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.
JEL Classification: G11, G12
Mathematics Subject Classification (2010): 91G20, 60H07
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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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Arai, T. (2016). Local Risk-Minimization for Barndorff-Nielsen and Shephard Models with Volatility Risk Premium. In: Kusuoka, S., Maruyama, T. (eds) Advances in Mathematical Economics Volume 20. Advances in Mathematical Economics, vol 20. Springer, Singapore. https://doi.org/10.1007/978-981-10-0476-6_1
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DOI: https://doi.org/10.1007/978-981-10-0476-6_1
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