Latent Volatility Contagion in Rough Volatility Models: Spectral Thresholds and Detectability

We study cross-asset volatility interactions in rough volatility models and identify a structural distinction between pricing-level observability and path-space statistical detectability. The model is driven by modulated Volterra kernels of the form (t - s) ^ (H - 1/2) L (t, s) with C¹ modulation, covering the class of rough volatility specifications used in practice. In a bivariate setting where asset Y's log-volatility is driven by an idiosyncratic kernel with Hurst exponent HY and a contagion kernel from asset X with exponent HXY, we show that two distinct thresholds govern cross-asset effects. A pricing threshold at HXY = HY determines whether contagion contributes to leading-order short-maturity implied-volatility asymptotics under the risk-neutral measure, while in the smoothing regime HXY > HY, a path-space threshold at HXY = HY + 1/4 determines whether the coupled and uncoupled volatility laws are equivalent or mutually singular. The gap HY < HXY ≤ HY + 1/4 defines a latent contagion regime, in which cross-asset volatility spillovers are asymptotically invisible to leading-order option prices yet remain statistically detectable at the level of the volatility path law in the smoothing regime. These results are obtained via a functional-analytic approach based on Volterra operator decompositions and the Feldman–Hájek theorem. We show that, under smooth non-degenerate modulation, the classical 1/4 threshold persists beyond pure fractional kernels, and arises from the spectral behaviour of a relative covariance operator whose leading contribution is governed by a weighted fractional integral.