A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models

Recently, Duan (1995) proposed a GARCH option pricing formula and a corresponding hedging formula. In a similar ARCH-type model for the underlying asset, Kallsen and Taqqu (1994) arrived at a hedging formula different from Duan's although they concur on the pricing formula. In this note, we explain this difference by pointing out that the formula developed by Kallsen and Taqqu corresponds to the usual concept of hedging in the context of ARCH-type models. We argue, however, that Duan's formula has some appeal and we propose a stochastic volatility model that ensures its validity. We conclude by a comparison of ARCH-type and stochastic volatility option pricing models.