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Capturing Smile Dynamics with the Quintic Volatility Model: SPX, Skew-Stickiness Ratio and VIX

Author

Listed:
  • Eduardo Abi Jaber

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Shaun Xiaoyuan Li

Abstract

We introduce the two-factor Quintic Ornstein-Uhlenbeck model, where volatility is modeled as a polynomial of degree five based on the sum of two Ornstein-Uhlenbeck processes driven by the same Brownian Motion, each mean-reverting at a different speed. We demonstrate that the Quintic model effectively captures the volatility surfaces of SPX and VIX while aligning with the skew-stickiness ratio (SSR) across maturities ranging from a few days to two over years. Furthermore, the Quintic model shows consistency with key empirical stylized facts, notably reproducing the Zumbach effect.

Suggested Citation

  • Eduardo Abi Jaber & Shaun Xiaoyuan Li, 2025. "Capturing Smile Dynamics with the Quintic Volatility Model: SPX, Skew-Stickiness Ratio and VIX," Working Papers hal-04995809, HAL.
    • Handle: RePEc:hal:wpaper:hal-04995809
    Note: View the original document on HAL open archive server: https://hal.science/hal-04995809v1
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