Seize the Moments: Approximating American Option Prices in the GARCH Framework

This paper proposes an efficient approach to compute 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. Since the resulting tree is univariate, the proposed approach represents a convenient approximation of the bivariate GARCH system. Numerical analyses are used to demonstrate the speed and accuracy of the proposed approximation. ∗Duan is at Rotman School of Management, University of Toronto; Gauthier and Simonato are at HEC (Montréal); Sasseville is a Ph.D. candidate at Northwestern University. Duan, Gauthier and Simonato acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), Les Fonds pour la Formation de Chercheurs et l’Aide à la Recherche du Québec (FCAR) and from the Social Sciences and Humanities Research Council of Canada (SSHRC).