A randomized Kolmogorov-Smirnov estimator for the Hurst exponent applied to VIX implied volatility and S&P 500 realized volatility finds both rougher than Brownian motion with a statistically significant smoothness hierarchy.
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Randomized Kolmogorov-Smirnov Analysis of Volatility Roughness
A randomized Kolmogorov-Smirnov estimator for the Hurst exponent applied to VIX implied volatility and S&P 500 realized volatility finds both rougher than Brownian motion with a statistically significant smoothness hierarchy.