In recent years, there has been substantive empirical evidence that stochastic volatility is rough. In other words, 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，大量实证证据表明随机波动率具有粗糙性。换言之，随机波动率的局部行为比半鞅过程更为不规则，其特性类似于Hurst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$H$的相合且渐近混合正态估计量。与先前研究不同，我们在半参数框架下开展工作，既不假设波动率估计量与真实波动率之间存在任何先验关系，也不依赖此类假设。此外，我们的估计量达到了参数粗糙波动率模型中已知的极小化最优收敛速率。