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Hedging of options for jump-diffusion stochastic volatility models by Malliavin calculus

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Abstract

We study the locally risk minimizing approach in a market driven by jump-diffusion stochastic volatility models. We show that the Malliavin calculus, especially a jump-diffusion version of the Clark–Ocone formula, can generate the locally risk minimizing portfolio under weaker restrictions. This means thereafter we do not have to verify the strong condition \(\mathcal {V}(t,s,y)\in C^{1,2,2}\) and the differentiability condition \(\mathcal {V}\) in s and y with bounded derivatives is sufficient. Also, this tool shortens calculations of the hedge.

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Acknowledgements

The authors acknowledge the financial support of Iran National Science Foundation (INSF) Under the proposal number 96000627. We are also grateful for comments and questions from a referee and an associate editor which led to a number of improvements.

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  1. Iran University of Science and Technology, Tehran, Iran

    Minoo Bakhshmohammadlou & Rahman Farnoosh

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  1. Minoo Bakhshmohammadlou
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  2. Rahman Farnoosh
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Correspondence to Minoo Bakhshmohammadlou.

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Bakhshmohammadlou, M., Farnoosh, R. Hedging of options for jump-diffusion stochastic volatility models by Malliavin calculus. Math Sci 15, 337–343 (2021). https://doi.org/10.1007/s40096-020-00371-4

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  • DOI: https://doi.org/10.1007/s40096-020-00371-4

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