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

Author

Listed:
  • Elisa Alos

    (Department of Economics and Business, University Pompeu Fabra, and Barcelona GSE)

  • Frido Rolloos
  • Kenichiro Shiraya

    (Graduate School 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

Suggested Citation

  • Elisa Alos & Frido Rolloos & Kenichiro Shiraya, 2025. "Estimating the Hurst parameter from the zero vanna implied volatility and its dual," CARF F-Series CARF-F-607, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf607
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