Short-maturity skew stickiness ratio under local volatility

Paper: arXiv 2609.11586

Authors: Masaaki Fukasawa

Abstract

We prove that the skew stickiness ratio converges to two at short maturity under local volatility models. This appears to be the first rigorous proof of this limit for a general time-dependent local volatility function. As a by-product, we strengthen the one-half rule of the implied volatility skew by removing uniform ellipticity and global bounds on spatial derivatives of order at least two. The proof uses a first-order Watanabe expansion.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly mathematical and novel proof regarding the short-maturity skew stickiness ratio. While the theoretical contribution is significant, it lacks any empirical validation or backtesting, focusing purely on mathematical derivation. The clarity is good for a highly technical paper, and the methodology is detailed enough for replication by experts.

Research Flowchart

  flowchart TD
    A[Research Goal: Skew Stickiness Ratio at Short Maturity] --> B{Methodology: Local Volatility & Watanabe Expansion};
    B --> C[Inputs: General Time-Dependent Local Volatility Function];
    C --> D{Computational Process: First-Order Watanabe Expansion & Asymptotic Analysis};
    D --> E[Outcome 1: Skew Stickiness Ratio converges to 2 at short maturity];
    D --> F[Outcome 2: Strengthened One-Half Rule (removed ellipticity/derivative bounds)];