In order to access efficient methods in evaluating financial derivative (option) in this thesis. Using Black-Scholes differential Eq. discretization in the finite differential method, the value of American option is calculated. In order to obtain more precise methods, we need to so consider the problem solution conditions that more accommodation is gained with real markets. For this reason, Black-Scholes differential Eq. is discussed discretized in the presence of stochastic volatility. As a result, a linear complementarity problem is generated by solving of which in different methods, the value of option is calculated. At the end, gain precision and seed of these methods are compared.