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arXiv · 2210.01216

Statistical inference for rough volatility: Central limit theorems

Carsten Chong·Marc Hoffmann·Yanghui Liu·Mathieu Rosenbaum·Grégoire Szymanski
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Abstract

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.

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BibTeXRIS

Carsten Chong, Marc Hoffmann, Yanghui Liu, Mathieu Rosenbaum, Grégoire Szymanski. 2022-10-03. Statistical inference for rough volatility: Central limit theorems. https://doi.org/10.1214/23-aap2002

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