Short-maturity skew stickiness ratio under local volatility

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Highly relevant for options traders and risk managers working with local volatility models. The SSR=2 result provides a benchmark for model validation: if observed SSR deviates significantly from 2, it suggests the local volatility framework is inadequate. This is directly applicable to smile dynamics modeling, cross-gamma risk management, and calibration of implied volatility surfaces. However, the result is theoretical and does not provide a trading strategy or numerical implementation directly.

The result itself (SSR converges to 2) is trivially simple to implement as a benchmark check. The proof is mathematically sophisticated but does not require computational implementation. For practitioners, verifying SSR=2 in a local vol model calibration is straightforward. The theoretical machinery (Watanabe expansion, Malliavin calculus) is not needed for practical application of the result.

The paper is a pure mathematical proof with all assumptions clearly stated (Assumption 1) and a complete proof provided. The methodology relies on well-established tools (Watanabe expansion, Malliavin calculus, Burkholder-Davis-Gundy inequality). No numerical experiments are needed to verify the result. The proof is self-contained and can be verified by experts in stochastic analysis. However, the advanced nature of the mathematics (Watanabe's theory of generalized Wiener functionals) limits accessibility.