Alternative Approach for the Solution of the Black-Scholes Partial Differential Equation for European Call Option

Abstract

In this paper we present an alternative approach for the solution of the Black-Scholes partial differential equation for European call option which pays dividend yield using the modified Mellin transform method. The approach used in this paper does not require variables transformation. We also extend the modified Mellin transform method for the valuation of European call option which pays dividend yield. The numerical results show that the modified Mellin transform is accurate, mutually consistent and agrees with the values of the Black-Scholes model.

A New Technique for Solving Black-Scholes Equation for Vanilla Put Options

“…the solution of the Black-Scholes partial differential equation for European call option which pays dividend yield was considered by [4]. [5] introduced the Mellin transforms in the theory of option pricing.…”

“…Next shall show that (20) is a solution of the Black-Scholes equation for vanilla put options given by (7a). Following the procedures in [4], we assume that , where…”

“…Nowadays, the Black-Scholes equation derived by [2] is widely used in the field of mathematical finance. Despite the success of the Black-Scholes model on hedging and pricing contingent claims, [3] noted early that options quoted on the markets differ systematically from their predicted values, which led up to questioning the distributional assumptions based on geometric wiener process [4]. Alternative approach for…”