(In)Efficient Market States and Rough Volatility Detected via Grünwald-Letnikov Fractional Derivative

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The paper provides a robust statistical framework for detecting market inefficiencies (persistent/anti-persistent regimes) and validating rough volatility models. This is directly relevant to: (1) volatility modeling for option pricing and hedging, (2) regime detection for adaptive trading strategies, (3) risk management through accurate Hurst exponent estimation, and (4) testing weak-form efficiency assumptions. However, the method is primarily diagnostic rather than prescriptive—it identifies market states but does not directly generate trading signals or portfolio allocations.

The theoretical framework involves advanced concepts: fractional calculus (Grünwald-Letnikov derivative), empirical process theory, Hermite expansions, and long-range dependence asymptotics. Implementation requires: (1) computing GL fractional derivatives with proper burn-in correction, (2) constructing crossed fGn samples at multiple scales, (3) computing two-sample KS statistics between empirical distributions, (4) Monte Carlo calibration of critical values (since the limiting distribution is not distribution-free), and (5) regime-adaptive selection of filter order. The Monte Carlo calibration step is computationally intensive. However, the core algorithm is well-defined and the paper provides clear parameter choices.

The paper provides detailed mathematical derivations, Monte Carlo simulation parameters (H values, sample sizes, scaling factors, burn-in exponents), and references to specific MATLAB functions (fbmwoodchan from FracLab Toolbox 2.02). Data sources are identified (Oxford-Man Institute Realized Library). However, no explicit code repository is provided. The theoretical proofs are complete in appendices.