Longstaff Schwartz

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

Francis A. Longstaff UCLA Eduardo S. Schwartz UCLA

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, agency, municipal, mortgage, credit, real estate, convertible, swap, and emerging markets. Despite recent advances, however, the valuation and optimal exercise of American options remains one of the most challenging problems in derivatives finance, particularly when more than one factor affects the value of the option. This is primarily because finite difference and binomial techniques become impractical in situations where there are multiple factors.'

We are grateful for the cotnl~lelitsof Yaser Abu-Mostafa, Giovanlii Barone-Adesi, Marco Avellaneda, Peter Bossaerts, Peter Carr, Peter DeCrem, Craig F~thian, Bjorn Flesaker, James Cammill, Gordon Gemmill, Robert Geske, Eric Ghysels, Ravit Efraty Mandell. Soetojo Tanudjaja. John Thornley, Bruce Tuckman. Pedro SantaClara, Pratap Sondhi. Ross Valkanov, and seminar participants at Bear Stearns, the University of British Columbia, the California Institute of...