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Roughness Analysis of Realized Volatility and VIX through Randomized Kolmogorov-Smirnov Distribution
Sergio Bianchi, Daniele Angelini
https://arxiv.org/abs/2509.20015 https://…

Roughness Analysis of Realized Volatility and VIX through Randomized Kolmogorov-Smirnov Distribution
We introduce a novel distribution-based estimator for the Hurst parameter of log-volatility, leveraging the Kolmogorov-Smirnov statistic to assess the scaling behavior of entire distributions rather than individual moments. To address the temporal dependence of financial volatility, we propose a random permutation procedure that effectively removes serial correlation while preserving marginal distributions, enabling the rigorous application of the KS framework to dependent data. We establish th…