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Pathwise super-replication via Vovk's outer measure

Author

Listed:
  • Mathias Beiglbock
  • Alexander M. G. Cox
  • Martin Huesmann
  • Nicolas Perkowski
  • David J. Promel

Abstract

Since Hobson's seminal paper [D. Hobson: Robust hedging of the lookback option. In: Finance Stoch. (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 super-replication 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 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.
    • Handle: RePEc:arx:papers:1504.03644
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    References listed on IDEAS

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    1. Alfred Galichon & Pierre Henri-Labordère & Nizar Touzi, 2013. "A stochastic control approach to No-Arbitrage bounds given marginals, with an application to Lookback options," Sciences Po publications info:hdl:2441/5rkqqmvrn4t, Sciences Po.
    2. David G. Hobson, 1998. "Robust hedging of the lookback option," Finance and Stochastics, Springer, vol. 2(4), pages 329-347.
    3. Alexander M. G. Cox & Jiajie Wang, 2013. "Optimal robust bounds for variance options," Papers 1308.4363, arXiv.org.
    4. Vladimir Vovk, 2012. "Continuous-time trading and the emergence of probability," Finance and Stochastics, Springer, vol. 16(4), pages 561-609, October.
    5. Alexander Cox & Jan Obłój, 2011. "Robust pricing and hedging of double no-touch options," Finance and Stochastics, Springer, vol. 15(3), pages 573-605, September.
    6. Mathias Beiglbock & Pierre Henry-Labord`ere & Friedrich Penkner, 2011. "Model-independent Bounds for Option Prices: A Mass Transport Approach," Papers 1106.5929, arXiv.org, revised Feb 2013.
    7. Haydyn Brown & David Hobson & L. C. G. Rogers, 2001. "Robust Hedging of Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 285-314, July.
    8. David Hobson & Martin Klimmek, 2012. "Model-independent hedging strategies for variance swaps," Finance and Stochastics, Springer, vol. 16(4), pages 611-649, October.
    9. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
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    11. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    12. Mathias Beiglböck & Pierre Henry-Labordère & Friedrich Penkner, 2013. "Model-independent bounds for option prices—a mass transport approach," Finance and Stochastics, Springer, vol. 17(3), pages 477-501, July.
    13. Vladimir Vovk, 2010. "Rough paths in idealized financial markets," Papers 1005.0279, arXiv.org, revised Nov 2016.
    14. Dylan Possamai & Guillaume Royer & Nizar Touzi, 2013. "On the Robust superhedging of measurable claims," Papers 1302.1850, arXiv.org, revised Feb 2013.
    15. Ariel Neufeld & Marcel Nutz, 2012. "Superreplication under Volatility Uncertainty for Measurable Claims," Papers 1208.6486, arXiv.org, revised Apr 2013.
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    17. Zhaoxu Hou & Jan Obloj, 2015. "On robust pricing-hedging duality in continuous time," Papers 1503.02822, arXiv.org, revised Jul 2015.
    18. Peter Imkeller & Nicolas Perkowski, 2015. "The existence of dominating local martingale measures," Finance and Stochastics, Springer, vol. 19(4), pages 685-717, October.
    19. Beatrice Acciaio & Mathias Beiglbock & Friedrich Penkner & Walter Schachermayer, 2013. "A model-free version of the fundamental theorem of asset pricing and the super-replication theorem," Papers 1301.5568, arXiv.org, revised Mar 2013.
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    Cited by:

    1. Alexander Schied & Iryna Voloshchenko, 2015. "Pathwise no-arbitrage in a class of Delta hedging strategies," Papers 1511.00026, arXiv.org, revised Jun 2016.
    2. Beatrice Acciaio & Martin Larsson, 2015. "Semi-static completeness and robust pricing by informed investors," Papers 1510.01890, arXiv.org, revised Sep 2016.

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