Before revision:  Local risk minimization is investigated in the context of Gaussian driven models, and two other minimum variance hedges are proposed in order to extend Duan's delta hedge. These two methods are constructed using local risk minimizing hedges for bivariate diffusion limits of GARCH models. Numerical experiments are carried out in order to compare the different hedging schemes; in particular,  the sensitivity of the hedging strategies with respect to several pricing measures is tested for a special class of non-Gaussian GARCH models for European style options with different moneyness and maturities .
After revision:  Local risk minimization is 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 the sensitivity of the hedging strategies with respect to several pricing measures is tested for a special class of non-Gaussian GARCH models for European style options with different moneyness and maturities .