101. Local risk-minimization for Barndorff-Nielsen and Shephard models
- Author
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Ryoichi Suzuki, Yuto Imai, and Takuji Arai
- Subjects
Statistics and Probability ,050208 finance ,Stochastic volatility ,Mathematical finance ,05 social sciences ,Probability (math.PR) ,Malliavin calculus ,01 natural sciences ,Lévy process ,Mathematical Finance (q-fin.MF) ,FOS: Economics and business ,010104 statistics & probability ,Quantitative Finance - Mathematical Finance ,0502 economics and business ,FOS: Mathematics ,Minification ,Differentiable function ,0101 mathematics ,Statistics, Probability and Uncertainty ,Martingale (probability theory) ,Mathematical economics ,Finance ,Mathematics - Probability ,Mathematics - Abstract
We obtain explicit representations of locally risk-minimizing strategies of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein--Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for Levy processes, Arai and Suzuki (2015) obtained a formula for locally risk-minimizing strategies for Levy markets under many additional conditions. Supposing mild conditions, we make sure that the Barndorff-Nielsen and Shephard models satisfy all the conditions imposed in Arai and Suzuki (2015). Among others, we investigate the Malliavin differentiability of the density of the minimal martingale measure. Moreover, some numerical experiments for locally risk-minimizing strategies are introduced., Comment: 39 pages, 2figures
- Published
- 2015
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