The Chirality Bound

Ambarish, Kreuser, and Seigel (AKS 2026a) introduced market chirality as the measurable handedness of the implied-volatility surface and proposed a local slope-to-curvature index to quantify that asymmetry. This paper develops a probabilistic restriction associated with that geometric object. We identify two centred second-order innovations that enter finite-horizon option profit and loss: an unexpected spotvolatility product shock and an unexpected volatility-squared shock. Under conditional joint Gaussianity, their correlation is available in closed form and is governed by the spot-volatility correlation. We then use a local stochastic-volatility skew relation to connect that dynamic correlation to the chirality index introduced in the earlier AKS paper. The resulting theory yields a simple chirality frontier and, crucially, an exact condition under which that frontier is a lower envelope for the magnitude of the correlation between the two quadratic innovations. We call this the chirality dominance condition. The paper therefore moves chirality from a geometric characterization to a falsifiable restriction on the dependence of option-risk innovations. We also correct the exact SVI representation of the local chirality index and distinguish it from its commonly used first-order approximation. Preliminary SPX surface evidence reproduces the negative chirality, hump-shaped maturity structure, and stress amplification documented in AKS-I, but these surface facts are treated only as motivation. The decisive empirical test must construct the quadratic innovations independently, estimate the surface-to-dynamics conversion, and test the lower envelope only in the dominance region.