Abstract: We proposed a finite difference method based on Landau’s transformation for the standard American put option pricing problem. Firstly, the Landau’s transformation and truncation technique was used to transform the American option problem into a parabolic problem on a regular bounded domain, and then we used the finite difference method to solve the option price and used the Newton iteration method to solve the optimal exercise boundary at the same
time. The numerical results show that the algorithm can effectively solve the optimal exercise boundary more smoothly than traditional binomial tree method, and can accurately simulate the American put option price.

Key words:  American put option, Landau’s transformation, finite difference method