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VIX options in Bergomi models

Author

Listed:
  • Desen Guo
  • Dan Pirjol
  • Lingjiong Zhu

Abstract

We present a study of the leading-order asymptotics for VIX option prices in Bergomi models in the short-maturity and small volatility-of-volatility regimes. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered for one-factor, two-factor Bergomi and $N$-factor models. The leading-order asymptotics are obtained in closed-form, which are translated into predictions for the small-maturity asymptotics of the VIX implied volatility. Numerical illustrations are provided to illustrate the efficiency of the closed-form asymptotic formulas.

Suggested Citation

  • Desen Guo & Dan Pirjol & Lingjiong Zhu, 2026. "VIX options in Bergomi models," Papers 2606.02336, arXiv.org.
    • Handle: RePEc:arx:papers:2606.02336
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    References listed on IDEAS

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    1. Dan Pirjol & Lingjiong Zhu, 2025. "VIX options in the SABR model," Papers 2501.06398, arXiv.org, revised Jul 2025.
    2. repec:hal:wpaper:hal-03909334 is not listed on IDEAS
    3. Eduardo Abi Jaber & Camille Illand & Shaun & Li, 2022. "The quintic Ornstein-Uhlenbeck volatility model that jointly calibrates SPX & VIX smiles," Papers 2212.10917, arXiv.org, revised May 2023.
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    5. Desen Guo & Dan Pirjol & Xiaoyu Wang & Lingjiong Zhu, 2026. "VIX and European options with jumps in the short-maturity regime," Papers 2601.17248, arXiv.org.
    6. Julien Guyon, 2024. "Dispersion-constrained martingale Schrödinger problems and the exact joint S&P 500/VIX smile calibration puzzle," Finance and Stochastics, Springer, vol. 28(1), pages 27-79, January.
    7. Eduardo Abi Jaber & Camille Illand & Shaun Xiaoyuan Li, 2023. "The quintic Ornstein-Uhlenbeck volatility model that jointly calibrates SPX & VIX smiles," Post-Print hal-03909334, HAL.
    8. Thomas Kokholm & Martin Stisen, 2015. "Joint pricing of VIX and SPX options with stochastic volatility and jump models," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 16(1), pages 27-48, January.
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    11. Christa Cuchiero & Guido Gazzani & Janka Möller & Sara Svaluto‐Ferro, 2025. "Joint calibration to SPX and VIX options with signature‐based models," Mathematical Finance, Wiley Blackwell, vol. 35(1), pages 161-213, January.
    12. Nelson Kyakutwika & Mesias Alfeus & Erik Schlogl, 2025. "Pricing and Calibration of VIX Derivatives in Mixed Bergomi Models via Quantisation," Papers 2506.23409, arXiv.org.
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