Laplace Decomposition Method for Solving Fractional Black-Scholes European Option Pricing Equation

Abstract

Fractional calculus is related to derivatives and integrals with the order is not an integer. Fractional Black-Scholes partial differential equation to determine the price of European-type call options is an application of fractional calculus in the economic and financial fields. Laplace decomposition method is one of the reliable and effective numerical methods for solving fractional differential equations. Thus, this paper aims to apply the Laplace decomposition method for solving the fractional Black-Scholes equation, where the fractional derivative used is the Caputo sense. Two numerical illustrations are presented in this paper. The results show that the Laplace decomposition method is an efficient, easy and very useful method for finding solutions of fractional Black-Scholes partial differential equations and boundary conditions for European option pricing problems.