Pricing a Path-dependent American Option by Monte Carlo Simulation

In this paper, we evaluate anytime Bermudan options, a class of path-dependent American options, by Monte Carlo simulation. Assuming that the state variable is Markovian, we show that the price of the path-dependent American option satisfies a dynamic programming equation. The continuation value in the dynamic programming is represented by a conditional expectation. It is shown that the conditional expectation can be converted to an uncoditional expectation, using the Malliavin Calculus, which in turn enables us to evaluate the price by Monte Carlo simulation. Some numerical examples are given to demonstrate the usefulness of our method