In this paper we propose different schemes for option hedging when asset returns are modeled by dynamics from a general class of GARCH models.  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 risk neutral measure. 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 .
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 .
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In this paper we
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by dynamics from
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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.
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risk neutral measure. Local risk minimization is
pricing kernel. These approaches are
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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,
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
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P 500 European Call options is provided to assess the empirical performance of the proposed schemes. We also test
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several pricing measures is tested for a special class of non-Gaussian GARCH models for European style options with different moneyness and maturities
the risk neutral measure used by recomputing some of our results with an exponential affine pricing kernel