 A GMM approach to estimate the roughness of stochastic volatilityAnine E. Bolko, Kim Christensen, Mikko S. Pakkanen and Bezirgen Veliyev Abstract: We develop a GMM approach for estimation of log-normal stochastic volatility models driven by a fractional Brownian motion with unrestricted Hurst exponent. We show that a parameter estimator based on the integrated variance is consistent and, under stronger conditions, asymptotically normally distributed. We inspect the behavior of our procedure when integrated variance is replaced with a noisy measure of volatility calculated from discrete high-frequency data. The realized estimator contains sampling error, which skews the fractal coefficient toward "illusive roughness." We construct an analytical approach to control the impact of measurement error without introducing nuisance parameters. In a simulation study, we demonstrate convincing small sample properties of our approach based both on integrated and realized variance over the entire memory spectrum. We show the bias correction attenuates any systematic deviance in the parameter estimates. Our procedure is applied to empirical high-frequency data from numerous leading equity indexes. With our robust approach the Hurst index is estimated around 0.05, confirming roughness in stochastic volatility. Date: 2020-10, Revised 2022-04 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2010.04610 Access Statistics for this paper More papers in Papers from arXiv.org |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.