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Pricing Bounds on Barrier Options (forthcoming in "Journal of Futures Markets")

Author

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  • Yukihiro Tsuzuki

    (The University of Tokyo)

Abstract

This paper 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-hedging 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 a 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 which are calibrated to market prices of plain-vanilla options, but not to that of a no-touch option.

Suggested Citation

  • Yukihiro Tsuzuki, 2013. "Pricing Bounds on Barrier Options (forthcoming in "Journal of Futures Markets")," CARF F-Series CARF-F-325, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    • Handle: RePEc:cfi:fseres:cf325
    as

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    File URL: https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/F325.pdf
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    References listed on IDEAS

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