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The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem

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  • Jim Gatheral
  • Paul Jusselin
  • Mathieu Rosenbaum

Abstract

Fitting simultaneously SPX and VIX smiles is known to be one of the most challenging problems in volatility modeling. A long-standing conjecture due to Julien Guyon is that it may not be possible to calibrate jointly these two quantities with a model with continuous sample-paths. We present the quadratic rough Heston model as a counterexample to this conjecture. The key idea is the combination of rough volatility together with a price-feedback (Zumbach) effect.

Suggested Citation

  • Jim Gatheral & Paul Jusselin & Mathieu Rosenbaum, 2020. "The quadratic rough Heston model and the joint S&P 500/VIX smile calibration problem," Papers 2001.01789, arXiv.org.
    • Handle: RePEc:arx:papers:2001.01789
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Sep 2023.
    2. Léo Parent, 2022. "The EWMA Heston model," Post-Print hal-04431111, HAL.
    3. Julien Guyon, 2020. "Inversion of convex ordering in the VIX market," Quantitative Finance, Taylor & Francis Journals, vol. 20(10), pages 1597-1623, October.
    4. Zhiqiang Zhou & Wei Xu & Alexey Rubtsov, 2024. "Joint calibration of S&P 500 and VIX options under local stochastic volatility models," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(1), pages 273-310, January.
    5. Mathieu Rosenbaum & Jianfei Zhang, 2021. "Deep calibration of the quadratic rough Heston model," Papers 2107.01611, arXiv.org, revised May 2022.
    6. Brian Huge & Antoine Savine, 2020. "Differential Machine Learning," Papers 2005.02347, arXiv.org, revised Sep 2020.
    7. Sudarshan Kumar & Sobhesh Kumar Agarwalla & Jayanth R. Varma & Vineet Virmani, 2023. "Harvesting the volatility smile in a large emerging market: A Dynamic Nelson–Siegel approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(11), pages 1615-1644, November.
    8. Martino Grasselli & Andrea Mazzoran & Andrea Pallavicini, 2020. "A general framework for a joint calibration of VIX and VXX options," Papers 2012.08353, arXiv.org, revised Jun 2021.
    9. Lech A. Grzelak, 2022. "On Randomization of Affine Diffusion Processes with Application to Pricing of Options on VIX and S&P 500," Papers 2208.12518, arXiv.org.
    10. Carsten Chong & Marc Hoffmann & Yanghui Liu & Mathieu Rosenbaum & Gr'egoire Szymanski, 2022. "Statistical inference for rough volatility: Minimax Theory," Papers 2210.01214, arXiv.org, revised Feb 2024.
    11. Mathieu Rosenbaum & Jianfei Zhang, 2022. "Multi-asset market making under the quadratic rough Heston," Papers 2212.10164, arXiv.org.
    12. Ivan Guo & Gregoire Loeper & Jan Obloj & Shiyi Wang, 2020. "Joint Modelling and Calibration of SPX and VIX by Optimal Transport," Papers 2004.02198, arXiv.org, revised Sep 2021.
    13. Carsten Chong & Marc Hoffmann & Yanghui Liu & Mathieu Rosenbaum & Gr'egoire Szymanski, 2022. "Statistical inference for rough volatility: Central limit theorems," Papers 2210.01216, arXiv.org, revised Jul 2023.
    14. Nelson Vadori, 2022. "Calibration of Derivative Pricing Models: a Multi-Agent Reinforcement Learning Perspective," Papers 2203.06865, arXiv.org, revised Oct 2023.
    15. Ofelia Bonesini & Giorgia Callegaro & Martino Grasselli & Gilles Pag`es, 2023. "From elephant to goldfish (and back): memory in stochastic Volterra processes," Papers 2306.02708, arXiv.org, revised Sep 2023.
    16. Jean-Philippe Bouchaud, 2021. "Radical Complexity," Papers 2103.09692, arXiv.org.
    17. Siu Hin Tang & Mathieu Rosenbaum & Chao Zhou, 2023. "Forecasting Volatility with Machine Learning and Rough Volatility: Example from the Crypto-Winter," Papers 2311.04727, arXiv.org, revised Feb 2024.
    18. Christa Cuchiero & Guido Gazzani & Janka Moller & Sara Svaluto-Ferro, 2023. "Joint calibration to SPX and VIX options with signature-based models," Papers 2301.13235, arXiv.org.
    19. Mathieu Rosenbaum & Jianfei Zhang, 2022. "On the universality of the volatility formation process: when machine learning and rough volatility agree," Papers 2206.14114, arXiv.org.

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