Comparative Study Analytic and Numerical Methods for Solving Non-Linear Black-Scholes Equation with European Call Option

In this work, we apply He’s variotional iteration method for obtaining analytic solutions to nonlinear Black-Scholes equation with boundary conditions for European option pricing problem. The analytical solution of the equation is calculated in the form a convergent power series with easily computable components. The powerful VIM method is capable of handling both linear and non-linear equations in direct manner. And, three approximate numerical methods of the non linear Black-Scholes equation with European call option are defined using finite differences, finite difference equations with alternative derivation, and Euler method of finite difference equations with alternative derivation. The results obtained expilicit finite difference method and finite difference method with alternative derivation and Euler method of finite difference method with alternative derivation and the results gave a good agreement with the previous methods [4, 5, 6, 10].