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

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