Abstract

Short-maturity option prices and physical path laws need not observe the same directed rough-volatility channel. This paper separates the pricing projection from the path-law projection in a bivariate Gaussian Volterra model where asset $Y$ has its own rough component and receives a directed contagion component from asset $X$. The pricing threshold $H_{XY}=H_Y$ determines whether contagion enters the leading Bachelier skew. In the smoothing regime, the path-space threshold $H_{XY}=H_Y+\frac{1}{4}$ determines whether the coupled and uncoupled Gaussian volatility laws are mutually singular or equivalent. The interval $H_Y<H_{XY}\le H_Y+\frac{1}{4}$ is the latent contagion regime: the channel is absent from leading option asymptotics but remains detectable in the physical path law. Smooth non-degenerate modulation preserves the same threshold geometry through the singular-value order of the relative covariance operator.

Citation

Vidal Llauradó, Joan. “Latent Volatility Contagion in Rough Volatility Models: Spectral Thresholds and Detectability.” 2026. doi:10.2139/ssrn.6520718