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arXiv · 2504.09276

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

Xiyue Han·Alexander Schied
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Abstract

In [Han \& Schied, 2023, \textit{arXiv 2307.02582}], an 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 rough fractional stochastic volatility model.

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Xiyue Han, Alexander Schied. 2025-04-12. On the rate of convergence of estimating the Hurst parameter of rough stochastic volatility models. https://arxiv.org/abs/2504.09276

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