Abstract

Continuous microscopic volatility can generate market-level roughness, synchronized stress, jump-like coarse observations, and residual hedge risk. This paper derives that sequence in an $N$-asset Gaussian Volterra market with directed latent-contagion kernels and an aggregate market-volatility functional. Admissible off-diagonal channels are selected by the projected experiment: they must be source-screened visible, carry nonzero market loading, and admit a shrinking projected local normalization. In the high-frequency market array, this selects rough channels as the stable observable contagion phase while smooth directional contagion becomes locally degenerate. Dominant rough edges form a screened contagion operator, and crossing its Perron threshold aligns latent stress along a common mode. Threshold-triggered activation can converge to jump-like behavior for coarse observers even though primitive paths remain continuous. Pricing and hedging consequences appear as visible compressions of latent market-variance risk, with residual lower bounds when the synchronized mode retains conditional variance.

Citation

Vidal Llauradó, Joan. “A Rough Theory of Markets: Latent Contagion, Market Phases, and Market-Variance Risk.” 2026. doi:10.2139/ssrn.6616121