A finite dimensional approximation for pricing moving average options

TL;DR

This paper introduces a finite dimensional approximation method for pricing American options with payoffs based on moving averages, using Laguerre series expansion and Monte Carlo techniques.

Contribution

It presents a novel finite-dimensional approximation approach for moving average options and analyzes its convergence, with numerical validation in the Black-Scholes model.

Findings

The method converges at a quantifiable rate.

Numerical results demonstrate accuracy in Black-Scholes framework.

Efficiently reduces infinite-dimensional problem to finite dimensions.

Abstract

We propose a method for pricing American options whose pay-off 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 to solve 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.