American Options from MARS

We develop a class of control variates for the American option pricing problem that are constructed through the use of MARS - multivariate adaptive regression splines. The splines approximate the option´s value function at each time step, and the value function approximations are then used to construct a martingale that serves as the control variate. Significant variance reduction is possible even in high dimensions. The primary restriction is that we must be able to compute certain one-step conditional expectations