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Robust bounds for the American Put

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  • David Hobson
  • Dominykas Norgilas

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 $T_1$ or $T_2$ 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 and an associated exercise time, for which the price of the American put is maximal. Moreover we derive a cheapest superhedge. The model associated with the highest price of the American put is constructed from the left-curtain martingale transport of Beiglb\"{o}ck and Juillet.

Suggested Citation

  • David Hobson & Dominykas Norgilas, 2017. "Robust bounds for the American Put," Papers 1711.06466, arXiv.org, revised May 2018.
    • Handle: RePEc:arx:papers:1711.06466
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    References listed on IDEAS

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    1. 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.
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    3. 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.
    4. Peter Carr & Roger Lee, 2010. "Hedging variance options on continuous semimartingales," Finance and Stochastics, Springer, vol. 14(2), pages 179-207, April.
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    6. Alexander M. G. Cox & Jiajie Wang, 2013. "Optimal robust bounds for variance options," Papers 1308.4363, arXiv.org.
    7. 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.
    8. David Hobson & Anthony Neuberger, 2016. "More on hedging American options under model uncertainty," Papers 1604.02274, arXiv.org.
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