Pricing Bermudan Options via Multilevel Approximation Methods

Abstract

In this article we propose a novel approach to reducing 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 multilevel low biased estimate for the price of the option. It turns out that the resulting complexity gain can be of order $\varepsilon^{-1}$ with $\varepsilon$ denoting the desired precision. The performance of the proposed multilevel algorithms is illustrated by a numerical example.