Dynamic Observability of Latent Contagion in Rough Volatility Models

We study how cross-asset volatility contagion becomes dynamically visible in rough volatility models once information is revealed sequentially rather than through a single pricing or path-space comparison. The setting is a bivariate Gaussian Volterra model with idiosyncratic roughness exponent HY and cross-asset exponent HXY, viewed as a sequel to the spectral threshold analysis of latent contagion developed in the companion paper. In the smoothing regime HXY > HY, we first derive the canonical finite-resolution Gaussian experiment associated with the relative covariance operator and obtain exact likelihood, Kullback–Leibler, Hellinger, and Bayes-error formulas. This yields a sharp finite-resolution discrimination threshold at HXY = HY + 1/4, recovering the statistical boundary from the companion paper in a quantitative form. We then formulate a short-horizon sequential prediction problem. At the oracle latent-driver level, we prove that the dynamic threshold is HXY = HY: rougher contagion improves prediction at leading order, smoother contagion is dynamically latent at leading order, and the boundary case mixes the two channels on the same scale. Passing from latent-driver filtrations to observed Gaussian channels reduces the problem to an exact posterior-variance geometry governed by a hidden transfer operator. In the rougher regime 0 < HXY < HY < 1/2, and under the paper’s C² amplitude regularity hypotheses, we develop a two-scale Volterra localization and frozen fractional model for that transfer operator. The resulting observable screening theorem shows that the leading oracle gain is suppressed by the target’s own past: ||Fₓ, ₇|| = o (h^HXY), Gₗ→ₘ (t, h) = o (h^2HXY). The sequel therefore identifies a three-level structure of contagion visibility: pricing, path-space detectability, and dynamic observability need not coincide.