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Performance Of Robust Hedges For Digital Double Barrier Options

In: Finance at Fields

Author

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  • JAN OBŁÓJ

    (Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford OX1 3LB, United Kingdom and Oxford-Man Institute of Quantitative Finance, Eagle House, Walton Well Road, Oxford OX2 6ED, United Kingdom)

  • FRÉDÉRIK ULMER

    (Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford OX1 3LB, United Kingdom)

Abstract

We analyze the performance of robust hedging strategies of digital double barrier options of Cox and Obłój (2011) against that of traditional hedging methods such as delta and delta/vega hedging. Digital double barrier options are financial derivative contracts which pay out a fixed amount on the condition that the underlying asset remains within or breaks into a range defined by two distinct barrier levels. We perform the analysis in hypothetical forward markets driven by models with stochastic volatility and jumps, calibrated to the AUD/USD foreign exchange rate market. Our findings are strikingly unanimous and suggest that, in the presence of model uncertainty and/or transaction costs, robust hedging strategies typically outperform in a substantial way model-specific hedging methods.

Suggested Citation

  • Jan Obłój & Frédérik Ulmer, 2012. "Performance Of Robust Hedges For Digital Double Barrier Options," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 23, pages 521-554, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814407892_0023
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    Citations

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    Cited by:

    1. Sergey Nadtochiy & Jan Obloj, 2016. "Robust Trading of Implied Skew," Papers 1611.05518, arXiv.org.
    2. Zhaoxu Hou & Jan Obloj, 2015. "On robust pricing-hedging duality in continuous time," Papers 1503.02822, arXiv.org, revised Jul 2015.
    3. 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.
    4. Sergey Nadtochiy & Jan Obłój, 2017. "Robust Trading Of Implied Skew," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(02), pages 1-41, March.
    5. Sebastian Herrmann & Johannes Muhle-Karbe, 2017. "Model uncertainty, recalibration, and the emergence of delta–vega hedging," Finance and Stochastics, Springer, vol. 21(4), pages 873-930, October.
    6. Zhaoxu Hou & Jan Obłój, 2018. "Robust pricing–hedging dualities in continuous time," Finance and Stochastics, Springer, vol. 22(3), pages 511-567, July.
    7. Sebastian Herrmann & Johannes Muhle-Karbe, 2017. "Model Uncertainty, Recalibration, and the Emergence of Delta-Vega Hedging," Papers 1704.04524, arXiv.org.
    8. Sergey Badikov & Mark H. A. Davis & Antoine Jacquier, 2018. "Perturbation analysis of sub/super hedging problems," Papers 1806.03543, arXiv.org, revised May 2021.

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