Approximating American option prices in the GARCH framework

Abstract

This article proposes an efficient approach for computing the prices of American style options in the GARCH framework. Rubinstein's (1998) Edgeworth tree idea is combined with the analytical formulas for moments of the cumulative return under GARCH developed in Duan et al. (1999, 2002) to yield a simple recombining binomial tree for option valuation in the GARCH context. Because the resulting tree is univariate, the proposed approach represents a convenient approximation of the bivariate GARCH system. Numerical analysis is used to demonstrate the speed and accuracy of the proposed approximation. © 2003 Wiley Periodicals, Inc.