论文标题
粗糙波动率的统计推断：中心极限定理
Statistical inference for rough volatility: Central limit theorems
论文作者
论文摘要
近年来，对粗糙的波动模型引起了实质性的兴趣。在这类模型中，随机波动率的局部行为比半明星的局部行为更加不规则，并且类似于hurst参数$ h <0.5 $的分数布朗运动的局部行为。在本文中，我们根据高频价格观察得出了$ h $的一致且渐近混合的正常估计器。与以前的工作相反，我们在半摩托环境中工作，并且不假定波动率估计器与真实波动率之间的任何先验关系。此外，我们的估计器达到了一种收敛速率，在参数粗糙的波动率模型中，在最小值意义上是最佳的收敛速率。
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.
