Risk Minimization in Stochastic Volatility Models: Model Risk and Empirical Performance

In this paper the performance of locally risk-minimizing hedge strategies for European options in stochastic volatility models is studied from an experimental as well as from an empirical perspective. These hedge strategies are derived for a large class of diffusion-type stochastic volatility models, and they are as easy to implement as usual delta hedges. Our simulation results on model risk show that the locally risk-minimizing hedges are robust with respect to uncertainty and even misconceptions about the underlying data generating process. The empirical study indicates that locally risk-minimizing hedge strategies consistently produce lower standard deviations of profit-and-loss-ratios than delta hedges (over different time periods as well as in different markets). The more skewed the market and the more out-of-the-money the option, the higher the benefit.