Hedging of options in presence of jump clustering

This paper analyzes the efficiency of hedging strategies for stock options, in presence of jump clus- tering. In the proposed model, the asset is ruled by a jump diffusion process wherein the arrival of jumps is correlated to the amplitude of past shocks. This feature adds feedback effects and time heterogeneity to the initial jump diffusion. After a presentation of main properties of the process, a numerical method for options pricing is proposed. Next, we develop four hedging policies minimizing the variance of the final wealth. These strategies are based on first and second order approximations of option prices. The hedging instrument is either the underlying asset or either another option. The performance of these hedges is measured by simulations for put and call options, with a model fitted to the S&P 500.