Journal of Computational Finance

Risk.net

Hedging of options in the presence of jump clustering

Donatien Hainaut and Franck Moraux

  • We study quadratic hedges in presence of self-excited jumps in stock returns.
  • We propose new first and second order hedging ratios, including this jump risk.
  • Hedges with stocks instead of options do not mitigate the risk of jumps clustering.

This paper analyzes the efficiency of hedging strategies for stock options in the presence of jump clustering. 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 the 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 another option. The performance of these hedges is measured by simulations for put and call options, with a model fitted to the Standard & Poor’s 500.

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