篮子隐含波动率偏斜与粘性

中文摘要 AI 辅助

我们研究了具有连续、可能粗糙的随机波动率的资产篮子的短期隐含波动率及偏斜粘性比率。瞬时篮子方差的波动有两个来源：成分方差的波动和篮子权重的波动。我们推导了一个近平价隐含波动率展开式，将这两部分贡献分开。随后，我们将结果专门应用于由高斯Volterra因子的一般函数给出的波动率模型，并根据短时核渐近性、因子敏感性和收益-因子相关性获得了显式的篮子偏斜系数。密度展开证明了近平价展开式在平价处的可微性。最后，利用总隐含方差动力学的Malliavin表示，我们证明了对于H∈(0,1/2]的高斯因子篮子模型，短期偏斜粘性比率收敛到普适极限H+3/2。

英文摘要

We study the short-maturity implied volatility and the skew stickiness ratio for baskets of assets with continuous, possibly rough, stochastic volatility. The fluctuation of the instantaneous basket variance has two sources: fluctuations of the constituent variances and fluctuations of the basket weights. We derive a near-the-money implied volatility expansion that separates these contributions. We then specialize the result to volatility models given by general functions of Gaussian Volterra factors and obtain an explicit basket skew coefficient in terms of the short-time kernel asymptotics, the factor sensitivities, and the return-factor correlations. A density expansion justifies differentiation of the near-the-money expansion at the money. Finally, using a Malliavin representation of the dynamics of total implied variance, we prove that the short-maturity skew stickiness ratio converges to the universal limit $H + 3/2$ for Gaussian factor basket models with $H \in (0, 1/2]$.

发表机构

• The University of Osaka（大阪大学）
• Mizuho Securities Co., Ltd.（瑞穗证券株式会社）

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