On the Stability and Accuracy of Finite Difference Method for Options Pricing

Abstract

This paper presents finite difference methods for options pricing. These methods are useful to solve partial differential equations and provide a general numerical solution to the valuation problems, as well as an optimal early exercise strategy and other physical sciences. The methods considered are the basic implicit and Crank Nicolson finite difference methods. The stability and accuracy of each of the methods were considered. Crank Nicolson method is more accurate and converges faster than implicit method.

Key words: Convergence, Crank Nicolson Method, European Option, Finite Difference Method, Implicit Method, Option, Stability.