10.1007/s40096-020-00371-4

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

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  • Minoo Bakhshmohammadlou*1,
  • Rahman Farnoosh1,
  1. Iran University of Science and Technology, Tehran, IR

Published in Issue 2021-05-29

How to Cite

Bakhshmohammadlou, M., & Farnoosh, R. (2021). Hedging of options for jump-diffusion stochastic volatility models by Malliavin calculus. Mathematical Sciences, 15(4 (December 2021). https://doi.org/10.1007/s40096-020-00371-4
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Abstract

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 V(t,s,y)∈C1,2,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {V}(t,s,y)\in C^{1,2,2}$$\end{document} and the differentiability condition V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {V}$$\end{document} in s and y with bounded derivatives is sufficient. Also, this tool shortens calculations of the hedge.

Keywords

  • Jump-diffusion stochastic volatility model,
  • Locally risk minimizing portfolio,
  • Malliavin calculus,
  • Jump-diffusion version of the Clark–Ocone formula

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