American Option Pricing Using Simulation and Regression: Numerical Convergence Results

Abstract

Recently, simulation methods combined with regression techniques have gained importance when it comes to American option pricing. In this paper we consider such methods and we examine numerically their convergence properties. We first consider the Least Squares Monte-Carlo (LSM) method of Longstaff and Schwartz (2001) and report convergence rates for the cross-sectional regressions as well as for the estimated price. The results show that the method converges fast, and this holds even with multiple early exercises and with multiple stochastic factors as long as the payoff function is smooth. We also compare the convergence rates to those obtained when using the related methods proposed by Carriere (1996) and Tsitsiklis and Van Roy (2001). The results show that the price estimates from the latter methods converge significantly slower in the multi-period situation.

Keywords: American options, convergence, Monte Carlo simulation, regression

JEL Classification: C15, G12, G13