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On the rate of convergence of estimating the Hurst parameter of rough stochastic volatility models

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  • Xiyue Han
  • Alexander Schied

Abstract

In [8], easily computable scale-invariant estimator $\widehat{\mathscr{R}}^s_n$ was constructed to estimate the Hurst parameter of the drifted fractional Brownian motion $X$ from its antiderivative. This paper extends this convergence result by proving that $\widehat{\mathscr{R}}^s_n$ also consistently estimates the Hurst parameter when applied to the antiderivative of $g \circ X$ for a general nonlinear function $g$. We also establish an almost sure rate of convergence in this general setting. Our result applies, in particular, to the estimation of the Hurst parameter of a wide class of rough stochastic volatility models from discrete observations of the integrated variance, including the fractional stochastic volatility model.

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  • Xiyue Han & Alexander Schied, 2025. "On the rate of convergence of estimating the Hurst parameter of rough stochastic volatility models," Papers 2504.09276, arXiv.org.
    • Handle: RePEc:arx:papers:2504.09276
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    References listed on IDEAS

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    1. Bolko, Anine E. & Christensen, Kim & Pakkanen, Mikko S. & Veliyev, Bezirgen, 2023. "A GMM approach to estimate the roughness of stochastic volatility," Journal of Econometrics, Elsevier, vol. 235(2), pages 745-778.
    2. Masaaki Fukasawa & Tetsuya Takabatake & Rebecca Westphal, 2022. "Consistent estimation for fractional stochastic volatility model under high‐frequency asymptotics," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 1086-1132, October.
    3. Rama Cont & Purba Das, 2024. "Rough Volatility: Fact or Artefact?," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 191-223, May.
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