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.
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Duan et al. (2006) studied this question.
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