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

S.E. Fadugba, J.T. Okunlola

Abstract


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.

Keywords


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

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