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 infinite-dimensional 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.