A finite dimensional approximation for pricing moving average options

Marie Bernhart (1, 2) , Peter Tankov (3) , Xavier Warin (2, 4)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 EDF - EDF
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 FiME Lab - Laboratoire de Finance des Marchés d'Energie

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.

Keywords: American options; indexed swing options; moving average; finite-dimensional approximation; Laguerre polynomial; least squares Monte Carlo

Domains: Computational Finance [q-fin.CP]

Marie Bernhart, Peter Tankov, Xavier Warin. A finite dimensional approximation for pricing moving average options. 2010. ⟨hal-00554216⟩