A Fréchet derivative-based novel approach to option pricing models in illiquid markets

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dc.authorscopusid57210645950
dc.authorscopusid35273355700
dc.contributor.authorGülen, Seda
dc.contributor.authorSarı, M.
dc.date.accessioned2022-05-11T14:04:43Z
dc.date.available2022-05-11T14:04:43Z
dc.date.issued2022
dc.departmentFakülteler, Fen Edebiyat Fakültesi, Matematik Bölümü
dc.description.abstractNonlinear option pricing models have been increasingly concerning in financial industries since they build more accurate values by regarding more realistic assumptions such as transaction cost, market liquidity, or uncertain volatility. This study defines a nonclassical numerical method to effectively capture the behavior of the nonlinear option pricing model in illiquid markets where the implementation of a dynamic hedging strategy affects the price of the underlying asset. Unlike the conventional numerical approaches, this study describes a numerical scheme based on the Newton iteration technique and the Fréchet derivative for linearization of the model. The linearized time-dependent PDE is then discretized by a sixth-order finite difference scheme in space and a second-order trapezoidal rule in time. The computations revealed that the current approach appears to be somewhat more effective to some extent and at the same time economical for illustrative examples compared to the existing competitors. In addition, this method helps to prevent considering the convergence issues of the Newton approach applied to the nonlinear algebraic system. © 2021 John Wiley & Sons, Ltd.
dc.description.sponsorshipThere are no funders to report for this submission.
dc.identifier.doi10.1002/mma.7821
dc.identifier.endpage913
dc.identifier.issn0170-4214
dc.identifier.issue2en_US
dc.identifier.scopus2-s2.0-85117078690
dc.identifier.scopusqualityQ1
dc.identifier.startpage899
dc.identifier.urihttps://doi.org/10.1002/mma.7821
dc.identifier.urihttps://hdl.handle.net/20.500.11776/4735
dc.identifier.volume45
dc.identifier.wosWOS:000702732900001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthorGülen, Seda
dc.language.isoen
dc.publisherJohn Wiley and Sons Ltd
dc.relation.ispartofMathematical Methods in the Applied Sciences
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectFréchet derivative
dc.subjecthedge cost
dc.subjectilliquid markets
dc.subjectlinearization
dc.subjectNewton iteration
dc.subjectnonlinear Black–Scholes equation
dc.subjectAlgebra
dc.subjectCommerce
dc.subjectFinancial markets
dc.subjectFinite difference method
dc.subjectIterative methods
dc.subjectLinearization
dc.subjectNonlinear equations
dc.subjectNumerical methods
dc.subjectBlack-Scholes Equations
dc.subjectFinancial industry
dc.subjectFrechet derivative
dc.subjectHedge cost
dc.subjectIlliquid market
dc.subjectLinearisation
dc.subjectNewton's iteration
dc.subjectNonlinear black–schole equation
dc.subjectOption pricing models
dc.subjectTransaction cost
dc.subjectCosts
dc.titleA Fréchet derivative-based novel approach to option pricing models in illiquid markets
dc.typeArticle

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