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

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  • Eduardo Abi Jaber

    (Xiaoyuan)

  • 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 over two years. Furthermore, the Quintic model shows consistency with key empirical stylized facts, notably reproducing the Zumbach effect.

Suggested Citation

  • Eduardo Abi Jaber & Shaun & Li, 2025. "Capturing Smile Dynamics with the Quintic Volatility Model: SPX, Skew-Stickiness Ratio and VIX," Papers 2503.14158, arXiv.org.
    • Handle: RePEc:arx:papers:2503.14158
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    References listed on IDEAS

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    1. Gilles Zumbach, 2009. "Time reversal invariance in finance," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 505-515.
    2. Eduardo Abi Jaber & Camille Illand & Shaun & Li, 2022. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Papers 2212.08297, arXiv.org, revised Dec 2024.
    3. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    4. Gilles Zumbach, 2010. "Volatility conditional on price trends," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 431-442.
    5. Pagès Gilles & Printems Jacques, 2003. "Optimal quadratic quantization for numerics: the Gaussian case," Monte Carlo Methods and Applications, De Gruyter, vol. 9(2), pages 135-165, April.
    6. Eduardo Abi Jaber & Camille Illand & Shaun Xiaoyuan Li, 2024. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03902513, HAL.
    7. Eduardo Abi Jaber & Camille Illand & Shaun Xiaoyuan Li, 2024. "Joint SPX-VIX calibration with Gaussian polynomial volatility models: deep pricing with quantization hints," Post-Print hal-03902513, HAL.
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