Approximating free exercise boundaries for American-style options using simulation and optimization

Monte Carlo simulation can be readily applied to asset pricing problems with multiple state variables and possible path dependencies because convergence of Monte Carlo methods is independent of the number of state variables. This paper applies Monte Carlo simulation to the problem of determining free exercise boundaries for pricing American-style options. We use a simulation-optimization method to identify approximately optimal exercise thresholds that are defined by a minimal number of parameters. We demonstrate that asset prices calculated using this method are comparable to those found using other numerical asset pricing methods.