An forward difference method and a comparative study of the numerical methods for american put option pricing

Option pricing theory is one of the topics in financial mathematics and financial engineering discipline, which is under forefront and heated discussion. Compared with European option, American option has a privilege that can be executed in advance, which has led to significant difficulty of pricing issues. In this paper, we use three kinds of numerical method to obtain American put option price, including using the binomial tree model, Monte Carlo simulation and the finite difference method. Moreover, the convergence rate and accuracy of the three methods are compared. As a result, we obtain that the finite difference method has the fastest convergence rate under guaranteed accuracy.