Dynamic Observability of Latent Contagion

This paper asks what remains of latent cross-asset contagion once information is revealed sequentially and inference is restricted to observable filtrations. Working in the same bivariate Gaussian Volterra framework as the threshold paper, it develops the dynamic bridge between pricing visibility, path-space detectability, and feasible prediction. The paper establishes three main results. First, in the smoothing regime, it derives a finite-resolution Gaussian experiment whose exact likelihood, Kullback-Leibler, Hellinger, and Bayes-error formulas recover the path-detectability boundary H_XY = H_Y + 1/4 as the critical evidence-accumulation threshold. Second, at the oracle latent-driver level, it shows that short-horizon prediction is governed by a different boundary, H_XY = H_Y, which separates dynamically informative from dynamically latent contagion. Third, it proves that this oracle rough gain is screened once one passes to observed Gaussian channels and conditions on the target asset’s own past. The result is a closed observable-screening theorem showing that pricing visibility, path-space detectability, and dynamic observability need not coincide.