A Structural Volatility Surface Under Stress and Low Liquidity Conditions

This article presents the Kinetic Equation for Volatility Analysis (K-EVA), a primarily conceptual framework for the structural interpretation of implied volatility surfaces under stress conditions and low liquidity. Rather than treating the volatility surface as a uniformly continuous and continuously deformable object, the proposed approach considers the possibility that the surface may consist of maturity-dependent structural regions connected through either continuous or discontinuous transitions. K-EVA integrates structural reparameterization, geometric interpretation, and structural fractures into a unified representation. Under this perspective, the implied volatility surface is interpreted not only as the result of calibration but also as a structural system whose geometry reflects different information environments associated with market uncertainty, liquidity conditions, and scheduled or unexpected informational events. A mathematical definition of structural fractures is introduced on the basis of changes in the information set associated with neighboring option maturities. This distinction naturally leads to a structural interpretation of market regimes and volatility dynamics, in which transitions between latent, normal, and turbulent market conditions are represented by changes in the geometric configuration of the implied volatility surface rather than by latent stochastic states. The proposed parameterization preserves desirable properties commonly associated with Stochastic Volatility Inspired–based formulations, including parsimony and smooth extrapolation. It also introduces a set of geometrically interpretable structural coefficients that facilitate the identification of structural distortions, information-driven transitions, and market regimes. K-EVA provides a unified structural representation of implied volatility surfaces under stress and low-liquidity conditions, allowing discontinuities, local deformations, and information-driven transitions to be incorporated while preserving analytical tractability and geometric interpretability.