On the computation of hedging strategies in affine GARCH models

This paper discusses risk-minimizing hedging strategies under affine GARCH models driven by Gaussian innovations. First, we derive a closed-form expression for an optimal hedge ratio under this model that is applicable to European derivatives with payoff functions that admit an inverse Laplace transform representation, such as calls and puts. Second, by way of a first-order Taylor expansion, we relate our hedging strategy to delta hedging and specify an approximation of our formula in terms of the option's delta and vega. Third, we obtain an expression for our hedge ratio under the weak limit of the underlying GARCH model, and link it to minimum variance delta hedges in the continuous-time stochastic volatility literature. Several numerical experiments are conducted to compare our analytic formulas to Monte Carlo estimators, to investigate the accuracy of the first-order approximation, and to test the numerical convergence of the GARCH-based hedge ratio to its continuous-time counterpart. Finally, using S&P 500 European call option data, we perform an empirical analysis to test the performance of our hedging schemes relative to benchmark delta hedges used in the literature