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Pathwise superreplication via Vovk’s outer measure

Author

Listed:
  • Mathias Beiglböck

    (TU Wien)

  • Alexander M. G. Cox

    (University of Bath)

  • Martin Huesmann

    (Rheinische Friedrich-Wilhelms-Universität Bonn)

  • Nicolas Perkowski

    (Humboldt-Universität zu Berlin)

  • David J. Prömel

    (ETH Zürich)

Abstract

Since Hobson’s seminal paper (Hobson in Finance Stoch. 2:329–347, 1998), the connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance. We establish a general pricing–hedging duality for financial derivatives which are susceptible to the Skorokhod approach. Using Vovk’s approach to mathematical finance, we derive a model-independent superreplication theorem in continuous time, given information on finitely many marginals. Our result covers a broad range of exotic derivatives, including lookback options, discretely monitored Asian options, and options on realized variance.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:21:y:2017:i:4:d:10.1007_s00780-017-0338-2
    DOI: 10.1007/s00780-017-0338-2
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Łochowski, Rafał M. & Perkowski, Nicolas & Prömel, David J., 2018. "A superhedging approach to stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4078-4103.
    2. Terry Lyons & Sina Nejad & Imanol Perez Arribas, 2019. "Numerical method for model-free pricing of exotic derivatives using rough path signatures," Papers 1905.01720, arXiv.org, revised Feb 2020.
    3. Nutz, Marcel & Stebegg, Florian & Tan, Xiaowei, 2020. "Multiperiod martingale transport," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1568-1615.
    4. Hölzermann, Julian, 2020. "Pricing Interest Rate Derivatives under Volatility Uncertainty," Center for Mathematical Economics Working Papers 633, Center for Mathematical Economics, Bielefeld University.
    5. Zhaoxu Hou & Jan Obłój, 2018. "Robust pricing–hedging dualities in continuous time," Finance and Stochastics, Springer, vol. 22(3), pages 511-567, July.
    6. Christian Bender & Sebastian Ferrando & Alfredo Gonzalez, 2021. "Model-Free Finance and Non-Lattice Integration," Papers 2105.10623, arXiv.org.
    7. Rafa{l} M. {L}ochowski & Nicolas Perkowski & David J. Promel, 2021. "One-dimensional game-theoretic differential equations," Papers 2101.08041, arXiv.org.
    8. Patrick Cheridito & Matti Kiiski & David J. Promel & H. Mete Soner, 2019. "Martingale optimal transport duality," Papers 1904.04644, arXiv.org, revised Nov 2020.
    9. Daniel Bartl & Michael Kupper & Ariel Neufeld, 2017. "Pathwise superhedging on prediction sets," Papers 1711.02764, arXiv.org, revised Oct 2019.
    10. Huesmann, Martin & Stebegg, Florian, 2018. "Monotonicity preserving transformations of MOT and SEP," Stochastic Processes and their Applications, Elsevier, vol. 128(4), pages 1114-1134.
    11. Laurence Carassus & Jan Obloj & Johannes Wiesel, 2018. "The robust superreplication problem: a dynamic approach," Papers 1812.11201, arXiv.org, revised Feb 2019.
    12. 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.
    13. Julian Holzermann, 2020. "Pricing Interest Rate Derivatives under Volatility Uncertainty," Papers 2003.04606, arXiv.org, revised Nov 2021.
    14. 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.
    15. Cornelis, Erwin, 2019. "History and prospect of voluntary agreements on industrial energy efficiency in Europe," Energy Policy, Elsevier, vol. 132(C), pages 567-582.

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    More about this item

    Keywords

    Model-independent pricing; Optimal transport; Skorokhod embedding; Superreplication theorem; Vovk’s outer measure;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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