Consistent estimation for fractional stochastic volatility model under high‐frequency asymptotics. (23rd August 2022)

• Record Type: Journal Article
• Authors: Fukasawa, Masaaki; Takabatake, Tetsuya; Westphal, Rebecca
• Is Part Of: Mathematical finance. Volume 32:Number 4(2022)
• Page Start: 1086
• Page End: 1132
• Publication Date: 2022-08-23
• Subjects: fractional Brownian motion -- high‐frequency data analysis -- realized variance -- rough volatility -- stochastic volatility -- Whittle estimator; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12354
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract: We develop a statistical theory for a continuous time approximately log‐normal fractional stochastic volatility model to examine whether the volatility is rough, that is, whether the Hurst parameter is less than one half. We construct a quasi‐likelihood estimator and apply it to realized volatility time series. Our quasi‐likelihood is based on the error distribution of the realized volatility and a Whittle‐type approximation to the auto‐covariance of the log‐volatility process. We prove the consistency of our estimator under high‐frequency asymptotics, and examine by simulations its finite sample performance. Our empirical study suggests that the volatility of the time series examined is indeed rough.