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arXiv · 2503.14158

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

Eduardo Abi Jaber·Shaun·Li
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Abstract

We introduce the two-factor Quintic Ornstein-Uhlenbeck (OU) model, where volatility is modelled as a degree-five polynomial of the sum of two Ornstein-Uhlenbeck processes driven by the same Brownian motion, each mean-reverting at a different speed. We demonstrate that the 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, it is consistent with key empirical stylized facts, notably reproducing the Zumbach effect.

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Eduardo Abi Jaber, Shaun, Li. 2025-03-18. Capturing Smile Dynamics with the Quintic Volatility Model: SPX, Skew-Stickiness Ratio and VIX. https://arxiv.org/abs/2503.14158

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