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Basket implied volatility skew and stickiness

  • Masaaki Fukasawa
  • Jun Maeda
  • Tatsuya Ogiwara
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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 ∈ (0, 1/2].

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Cite

BibTeXRIS
BibTeX
@misc{fukasawa2026basket,
  title = {{Basket implied volatility skew and stickiness}},
  author = {Masaaki Fukasawa and Jun Maeda and Tatsuya Ogiwara},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38230},
  eprint = {2609.38230},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38230},
}
RIS
TY  - UNPB
TI  - Basket implied volatility skew and stickiness
AU  - Masaaki Fukasawa
AU  - Jun Maeda
AU  - Tatsuya Ogiwara
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.38230
UR  - https://arxiv.org/abs/2609.38230
AB  - 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 ∈ (0, 1/2].
ER  -