Numerous empirical proofs indicate the adequacy of the time discrete
auto-regressive stochastic volatility models introduced by Taylor in the
description of the log-returns of financial assets. The pricing and hedging of
contingent products that use these models for their underlying assets is a
non-trivial exercise due to the incomplete nature of the corresponding market.
In this paper we apply two volatility estimation techniques available in the
literature for these models, namely Kalman filtering and the
hierarchical-likelihood approach, in order to implement various pricing and
dynamical hedging strategies. Our study shows that the local risk minimization
scheme developed by F\"ollmer, Schweizer, and Sondermann is particularly
appropriate in this setup, especially for at and in the money options or for
low hedging frequencies.