Roughness in spot variance? A GMM approach for estimation of fractional log-normal stochastic volatility models using realized measures

Anine E. Bolko (), Kim Christensen (), Mikko S. Pakkanen () and Bezirgen Veliyev
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Anine E. Bolko: Aarhus University and CREATES, Postal: Aarhus University, Department of Economics and Business Economics, Fuglesangs Allé 4, 8210 Aarhus V, Denmark
Kim Christensen: Aarhus University and CREATES, Postal: Department of Economics and Business Economics, Fuglesangs Allé 4, 8210 Aarhus V, Denmark
Mikko S. Pakkanen: Imperial College London and CREATES, Postal: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: In this paper, we develop a generalized method of moments approach for joint estimation of the parameters of a fractional log-normal stochastic volatility model. We show that with an arbitrary Hurst exponent an estimator based on integrated variance is consistent. Moreover, under stronger conditions we also derive a central limit theorem. These results stand even when integrated variance is replaced with a realized measure of volatility calculated from discrete high-frequency data. However, in practice a realized estimator contains sampling error, the effect of which is to skew the fractal coefficient toward "roughness". We construct an analytical approach to control this error. 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 that the bias correction attenuates any systematic deviance in the estimated parameters. 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 integrated variance.

Keywords: GMM estimation; realized variance; rough volatility; stochastic volatility (search for similar items in EconPapers)
JEL-codes: C10 C50 (search for similar items in EconPapers)
Pages: 45
Date: 2020-10-19
New Economics Papers: this item is included in nep-ecm and nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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