Paper: arXiv 2602.05241

Authors: Masaaki Fukasawa

Abstract

The skew stickiness ratio is a statistic that captures the joint dynamics of an asset price and its volatility. We derive a representation formula for this quantity using the Itô-Wentzell and Clark-Ocone formulae, and we apply it to analyze its asymptotics under Bergomi-type stochastic volatility models.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical foundation for the Skew Stickiness Ratio (SSR) using the Itô-Wentzell and Clark-Ocone formulae under stochastic volatility and rough volatility models. While it excels in theoretical derivations and asymptotic analyses, it lacks empirical backtesting or real market data validation.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Analyze Skew Stickiness Ratio & Dynamics"] --> B["Inputs:<br>Asset Price, Volatility & Bergomi Models"]
    B --> C["Derive Representation:<br>Apply Itô-Wentzell & Clark-Ocone Formulae"]
    C --> D["Asymptotic Analysis:<br>Evaluate Behavior Under Bergomi Volatility"]
    D --> E["Key Outcome:<br>Asymptotic Formula for Joint Price-Vol Dynamics"]