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Khedher, Asma

Computation of the delta in multidimensional jump-diffusion setting with applications to stochastic volatility models. (English) Zbl 1242.91188

Stochastic Anal. Appl. 30, No. 3, 403-425 (2012).
Summary: 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.

Cited in 3 Documents

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60H07 Stochastic calculus of variations and the Malliavin calculus
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)

Keywords:

delta hedging; jump-diffusions; Malliavin calculus; robustness; stochastic volatility
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References:

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