Value Function Approximation or Stopping Time Approximation: A Comparison of Two Recent Numerical Methods for American Option Pricing using Simulation and Regression

Abstract

In Longstaff and Schwartz (2001) a method for American option pricing using simulation and regression is suggested, and since then the method has rapidly gained importance. However, the idea of using regression and simulation for American option pricing was used at least as early as in Carriere (1996). In the present paper we provide a thorough comparison of these two methods and relate them to the work of Tsitsiklis and Van Roy (2001). Although the methods are often considered to be similar this analysis allows us to point out an important but often overlooked difference between the methods. The paper further shows that due to this difference it is possible to provide arguments favoring the method suggested in Longstaff and Schwartz (2001). Finally, the paper compares the methods in a realistic numerical setting and shows that the practitioner does well in choosing the method of Longstaff and Schwartz (2001) instead of the methods of Carriere (1996) or Tsitsiklis and Van Roy (2001) for American option pricing.