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Pricing Bounds on Barrier Options

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  • Yukihiro Tsuzuki

Abstract

This article proposes the optimal pricing bounds on barrier options in an environment where plain‐vanilla options and no‐touch options can be used as hedging instruments. Super‐ and sub‐hedging portfolios are derived without specifying any underlying processes, which are static ones consisting of not only plain‐vanilla options but also cash‐paying no‐touch options and/or asset paying no‐touch options that pay one cash or one underlying asset, respectively, if the barrier has not been hit. Moreover, the prices of these portfolios turn out to be the optimal pricing bounds through finding risk‐neutral measures under which the barrier option price is equal to the hedging portfolio's value. The model‐independent pricing bounds are useful because the price of a barrier option is significantly dependent on a model. It is demonstrated through numerical examples that prices outside the pricing bounds can be produced by models that are calibrated to market prices of plain‐vanilla options, but not to that of a no‐touch option. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:1170–1184, 2014

Suggested Citation

  • Yukihiro Tsuzuki, 2014. "Pricing Bounds on Barrier Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(12), pages 1170-1184, December.
    • Handle: RePEc:wly:jfutmk:v:34:y:2014:i:12:p:1170-1184
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    Cited by:

    1. Frido Rolloos & Kenichiro Shiraya, 2024. "A model‐free approximation for barrier options in a general stochastic volatility framework," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(6), pages 923-935, June.
    2. Kenichiro Shiraya, 2016. "An approximation method for pricing continuous barrier options under multi-asset local stochastic volatility models (Forthcoming in International Journal of Theoretical and Applied Finance.)," CARF F-Series CARF-F-397, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Nov 2018.
    3. Baule, Rainer & Shkel, David, 2021. "Model risk and model choice in the case of barrier options and bonus certificates," Journal of Banking & Finance, Elsevier, vol. 133(C).

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