  We propose different schemes for option hedging when asset returns are
modeled using a general class of GARCH models. More specifically, we implement
local risk minimization and a minimum variance hedge approximation based on an
extended Girsanov principle that generalizes Duan's (1995) delta hedge. Since
the minimal martingale measure fails to produce a probability measure in this
setting, we construct local risk minimization hedging strategies with respect
to a pricing kernel. These approaches are investigated in the context of
non-Gaussian driven models. Furthermore, we analyze these methods for
non-Gaussian GARCH diffusion limit processes and link them to the corresponding
discrete time counterparts. A detailed numerical analysis based on S&P 500
European Call options is provided to assess the empirical performance of the
proposed schemes. We also test the sensitivity of the hedging strategies with
respect to the risk neutral measure used by recomputing some of our results
with an exponential affine pricing kernel.
