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Local Risk-Minimization for Barndorff-Nielsen and Shephard Models with Volatility Risk Premium

  • Takuji Arai
Research Article
Part of the Advances in Mathematical Economics book series (MATHECON, volume 20)

Abstract

We derive representations of locally risk-minimizing strategies of call and put options for Barndorff-Nielsen and Shephard models: jump type stochastic volatility models whose squared volatility process is given by a non-Gaussian Ornstein-Uhlenbeck process. The general form of Barndorff-Nielsen and Shephard models includes two parameters: volatility risk premium β and leverage effect ρ. Arai and Suzuki (Local risk minimization for Barndorff-Nielsen and Shephard models. submitted. Available at http://arxiv.org/pdf/1503.08589v1) dealt with the same problem under constraint \(\beta = -\frac{1} {2}\). In this paper, we relax the restriction on β; and restrict ρ to 0 instead. We introduce a Malliavin calculus under the minimal martingale measure to solve the problem.

Keywords

Locally risk-minimizing strategy Barndorff-Nielsen and Shephard models Stochastic volatility models Malliavin calculus Lévy processes 

Notes

Acknowledgements

The author would like to thank to Jean-Pierre Fouque for fruitful discussion, and an anonymous referee for valuable comments and suggestions. This research was supported by Ishii memorial securities research promotion foundation.

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Copyright information

© Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of EconomicsKeio UniversityTokyoJapan

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