Valuation of the American put option as a free boundary problem through a high-order difference scheme

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dc.authorscopusid35273355700
dc.authorscopusid57210645950
dc.contributor.authorSarı, Murat
dc.contributor.authorGülen, Seda
dc.date.accessioned2022-05-11T14:04:43Z
dc.date.available2022-05-11T14:04:43Z
dc.date.issued2021
dc.departmentFakülteler, Fen Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractValuation of the American options encountered commonly in finance is quite difficult due to the possibility of early exercise alternatives. Since an exact solution for the American options does not exist, effective numerical methods are needed to understand the behavior of option pricing models. Therefore, in this paper, a new approach based on a high-order difference scheme is proposed to discuss the valuation of an American put option as a free boundary problem. Using a front-fixing approach that transforms the unknown free boundary (optimal stopping) into a fixed one, a sixth-order finite difference scheme (FD6) in space and a third-order strong-stability preserving Runge-Kutta (SSPRK3) in time are applied to the model converted to a nonlinear partial differential equation. The computed results revealed that the combined method is seen to attempt to pull up the capacity of the algorithm to achieve higher accuracy. It is seen that the quantitative and qualitative results produced by the method proposed with minimal computational effort are sufficiently accurate and meaningful. Therefore, this article provides some new insights about the physical characteristics of financial problems and such realistic phenomena. © 2021 Walter de Gruyter GmbH, Berlin/Boston.
dc.identifier.doi10.1515/ijnsns-2020-0252
dc.identifier.issn1565-1339
dc.identifier.scopus2-s2.0-85120652252
dc.identifier.scopusqualityQ2
dc.identifier.urihttps://doi.org/10.1515/ijnsns-2020-0252
dc.identifier.urihttps://hdl.handle.net/20.500.11776/4733
dc.identifier.wosWOS:000738254800001
dc.identifier.wosqualityQ2
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorGülen, Seda
dc.language.isoen
dc.publisherDe Gruyter Open Ltd
dc.relation.ispartofInternational Journal of Nonlinear Sciences and Numerical Simulation
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectAmerican put option
dc.subjectfree boundary
dc.subjectfront-fixing method
dc.subjecthigh-order difference
dc.titleValuation of the American put option as a free boundary problem through a high-order difference scheme
dc.typeArticle

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