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Optimal robust bounds for variance options

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  • Alexander M. G. Cox
  • Jiajie Wang

Abstract

Robust, or model-independent properties of the variance swap are well-known, and date back to Dupire and Neuberger, who showed that, given the price of co-terminal call options, the price of a variance swap was exactly specified under the assumption that the price process is continuous. In Cox and Wang we showed that a lower bound on the price of a variance call could be established using a solution to the Skorokhod embedding problem due to Root. In this paper, we provide a construction, and a proof of optimality of the upper bound, using results of Rost and Chacon, and show how this proof can be used to determine a super-hedging strategy which is model-independent. In addition, we outline how the hedging strategy may be computed numerically. Using these methods, we also show that the Heston-Nandi model is 'asymptotically extreme' in the sense that, for large maturities, the Heston-Nandi model gives prices for variance call options which are approximately the lowest values consistent with the same call price data.

Suggested Citation

  • Alexander M. G. Cox & Jiajie Wang, 2013. "Optimal robust bounds for variance options," Papers 1308.4363, arXiv.org.
    • Handle: RePEc:arx:papers:1308.4363
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Tiziano De Angelis, 2020. "Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon," Papers 2009.01276, arXiv.org, revised Jan 2022.
    2. Sergey Badikov & Mark H. A. Davis & Antoine Jacquier, 2018. "Perturbation analysis of sub/super hedging problems," Papers 1806.03543, arXiv.org, revised May 2021.
    3. David Hobson & Dominykas Norgilas, 2017. "Robust bounds for the American Put," Papers 1711.06466, arXiv.org, revised May 2018.
    4. Alexander M. G. Cox & Annemarie M. Grass, 2023. "Robust option pricing with volatility term structure -- An empirical study for variance options," Papers 2312.09201, arXiv.org.
    5. De Angelis, Tiziano & Kitapbayev, Yerkin, 2017. "Integral equations for Rost’s reversed barriers: Existence and uniqueness results," Stochastic Processes and their Applications, Elsevier, vol. 127(10), pages 3447-3464.
    6. Sergey Badikov & Mark H.A. Davis & Antoine Jacquier, 2021. "Perturbation analysis of sub/super hedging problems," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1240-1274, October.
    7. Gassiat, Paul & Oberhauser, Harald & dos Reis, Gonçalo, 2015. "Root’s barrier, viscosity solutions of obstacle problems and reflected FBSDEs," Stochastic Processes and their Applications, Elsevier, vol. 125(12), pages 4601-4631.
    8. Mathias Beiglböck & Alexander M. G. Cox & Martin Huesmann & Nicolas Perkowski & David J. Prömel, 2017. "Pathwise superreplication via Vovk’s outer measure," Finance and Stochastics, Springer, vol. 21(4), pages 1141-1166, October.
    9. Mathias Beiglbock & Alexander M. G. Cox & Martin Huesmann & Nicolas Perkowski & David J. Promel, 2015. "Pathwise super-replication via Vovk's outer measure," Papers 1504.03644, arXiv.org, revised Jul 2016.
    10. Alexander M. G. Cox & Sam M. Kinsley, 2017. "Robust Hedging of Options on a Leveraged Exchange Traded Fund," Papers 1702.07169, arXiv.org.
    11. Cox, Alexander M.G. & Kinsley, Sam M., 2019. "Discretisation and duality of optimal Skorokhod embedding problems," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2376-2405.
    12. Mathias Beiglboeck & Alexander Cox & Martin Huesmann, 2017. "The geometry of multi-marginal Skorokhod Embedding," Papers 1705.09505, arXiv.org.

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