Beyond the Skew-Stickiness Ratio: Transport Geometry of Spot-Driven Variance Surface Dynamics

Battle Count: 69

Highly relevant to quantitative trading, particularly for derivatives desks and volatility trading. The paper provides a unified geometric framework for smile dynamics that directly extends the classical SSR used in practice. Key practical findings include: (1) SPX exhibits super-skew behavior (β>1) with monotonically declining term structure, (2) self-similar transport is rejected at all tenors, (3) the velocity profile v(k) is strike-dependent with U-shaped profiles at short tenors transitioning to decreasing profiles at long tenors, (4) the full (β,η,ψ) model outperforms SSR on curvature dynamics by 17-21% at medium tenors. The sequential forward-substitution estimator is directly implementable for real-time surface dynamics monitoring. The framework is particularly relevant for vanna/volga hedging, dynamic smile calibration, and risk management of option portfolios.

The theoretical framework involves advanced differential geometry, PDE theory, and functional analysis. However, the practical implementation (sequential forward-substitution estimator) is relatively straightforward: fit cubic polynomial to variance surface cross-sections, extract ATM jets, then solve a lower-triangular linear system via forward substitution. The main complexity lies in: (1) proper extraction of variance jets from market data with factorial scaling, (2) implementing the block-bootstrap Wald tests for strike-constancy, (3) handling the ill-conditioned covariance matrices, (4) the numerical PDE solver (Beam-Warming scheme) for transport equation validation. The empirical pipeline is well-specified but requires careful statistical implementation.

The paper provides detailed mathematical derivations, explicit estimation procedures (sequential forward substitution), and comprehensive empirical results with specific data parameters (n=1,118 observations, 7 tenors, 11 moneyness levels, July 2021-July 2026). However, the SPX data is proprietary (JPMorgan Chase), and no code repository is mentioned. The theoretical framework is fully specified with explicit equations, and the numerical validation section provides sufficient detail for replication on similar data. The estimator methodology is clearly described with all necessary formulas.