APPROXIMATE SOLUTION OF FRACTIONAL BLACK-SCHOLE’S EUROPEAN OPTION PRICING EQUATION BY USING ETHPM

Abstract

We proposed a new reliable combination of new Homotopy Perturbation Method (HPM) and Elzaki transform called as Elzaki Transform Homotopy Perturbation Method (ETHPM) is designed to obtain a exact solution to the fractional Black-Scholes equation with boundary condition for a European option pricing problem. The fractional derivative is in Caputo sense and the nonlinear terms in Fractional Black-Scholes Equation can be handled by using HPM. The Black-Scholes formula is used as a model for valuing European or American call and put options on a non-dividend paying stock. The methods give an analytic solution of the fractional Black-Scholes equation in the form of a convergent series. Finally, some examples are included to demonstrate the validity and applicability of the proposed technique.