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Statistical inference for rough volatility: Central limit theorems

Chong, Carsten; Hoffmann, Marc; Liu, Yanghui; Rosenbaum, Mathieu; Szymanski, Grégoire (2022), Statistical inference for rough volatility: Central limit theorems. https://basepub.dauphine.psl.eu/handle/123456789/23717

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
47
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Author(s)
Chong, Carsten
COLUMBIA UNIVERSITY USA
Hoffmann, Marc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Liu, Yanghui
Baruch College [CUNY]
Rosenbaum, Mathieu
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Szymanski, Grégoire
Centre de Mathématiques Appliquées - Ecole Polytechnique [CMAP]
Abstract (EN)
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.
Subjects / Keywords
Central limit theorem; fractional Brownian motion; Hurst parameter; nonparametric estimation; rough volatility; spot volatility; volatility of volatility