Parameter estimation approach to the free boundary for the pricing of an american call option

In this paper, we consider a free boundary problem which arises in the pricing of an American call option. The free boundary represents the optimal exercise price as a function of time before a maturity date. We are developing a parameter estimation technique to obtain both the optimal exercise curve of an American call option and its price. For the numerical solution of a forward problem, a time marching finite element method is adopted. Numerical experiment shows the convergence property of the approximation scheme.