Pricing American options by canonical least‐squares Monte Carlo

Abstract

AbstractOptions pricing and hedging under canonical valuation have recently been demonstrated to be quite effective, but unfortunately are only applicable to European options. This study proposes an approach called canonical least‐squares Monte Carlo (CLM) to price American options. CLM proceeds in three stages. First, given a set of historical gross returns (or price ratios) of the underlying asset for a chosen time interval, a discrete risk‐neutral distribution is obtained via the canonical approach. Second, from this canonical distribution independent random samples of gross returns are taken to simulate future price paths for the underlying. Third, to those paths the least‐squares Monte Carlo algorithm is then applied to obtain early exercise strategies for American options. Numerical results from simulation‐generated gross returns under geometric Brownian motions show that the proposed method yields reasonably accurate prices for American puts. The CLM method turns out to be quite similar to the nonparametric approach of Alcock and Carmichael and simulations done with CLM provide additional support for their recent findings. CLM can therefore be viewed as an alternative for pricing American options, and perhaps could even be utilized in cases when the nature of the underlying process is not known. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:175–187, 2010