Valuing American Options by Simulation: A Simple Least-Squares Approach

Abstract

This article presents a simple yet powerful new approach for approximating the value of America11 options by simulation. The kcy to this approach is the use of least squares to estimate the conditional expected payoff to the optionholder from continuation. This makes this approach readily applicable in path-dependent and multifactor situations where traditional finite difference techniques cannot be used. We illustrate this technique with several realistic exatnples including valuing an option when the underlying asset follows a jump-diffusion process and valuing an America11 swaption in a 20-factor string model of the term structure. One of the most important problems in option pricing theory is the valuation and optimal exercise of derivatives with American-style exercise features. These types of derivatives are found in all major financial markets including the equity, commodity, foreign exchange, insurance, energy, sovereign,