Solution of the Black-Scholes Equation by Finite Difference Schemes

Black-Scholes (BS) equation is a popular mathematical model for determining the value of option in financial derivatives. To predict the option value during the contract of the option is a big problem. Several studies have been shown that the option price value can be determined by applying different methods. In this paper, we have discussed three finite difference methods: Explicit, Implicit and Crank-Nicolson for solving Black-Scholes equation for European call option and compared the obtained results with the exact value. It is found that the Crank-Nicolson method is more accurate and cost effective in comparison with explicit and implicit methods.