# Approximating the GJR-GARCH and EGARCH option pricing models analytically

## Jin-Chuan Duan, Geneviève Gauthier, Jean-Guy Simonato, Caroline Sasseville

#### Abstract

ABSTRACT

In Duan, Gauthier and Simonato (1999), an analytical approximation to price European options in the generalized autoregressive conditional heteroskedastic (GARCH) framework was developed. The formula is, however, restricted to the non-linear asymmetric GARCH model. This paper extends the approximation to two other popular GARCH specifications, GJR-GARCH and EGARCH. We provide the corresponding formulas and study their numerical performance.