Computing the SSR

ArXiv ID: 2406.16131 “View on arXiv”

Authors: Unknown

Abstract

The skew-stickiness-ratio (SSR), examined in detail by Bergomi in his book, is critically important to options traders, especially market makers. We present a model-free expression for the SSR in terms of the characteristic function. In the diffusion setting, it is well-known that the short-term limit of the SSR is 2; a corollary of our results is that this limit is $H+3/2$ where $H$ is the Hurst exponent of the volatility process. The general formula for the SSR simplifies and becomes particularly tractable in the affine forward variance case. We explain the qualitative behavior of the SSR with respect to the shape of the forward variance curve, and thus also path-dependence of the SSR.

Keywords: Skew-Stickiness-Ratio (SSR), Hurst Exponent, Affine Forward Variance, Volatility Modeling

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper introduces highly advanced stochastic calculus and characteristic function techniques to derive a model-free expression for the SSR, with heavy reliance on derivatives and integrals. However, it lacks any backtesting, code, or implementation details, focusing purely on theoretical derivation without empirical data.

  flowchart TD
    A["Research Goal:<br/>Derive Model-Free Expression<br/>for Skew-Stickiness-Ratio (SSR)"] --> B["Methodology:<br/>Analysis via Characteristic Function"]
    B --> C["Key Input:<br/>Affine Forward Variance Model"]
    C --> D{"Computational Process"}
    D --> E["General Formula Derivation"]
    D --> F["Short-Term Limit Analysis"]
    E --> G["Key Findings/Outcomes"]
    F --> G
    G --> H["Limit: H + 3/2<br/>(H = Hurst Exponent)"]
    G --> I["SSR Behavior<br/>(Path-dependent & Shaped by<br/>Forward Variance Curve)"]
    style A fill:#f9f,stroke:#333,stroke-width:2px
    style G fill:#ccf,stroke:#333,stroke-width:2px