Open Access Open Access  Restricted Access Subscription or Fee Access

Solution of the Black-Scholes Partial Differential Equation for the Vanilla Options via the Reduced Differential Transform Method

S.E. Fadugba, J.T. Okunlola


This paper presents the Reduced Differential Transform Method (RDTM) for the solution of the Black-Scholes Partial Differential Equation (B-SPDE) for the vanilla option, namely the “European style”. The analytical solution of B-SPDE is calculated in the form of a convergent power series with easily computable components. The results showed that RDTM is very effective, reliable and can be applied to many other partial differential equations arising from the financial market. We assumed that the assets are driven by the geometric Brownian motion with non-dividend paying stock.


Black-Scholes equation, European call option, Geometric Brownian motion, Reduced differential transform method.

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.