Adaptive Control Variates for Pricing Multi-Dimensional American Options

We explore a class of control variates for the American option pricing problem. We construct the control variates by using multivariate adaptive linear regression splines to approximate the option’s value function at each time step; the resulting approximate value functions are then combined to construct a martingale that approximates a “perfect” control variate. We demonstrate that significant variance reduction is possible even in a high-dimensional setting. Moreover, the technique is applicable to a wide range of both option payoff structures and assumptions about the underlying risk-neutral market dynamics. The only restriction is that one must be able to compute certain one-step conditional expectations of the individual underlying random variables.