An Analytical Solution for The Black-Scholes Equation Using Functional Perturbation Method

AuthorsEbrahim Nasrabadi,mojtaba Ranjbar,Somayeh Pourghanbar
Journalmathematical analysis and convex optimization
Page number65-74
Serial number1
Volume number1
Paper TypeFull Paper
Published At2021
Journal GradeISI
Journal TypeTypographic
Journal CountryIran, Islamic Republic Of
Journal Indexisc

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.

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tags: Black-Scholes equation; European call option; Functional perturbation method.