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) arrive at a hedging formula different from Duan's , although they concur on the pricing formula. In this note, we explain the difference by pointing out that the formula developped 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 propose a stochastic volatility model which ensures its validity. We conclude by a comparison of ARCH-type and stochastic volatility option pricing models.