AI 中文总结
该研究采用统一流程测算多类资产2010-2025年的波动率粗糙性，发现所有资产已实现波动率均具粗糙性，推导了相关二阶矩估计的均值回复污染公式，提出了粗糙波动率方法的适用失效分类体系。
AI 中文摘要
我们采用统一的数据基础设施和流程，对各类资产的波动率粗糙性进行了测算。我们的数据覆盖了2010年至2025年间的3926只美国股票、34种CME期货标的（涵盖利率、外汇、大宗商品）以及44种标的资产的期权。研究发现，所有资产类别的已实现波动率均具有粗糙性：品类中位数的赫斯特（Hurst）估计值范围从0.05（ livestock，牲畜），到0.07-0.10（利率、外汇、农业、能源、金属），再到0.13（单只股票），最后到0.20（股票指数）。期权隐含的赫斯特（H）测度仅在杠杆效应产生清晰偏斜期限结构的场景下可识别H；对于股票指数，隐含估计值为0.21-0.28，略高于已实现波动率的H；而对于利率和外汇，尽管已实现波动率仍具粗糙性，但ATM偏斜回归的R平方接近零，无法有效测算H。此外，我们针对平稳分数奥恩斯坦-乌伦贝克（fractional Ornstein-Uhlenbeck）过程的粗糙度二阶矩估计量，提出了均值回复污染公式：增量二阶矩的局部斜率偏离2H的差值为(1-H)Γ(2H+1)(κΔ)^(2-2H)，适用于所有H∈(0,1)。当对数已实现波动率测度存在加性噪声时，二阶矩的修正框架会使H估计值略有上升，但仍远低于布朗扩散框架下的结果。最后，我们提出了粗糙波动率方法的适用与失效分类体系，为进一步探索粗糙波动率范式提供了替代路径。
英文摘要
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 $(1-H)Γ(2H+1)(κΔ)^{2-2H}$ 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.
