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Robust bounds for the American put

Author

Listed:
  • David Hobson

    (University of Warwick)

  • Dominykas Norgilas

    (University of Warwick)

Abstract

We consider the problem of finding a model-free upper bound on the price of an American put given the prices of a family of European puts on the same underlying asset. Specifically, we assume that the American put must be exercised at either T 1 $T_{1}$ or T 2 $T_{2}$ and that we know the prices of all vanilla European puts with these maturities. In this setting, we find a model which is consistent with European put prices, together with an associated exercise time, for which the price of the American put is maximal. Moreover, we derive the cheapest superhedge. The model associated with the highest price of the American put is constructed from the left-curtain martingale coupling of Beiglböck and Juillet (Ann. Probab. 44:42–106, 2016).

Suggested Citation

  • David Hobson & Dominykas Norgilas, 2019. "Robust bounds for the American put," Finance and Stochastics, Springer, vol. 23(2), pages 359-395, April.
    • Handle: RePEc:spr:finsto:v:23:y:2019:i:2:d:10.1007_s00780-019-00385-4
    DOI: 10.1007/s00780-019-00385-4
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    References listed on IDEAS

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    Cited by:

    1. Benjamin Jourdain & Gudmund Pammer, 2023. "An extension of martingale transport and stability in robust finance," Papers 2304.09551, arXiv.org.
    2. Erhan Bayraktar & Shuoqing Deng & Dominykas Norgilas, 2023. "Supermartingale Brenier’s Theorem with Full-Marginal Constraint," World Scientific Book Chapters, in: Robert A Jarrow & Dilip B Madan (ed.), Peter Carr Gedenkschrift Research Advances in Mathematical Finance, chapter 17, pages 569-636, World Scientific Publishing Co. Pte. Ltd..
    3. Julian Sester, 2023. "On intermediate Marginals in Martingale Optimal Transportation," Papers 2307.09710, arXiv.org, revised Nov 2023.

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    More about this item

    Keywords

    Model-independent pricing; American put; Martingale optimal transport; Left-curtain coupling; Optimal stopping;
    All these keywords.

    JEL classification:

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

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