Detecting Latent Volatility Contagion: A Projected Score Estimator for Rough Volatility Models

This paper addresses the persistent discrepancy between physical-measure roughness estimates based on realized volatility and pricing-measure roughness estimates inferred from options, as documented by Livieri, Mouti, Pallavicini, and Rosenbaum (2018). We develop an estimator that separates source-screened volatility contagion from target-specific confounding in rough volatility models and apply it to a balanced Oxford-Man realized-volatility panel of eight global equity indices. Starting from a reduced local Gaussian block experiment, the procedure represents local alternatives through covariance derivatives, projects out the target-only tangent space, and estimates the remaining source-screened component using a low-dimensional covariance-score GMM statistic. We derive the geometry of the projected score and establish local Gaussian efficiency, projected-rank properties in the rough regime, pilot-adaptive transfer, and uniform minimax optimality. The implementation is validated through reproducible synthetic experiments featuring closed-form expressions for information and noncentrality constants. Empirically, on the Oxford-Man panel, estimated physical-measure roughness values range from approximately 0.04 to 0.09. For the S&P 500, the estimator yields H_P ≈ 0.071, compared with the external option-implied benchmark H_Q ≈ 0.30 ). The full-sample physical-measure directed contagion network is dense, with all 56 ordered pairs detectable at a 5% false discovery rate. Accordingly, the economically relevant objects are the intensity ranking and the temporal stability of source-screened observability, rather than sparse edge selection. Building on spectral-threshold and dynamic-observability analyses in the literature, we translate these structural insights into a projected score estimator, a validation framework, and an empirical application under the physical measure. While the scalar residual-product statistic RYk,nXk,n remains a transparent analytical baseline, the primary empirical object is the projected covariance-score GMM statistic. The resulting framework integrates local asymptotic normality theory, source-orthogonal information diagnostics, size-calibrated simulation evidence, and empirical analysis of realized-volatility data, and provides a P/Q classification template for future matched option-panel studies.