We aim to obtain explicit representations of locally risk-minimizing  of call and put options for the Barndorff-Nielsen and Shephard models, which are Ornstein-Uhlenbeck type stochastic volatility models.  Arai and Suzuki (2015) obtained a formula of locally risk-minimizing for L\'evy markets under many additional conditions by using Malliavin calculus for L\'evy processes. In this paper, 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  .
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 .
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aim to
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strategies
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Ornstein-Uhlenbeck type
Ornstein--Uhlenbeck-type
A
Using Malliavin calculus for Levy processes,
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of
for
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for L\'evy
strategies for Levy
R
by using Malliavin calculus for L\'evy processes. In this paper, supposing
. Supposing
A
. Moreover, some numerical experiments for locally risk-minimizing strategies are introduced