Monte Carlo valuation of American options

Author: Rogers, L. C. G.

Source: Mathematical Finance, Volume 12, Number 3, July 2002 , pp. 271-286(16)

Buy & download fulltext article:

Price: $48.00 plus tax (Refund Policy)

Abstract:

This paper introduces a dual way to price American options, based on simulating the paths of the option payoff, and of a judiciously chosen Lagrangian martingale. Taking the pathwise maximum of the payoff less the martingale provides an upper bound for the price of the option, and this bound is sharp for the optimal choice of Lagrangian martingale. As a first exploration of this method, four examples are investigated numerically; the accuracy achieved with even very simple choices of Lagrangian martingale is surprising. The method also leads naturally to candidate hedging policies for the option, and estimates of the risk involved in using them.

Keywords: Monte Carlo; American option; duality; Lagrangian; martingale; Snell envelope

Document Type: Research article

DOI: http://dx.doi.org/10.1111/1467-9965.02010

Publication date: 2002-07-01