Authors | Ebrahim Nasrabadi,mojtaba Ranjbar,Somayeh Pourghanbar |
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Journal | mathematical analysis and convex optimization |
Page number | 65-74 |
Serial number | 1 |
Volume number | 1 |
Paper Type | Full Paper |
Published At | 2021 |
Journal Grade | ISI |
Journal Type | Typographic |
Journal Country | Iran, Islamic Republic Of |
Journal Index | isc |
Abstract
One of the greatest accomplishments in modern financial theory, in terms of both approach and applicability has been the Black-Scholes option pricing model. It is widely recognized that the value of a European option can be obtained by solving the BlackScholes equation. In this paper we use functional perturbation method (FPM) for solving Black-Scholes equation to price a European call option. The FPM is a tool based on considering the differential operator as a functional. The equation is expanded functionally by Frechet series. Then a number of successive partial differential equations (PDEs) are obtained that have constant coefficients and differ only in their right hand side part. Therefore we do not need to resolve the different equations for each step. In contrast to methods that have implicit solutions, the FPM yields a closed form explicit solution.
tags: Black-Scholes equation; European call option; Functional perturbation method.