Path-Dependent Options: Extending the Monte Carlo Simulation Approach

Abstract

Monte Carlo simulation has been used to value options since Boyle's seminal paper. Monte Carlo simulation, however, has not been used to its fullest extent for option valuation because of the belief that the method is not feasible for American-style options. This paper demonstrates how to incorporate optimal early exercise in the Monte Carlo method of valuing options by linking forward-moving simulation and the backward-moving recursion of dynamic programming through an iterative search process. To demonstrate the potential of this method, we use it to value American-style options on the average price (or Asian options). The computational experience reveals a flexible valuation technique with potential for application to a range of securities and financial decision problems.