A moving boundary approach to American option pricing

Our approach, which we term the Moving Boundary Approach, is based on using a boundary guess and the value associated with the guess to construct an improved boundary. It is also shown that on iteration, the sequence of boundaries converge monotonically to the optimal exercise boundary. Examples illustrating the convergence behavior as well as discussions providing insight into the method are also presented. Finally, we compare runtimes and speeds with other methods that solve the free-boundary problem and compute the optimal boundaries explicitly, like the front-fixing method, penalty method, method based on the integral representations and the method by Brennan and Schwartz [1977. The valuation of American put options. Journal of Finance 32 (2), 449-462].