A numerical comparative analysis between crank-Nicolson finite difference method and binomial model for European call option price

Abstract

There are several kinds of numerical techniques for solving option valuation problems. In this article Binomial model (BM) and Crank-Nicolson finite difference (CNFD) approach are applied and compared with the Black-Scholes analytic solution (BSAS) to determine the best numerical method. It has been noticed that, for the valuation of European call (EC) options at various factors, the Binomial model (BM) is found to be more accurate than the Crank-Nicolson finite difference (CNFD) technique. In addition, for the impact of high volatility, the technique of Crank-Nicolson finite difference (CNFD) approaches quicker to Black-Scholes analytic solution (BSAS) than the Binomial model (BM). Furthermore, in comparison to the Binomial model (BM), CNFD method consumes more time to determine the option price in each time step.