Latent Volatility Contagion in Rough Volatility Models

This paper studies when a latent cross-asset volatility channel is visible to option prices and when it remains detectable only through the underlying volatility path law. In a bivariate rough Volterra model, two distinct thresholds govern that distinction. A pricing threshold at H_XY = H_Y determines whether contagion enters the leading short-maturity Bachelier skew, while a path-space threshold at H_XY = H_Y + 1/4 determines, in the smoothing regime, whether the coupled and uncoupled Gaussian volatility laws are equivalent or mutually singular. The interval between these boundaries is identified as a latent contagion regime in which contagion is invisible at leading order to prices but still statistically detectable under the physical law. The paper also shows that this threshold structure persists beyond pure fractional kernels under smooth non-degenerate modulation, using the singular-value asymptotics of the relative covariance operator. It provides the theoretical foundation for the later dynamic-observability and econometric papers.