Approximate Dynamic Programming (ADP) and Dual Methods for Pricing American Options

It is only recently that simulation has begun to play an important role in pricing high-dimensional American options. This was due to the fact that since Monte Carlo simulation generally works forward in time while dynamic programming works backwards, it was generally believed that the two were somewhat incompatible. Research in recent years has shown that this is not the case and that Monte Carlo simulation is an important too for pricing American options. In these notes we describe some of the latest methods for pricing American options, including the ADP based methods for computing lower bounds on the true option price, and the dual based methods for computing upper bounds. First, however, we describe the properties of the financial market and define the American option pricing problem.