A finite-dimensional approximation for pricing moving average options

We propose a method for pricing American options whose payoff depends on the moving average of the underlying asset price. The method uses a finite-dimensional approximation of the infinitedimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a finite-dimensional optimal stopping problem, which we propose solving with a least squares Monte Carlo approach. We analyze the theoretical convergence rate of our method and present numerical results in the Black-Scholes framework.