STATISTICAL INFERENCE FOR ROUGH VOLATILITY: CENTRAL LIMIT THEOREMS

• 成果类型: Article
• 署名作者: Chong, Carsten H.; Hoffmann, Marc; Liu, Yanghui; Rosenbaum, Mathieu; Szymanski, Gregoire
• 署名单位: Hong Kong University of Science & Technology; Universite PSL; Universite Paris-Dauphine; City University of New York (CUNY) System; Baruch College (CUNY); Institut Polytechnique de Paris; Ecole Polytechnique
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP2002
• 发表日期: 2024
• 关键词: long-memory

摘要

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.