Local risk-minimization for Barndorff-Nielsen and Shephard models
Local risk-minimization for Barndorff-Nielsen and Shephard models
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DOI：
10.1007/s00780-017-0324-8
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发表时间：
2015-03
影响因子：
1.7
通讯作者：
Takuji Arai;Yuto Imai;R. Suzuki
中科院分区：
文献类型：
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作者：
Takuji Arai;Yuto Imai;R. Suzuki
我们得到了Ornstein-Uhlenbeck型随机波动率模型Barndorff-Nielsen和Shephard模型中看涨期权和看跌期权局部风险最小化策略的显式表示。将Malliavin演算用于L过程，Arai和Suzuki(Int.J.财务。英语。2：1550015,2015年)得到了L市场在许多附加条件下局部风险最小化策略的公式。假设条件温和，我们保证Barndorff-Nielsen和Shephard模型满足(Arai和Suzuki在Int.J.财务。英语。2015年2：1550015)。其中，我们研究了极小鞅测度密度的Malliavin可微性。此外，我们还介绍了一些局部风险最小化策略的数值实验。
We obtain explicit representations of locally risk-minimizing strategies for call and put options in Barndorff-Nielsen and Shephard models, which are Ornstein–Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for Lévy processes, Arai and Suzuki (Int. J. Financ. Eng. 2:1550015, 2015) obtained a formula for locally risk-minimizing strategies for Lévy 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 in Int. J. Financ. Eng. 2:1550015, 2015). Among others, we investigate the Malliavin differentiability of the density of the minimal martingale measure. Moreover, we introduce some numerical experiments for locally risk-minimizing strategies.