đ€ AI Summary
This study addresses inconsistencies and estimation biases in cross-asset volatility roughness measurements by proposing a mean-reversion contamination correction formula and an additive noise adjustment framework, supported by a unified data infrastructure and a method applicability taxonomy. Empirical results confirm that realized volatility is universally rough across asset classes, with corrected Hurst exponents remaining significantly below the Brownian diffusion benchmark. Furthermore, the analysis reveals that implied roughness estimates for equity indices slightly exceed realized values, whereas such estimates fail for interest rates and foreign exchange. By effectively mitigating noise interference in rough volatility modeling, this work clarifies the systematic discrepancies between implied and realized roughness measures, providing a robust foundation for cross-asset volatility analysis.
đ Abstract
We measure volatility roughness across asset classes using a common data infrastructure and pipeline. Our data covers 3,926 United States equities, 34 CME futures roots, rates, FX, and commodities, and options on 44 underlyings over 2010-2025. Realized volatility is rough everywhere. The class-median Hurst estimate ranges from $0.05$ (livestock) through $0.07-0.10$ (rates, FX, agriculture, energy, metals) to $0.13$ (single stocks) and $0.20$ (equity indices). The option-implied measure identifies $H$ only where the leverage effect produces a clean skew term structure. For the equity indices, implied estimates of $0.21-0.28$ are just above realized volatility $H$, while for rates and FX the ATM skew regression fails with an R-squared near zero even though realized volatility remains rough. We also show a mean-reversion contamination formula for the second-moment estimator of the roughness for the stationary fractional Ornstein-Uhlenbeck process. The local slope of the increment second moment deviates from $2H$ by $(1-H)Î(2H+1)(ÎșÎ)^{2-2H}$ for all $H\in(0,1)$. A correction framework for the second moment, when the log realized volatility measure has additive noise, raised the $H$ estimate slightly but nowhere near the Brownian diffusion framework. Finally, a failure taxonomy discusses where rough-volatility methods apply and where they fail, suggesting alternative paths to further explore the rough-volatility paradigm.