Approximating the GJR-GARCH and EGARCH Option Pricing Models Analytically

In Duan, Gauthier and Simonato (1999), an analytical approximate formula for European options in the GARCH framework was developed. The formula is however restricted to the nonlinear asymmetric GARCH model. This paper extends the same approach to two other important GARCH specifications GJR-GARCH and EGARCH. We provide the corresponding formulas and study their numerical performance. keywords: Option pricing, EGARCH, GJR-GARCH, analytical approximation Duan is with Rotman School of Management, University of Toronto; Gauthier and Simonato are with HEC Montréal; Sasseville is a Ph.D. candidate at the Kellog Graduate Business School. 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). Duan also acknowledges support received as the Manulife Chair in Financial Services.