Application of Homotopy Analysis Shehu Transform Method for Fractional Black-Scholes Equation

The Black - Scholes Model is commonly used for option pricing, which is one of the most important applications in finance. In the absence of a transaction cost, the value of the option is determined by using B-S model. In the view of Caputo sense, this study proposes a result for the fractional Black-Scholes equation (FBSE) problem. The main goal of this paper is to show how to solve the FBSE by a semi-analytical method called the homotopy analysis shehu transform method (HASTM) and compare that homotopy analysis method (HAM), homotopy perturbation method (HPM), elzaki transform homotopy perturbation method (ETHPM). The HASTM result is quite similar to the HAM, HPM, ETHPM solution. The HASTM and other methods analytical solutions are also represented.