Computation of the Delta in Multidimensional Jump-Diffusion Setting with Applications to Stochastic Volatility Models

Abstract

We study the robustness of options prices to model variation in a multidimensional jump-diffusion framework. In particular, we consider price dynamics in which small variations are modeled either by a Poisson random measure with infinite activity or by a Brownian motion. We consider both European and Exotic options and we study their deltas using two approaches: the Malliavin method and the Fourier method. We prove robustness of the deltas to model variation. We apply these results to the study of stochastic volatility models for the underlying and the corresponding options.

Keywords:

• Delta hedging
• Jump-diffusions
• Malliavin calculus
• Robustness
• Stochastic volatility

2000 Mathematics Subject Classification:

• 60H07
• 60H35
• 91G20

Acknowledgments

I am thankful to Fred Espen Benth and Giulia Di Nunno for their helpful comments and remarks.

Notes

Right-continuous with left limits, also called càdlàg.