Approximate Solution for Fractional Black-Scholes European Option Pricing Equation

The Black-Scholes equation is one of the most significant mathematical models for a financial market. In this paper, the homotopy perturbation method is combined with Mohand transform to obtain the approximate solution of the fractional Black-Scholes European option pricing equation. The fractional derivative is considered in the Caputo sense. The process of the methods which produce solutions in terms of convergent series is explained. Some examples are given to show a powerful and efficient method to find approximate analytical solutions for fractional Black-Scholes European option pricing equation. Further, the same equation is solved by the homotopy perturbation Sumudu transform method. The results obtained by the two methods are in agreement.