The classical linear Black-Scholes model for option pricing assumes a complete market without transaction cost, illiquidity or feedback issues like large investor performance. Several nonlinear Black-Scholes models have been proposed in recent years by several authors with taking one or some of theses parameters into account to have more reliable and accurate option price [1–5]. One of the most comprehensive models introduced by Barles and Soner [2] considers transaction cost in the hedging strategy and risk from an illiquid market. Nonlinearity in the nonlinear Black-Scholes models always arises from a nonlinear volatility function depending not only on time t and underlying asset price S but also on the Greek Gamma, that is the second derivative of the option price V (S, t) with respect to S. The main idea of the present work is based upon the solution of Barles and Soner model. Since these nonlinear PDEs do not have analytical solutions, therefore some finite difference schemes have been investigated to solve numerically such nonlinear equation and also those schemes have been compared with respect to efficiency and high accuracy.
