Randomized Kolmogorov–Smirnov Analysis of Volatility Roughness

Battle Count: 77

The paper is highly relevant for quantitative finance practitioners working on volatility modeling, option pricing, and risk management. The finding that implied volatility (VIX, H≈0.38) is smoother than realized volatility (RV5, H≈0.14) has direct implications for volatility surface modeling and hedging strategies. The rough volatility paradigm (H < 0.5) affects option pricing models used in trading. However, the paper is primarily methodological/estimation-focused rather than directly proposing trading strategies. The computational efficiency improvements (Brent's method, Nelder-Mead) are practically useful for real-time or rolling-window estimation in trading systems.

The methodology involves multiple components: (1) computing multi-scale increments, (2) random permutation for decorrelation, (3) KS statistic evaluation across a grid of H values, (4) derivative-free optimization, (5) repeated subsampling for variance reduction, (6) rolling-window estimation, and (7) Kalman filter for state-space filtering. The mathematical framework is well-specified but requires careful implementation of the permutation scheme, proper handling of the KS test under dependence, and tuning of parameters (a, T, K, window length). The use of standard optimization routines (Brent, Nelder-Mead) and publicly available fBm simulation tools (FracLab) reduces some complexity. Overall, a competent quantitative researcher could implement this in 2-4 weeks.

The paper provides detailed algorithmic descriptions (Algorithm 1 for Grid Search), mathematical formulations, and parameter settings (a=50, T=508, K=16, window length ν=1008). However, no code repository is explicitly provided. The Oxford-Man Institute Realized Library is referenced for RV5 data, and VIX data is publicly available from CBOE. The methodology is fully specified mathematically, enabling reimplementation, but practical code availability is uncertain.