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Basket implied volatility skew and stickiness

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Listed:
  • Masaaki Fukasawa
  • Jun Maeda
  • Tatsuya Ogiwara

Abstract

We study the short-maturity implied volatility and the skew stickiness ratio for baskets of assets with continuous, possibly rough, stochastic volatility. The fluctuation of the instantaneous basket variance has two sources: fluctuations of the constituent variances and fluctuations of the basket weights. We derive a near-the-money implied volatility expansion that separates these contributions. We then specialize the result to volatility models given by general functions of Gaussian Volterra factors and obtain an explicit basket skew coefficient in terms of the short-time kernel asymptotics, the factor sensitivities, and the return-factor correlations. A density expansion justifies differentiation of the near-the-money expansion at the money. Finally, using a Malliavin representation of the dynamics of total implied variance, we prove that the short-maturity skew stickiness ratio converges to the universal limit $H + 3/2$ for Gaussian factor basket models with $H \in (0, 1/2]$.

Suggested Citation

  • Masaaki Fukasawa & Jun Maeda & Tatsuya Ogiwara, 2026. "Basket implied volatility skew and stickiness," Papers 2609.38230, arXiv.org.
    • Handle: RePEc:arx:papers:2609.38230
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    References listed on IDEAS

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    1. Masaaki Fukasawa, 2026. "On the Skew Stickiness Ratio," Papers 2602.05241, arXiv.org, revised Jun 2026.
    2. 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, revised Apr 2026.
    3. Masaaki Fukasawa, 2026. "Short-maturity skew stickiness ratio under local volatility," Papers 2609.11586, arXiv.org.
    4. Peter K. Friz & Thomas Wagenhofer, 2023. "Reconstructing volatility: Pricing of index options under rough volatility," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 19-40, January.
    5. Omar El Euch & Masaaki Fukasawa & Jim Gatheral & Mathieu Rosenbaum, 2018. "Short-term at-the-money asymptotics under stochastic volatility models," Papers 1801.08675, arXiv.org, revised Mar 2019.
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