Mathematical Analysis of Black-Scholes Partial Differential Equation on Stock Prices

Amadi I. U.; Nwaigwe E.; Azor P. A.

Mathematical Analysis of Black-Scholes Partial Differential Equation on Stock Prices | AB Journals

Mathematical Analysis of Black-Scholes Partial Differential Equation on Stock Prices

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African Journal of Mathematics and Statistics Studies

Vol. 3Issue 42020pp. 1–11Published 24 July 2020

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Abstract:

This paper is centered on Black-Scholes (BS) partial differential equation (PDE) and Crank-Nicolson (CN) numerical solutions for the valuation of European call option. In particular, Crank-Nicolson’s method was successfully applied to the transformed boundary value problems of European call option with results obtained. It was observed that Black-Scholes and Crank-Nicolson are impossible to differentiate but in terms of precisions Black-Scholes analytical values were found to be adequate. Also, a statistical test was performed, using Kolmogorov-Smirnov (KS) for goodness of fit test; results showed that BS and CN came from a common distribution. However, this paper presented here has a vital role in this dynamic area of financial Mathematics.

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