Open Access Open Access  Restricted Access Subscription or Fee Access

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


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.


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

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.