Pricing American options via multi-level approximation methods

Abstract

In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American or Bermudan options. Given a sequence of continuation values estimates corresponding to different levels of spatial approximation, we propose a multi-level low biased estimate for the price of the option. It turns out that the resulting complexity gain can be of order epsilon -1 with epsilon denoting the desired precision. The performance of the proposed multilevel algorithms is illustrated by a numerical example.