Detecting Latent Volatility Contagion

This paper develops a feasible estimator for the source-screened latent contagion object isolated in the first two papers and applies it to a balanced Oxford-Man realized-volatility panel of eight global equity indices. Starting from the reduced local Gaussian block experiment, it represents local alternatives by covariance derivatives, removes the target-only tangent space, and estimates the remaining source-screened component with a low-dimensional projected covariance-score GMM statistic. The paper derives the projected-score geometry, proves the associated local Gaussian efficiency, rough-regime projected-rank, pilot-adaptive transfer, and uniform minimax results, and validates the implementation in synthetic experiments using closed-form information and noncentrality constants. In the Oxford-Man application, estimated physical-measure roughness lies between about 0. 04 and 0. 09 across the panel, with HP approximately 0. 071 for SPX, while the full-sample directed contagion map is dense and economically informative through intensity ranking and rolling stability rather than sparse edge selection. The paper closes the trilogy with a feasible estimator, a validation protocol, and a real-data physical-measure application, while leaving matched option-panel P/Q classification for later work.