IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1910.05750.html
   My bibliography  Save this paper

Inversion of Convex Ordering: Local Volatility Does Not Maximize the Price of VIX Futures

Author

Listed:
  • Beatrice Acciaio
  • Julien Guyon

Abstract

It has often been stated that, within the class of continuous stochastic volatility models calibrated to vanillas, the price of a VIX future is maximized by the Dupire local volatility model. In this article we prove that this statement is incorrect: we build a continuous stochastic volatility model in which a VIX future is strictly more expensive than in its associated local volatility model. More generally, in this model, strictly convex payoffs on a squared VIX are strictly cheaper than in the associated local volatility model. This corresponds to an inversion of convex ordering between local and stochastic variances, when moving from instantaneous variances to squared VIX, as convex payoffs on instantaneous variances are always cheaper in the local volatility model. We thus prove that this inversion of convex ordering, which is observed in the SPX market for short VIX maturities, can be produced by a continuous stochastic volatility model. We also prove that the model can be extended so that, as suggested by market data, the convex ordering is preserved for long maturities.

Suggested Citation

  • Beatrice Acciaio & Julien Guyon, 2019. "Inversion of Convex Ordering: Local Volatility Does Not Maximize the Price of VIX Futures," Papers 1910.05750, arXiv.org.
    • Handle: RePEc:arx:papers:1910.05750
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1910.05750
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Daniel Lacker & Mykhaylo Shkolnikov & Jiacheng Zhang, 2019. "Inverting the Markovian projection, with an application to local stochastic volatility models," Papers 1905.06213, arXiv.org.
    2. Frédéric Abergel & Rémi Tachet, 2010. "A nonlinear partial integro-differential equation from mathematical finance," Post-Print hal-00611962, HAL.
    3. Mathias Beiglboeck & Peter Friz & Stephan Sturm, 2010. "Is the minimum value of an option on variance generated by local volatility?," Papers 1001.4031, arXiv.org, revised Jan 2011.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Acciaio, Beatrice & Guyon, Julien, 2020. "Short communication: inversion of convex ordering: local volatility does not maximise the price of VIX futures," LSE Research Online Documents on Economics 102984, London School of Economics and Political Science, LSE Library.
    2. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A Generative Adversarial Network Approach to Calibration of Local Stochastic Volatility Models," Risks, MDPI, vol. 8(4), pages 1-31, September.
    3. Martin Larsson & Shukun Long, 2024. "Markovian projections for It\^o semimartingales with jumps," Papers 2403.15980, arXiv.org.
    4. Ivan Guo & Gregoire Loeper, 2018. "Path Dependent Optimal Transport and Model Calibration on Exotic Derivatives," Papers 1812.03526, arXiv.org, revised Sep 2020.
    5. Fairouz Tchier & Ioannis Dassios & Ferdous Tawfiq & Lakhdar Ragoub, 2021. "On the Approximate Solution of Partial Integro-Differential Equations Using the Pseudospectral Method Based on Chebyshev Cardinal Functions," Mathematics, MDPI, vol. 9(3), pages 1-14, February.
    6. Mao Fabrice Djete, 2022. "Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility models," Papers 2208.09986, arXiv.org, revised Oct 2024.
    7. Christa Cuchiero & Wahid Khosrawi & Josef Teichmann, 2020. "A generative adversarial network approach to calibration of local stochastic volatility models," Papers 2005.02505, arXiv.org, revised Sep 2020.
    8. Frédéric Abergel & Rémy Tachet Des Combes & Riadh Zaatour, 2017. "Nonparametric model calibration for derivatives," Post-Print hal-01686114, HAL.
    9. Frédéric Abergel & Rémy Tachet Des Combes & Riadh Zaatour, 2017. "Nonparametric model calibration for derivatives," Post-Print hal-01399542, HAL.
    10. Ivan Guo & Grégoire Loeper & Shiyi Wang, 2022. "Calibration of local‐stochastic volatility models by optimal transport," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 46-77, January.
    11. Christoph Reisinger & Maria Olympia Tsianni, 2023. "Convergence of the Euler--Maruyama particle scheme for a regularised McKean--Vlasov equation arising from the calibration of local-stochastic volatility models," Papers 2302.00434, arXiv.org, revised Aug 2023.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1910.05750. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.