A GMM approach to estimate the roughness of stochastic volatility

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Title: A GMM approach to estimate the roughness of stochastic volatility
Authors: Bolko, AE
Christensen, K
Pakkanen, MS
Veliyev, B
Item Type: Journal Article
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 of Acceptance: 4-Jun-2022
URI: http://hdl.handle.net/10044/1/97662
ISSN: 0304-4076
Publisher: Elsevier
Journal / Book Title: Journal of Econometrics
Copyright Statement: © Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords: q-fin.ST
Primary 91G70, Secondary 62M09
0104 Statistics
1402 Applied Economics
1403 Econometrics
Publication Status: Accepted
Embargo Date: Embargoed for 24 months after publication date
Appears in Collections:Financial Mathematics

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