具有波动风险溢价的Barndorff-Nielsen和Shephard模型的局部风险最小化
Local risk-minimization for Barndorff-Nielsen and Shephard models with volatility risk premium
摘要：
本文给出了Barndorff-Nielsen和Shephard模型的看涨期权和看跌期权的局部风险最小化表示：跳跃型随机波动率模型，其平方波动率过程由非高斯rnstein-Uhlenbeck过程给出. Barndorff-Nielsen和Shephard模型的一般形式包括两个参数：波动风险溢价$β$和杠杆效应$ρ$。Arai和Suzuki（2015，arxiv：1503.08589）在约束$β=-\frac{1}{2}$下处理了相同的问题。在本文中，我们放松了对$β$的限制，而将$ρ$限制为$0$。在最小鞅测度下引入Malliavin演算来解决这个问题。
英文摘要：
We derive representations of local risk-minimization 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 rnstein-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 (2015, arxiv:1503.08589) dealt with the same problem under constraint $β=-\frac{1}{2}$. 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.
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