A New Algorithm for Monte Carlo for American Options

2000 Mathematics Subject Classification: 91B28, 65C05.

We consider the valuation of American options using Monte Carlo simulation, and propose a new technique which involves approximating the optimal exercise boundary. Our method involves splitting the boundary into a linear term and a Fourier series and using stochastic optimization in the form of a relaxation method to calculate the coefficients in the series. The cost function used is the expected value of the option using the the current estimate of the location of the boundary. We present some sample results and compare our results to other methods.