In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian motion with Hurst parameter $H < 0.5$. In this paper, we derive a consistent and asymptotically mixed normal estimator of $H$ based on high-frequency price observations. In contrast to previous works, we work in a semiparametric setting and do not assume any a priori relationship between volatility estimators and true volatility. Furthermore, our estimator attains a rate of convergence that is known to be optimal in a minimax sense in parametric rough volatility models.

翻译：近年来，粗糙波动率模型引起了实质性关注。在此类模型中，随机波动率的局部行为比半鞅过程更为不规则，类似于赫斯特参数$H < 0.5$的分数布朗运动。本文基于高频价格观测数据，推导出$H$的一致且渐近混合正态估计量。与先前研究不同，我们在半参数设定下展开分析，且未假设波动率估计量与真实波动率之间存在任何先验关系。此外，我们的估计量达到了在参数化粗糙波动率模型中已知为极小极大意义下最优的收敛速率。