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Comparative Study of the Reduced Differential Transform and Sumudu Transform for Solving Fractional Black-Scholes Equation for a European Call Option Problem

Sunday Emmanuel Fadugba

Abstract



This paper presents the comparative study of the reduced differential transform and the Sumudu transform for solving fractional Black-Scholes equation with boundary condition for a European call option problem on a non-dividend paying stock. It is assumed that assets are driven by the geometric Brownian motion. The fractional derivative is described in Caputo sense. The reduced differential transform provides the solutions in the form
of a convergent power series with easily computable components without any restrictive assumptions and is free from round-off errors whereas the Sumudu transform finds the solutions by means of the homotopy perturbation method. Two illustrative examples and their applications to financial markets were presented. The results show that the two approaches are in agreement with the exact solution. Hence it is concluded that the reduced
differential transform is easy to implement, reduces the numerical computations to a great extent and is a good alternative approach for the solution of the fractional Black-Scholes equation for a European call option arising in financial market.

Keywords


European call option, Financial market, Fractional differential equation, Reduced differential transform, Sumudu transform.

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