On the rate of convergence of estimating the Hurst parameter of rough stochastic volatility models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916938586783744 |
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| author | Han, Xiyue Schied, Alexander |
| author_facet | Han, Xiyue Schied, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the rate of convergence of estimating the Hurst parameter of rough stochastic volatility models Han, Xiyue Schied, Alexander Statistical Finance Probability Statistics Theory Mathematical Finance 62P05, 60F15, 60G22, 91G70 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. |
| title | On the rate of convergence of estimating the Hurst parameter of rough stochastic volatility models |
| topic | Statistical Finance Probability Statistics Theory Mathematical Finance 62P05, 60F15, 60G22, 91G70 |
| url | https://arxiv.org/abs/2504.09276 |