Estimating the Hurst parameter from the zero vanna implied volatility and its dual

Elisa Alos, Frido Rolloos and Kenichiro Shiraya
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Elisa Alos: Department of Economics and Business, University Pompeu Fabra, and Barcelona GSE
Kenichiro Shiraya: Graduate School of Economics, The University of Tokyo

No CARF-F-607, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: The covariance between the return of an asset and its realized volatility can be approxi- mated as the difference between two specific implied volatilities. In this paper it is proved that in the small time-to-maturity limit the approximation error tends to zero. In addition a direct relation between the short time-to-maturity covariance and slope of the at-the-money implied volatility is established. The limit theorems are valid for stochastic volatility models with Hurst parameter H \in (0,1). An application of the results is to accurately approximate the Hurst parameter using only a discrete set of implied volatilities. Numerical examples under the rough Bergomi model are presented. This paper is available at https://arxiv.org/abs/2510.26310

Pages: 20
Date: 2025-10
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Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf607

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