091510487en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage1653en_US
dc.identifier.urihttps://doi.org/10.1007/s40840-020-01025-3
dc.identifier.urihttps://hdl.handle.net/11411/7275
dc.identifier.volume44en_US
dc.identifier.wosWOS:000572939600001en_US
dc.identifier.wosqualityQ1en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherMalaysian Mathematical Sciences Socen_US
dc.relation.ispartofBulletin of The Malaysian Mathematical Sciences Societyen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectLevy Processesen_US
dc.subjectOption Pricingen_US
dc.subjectCharacteristic Functionen_US
dc.subjectFourier Transformen_US
dc.subjectStochastic Volatilityen_US
dc.subjectTransformen_US
dc.subjectReturnsen_US
dc.subjectPricesen_US
dc.titleLewis Model Revisited: Option Pricing with Levy Processesen_US
dc.typeArticleen_US

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