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Root's barrier: Construction, optimality and applications to variance options

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  • Alexander M. G. Cox
  • Jiajie Wang
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    Abstract

    Recent work of Dupire and Carr and Lee has highlighted the importance of understanding the Skorokhod embedding originally proposed by Root for the model-independent hedging of variance options. Root's work shows that there exists a barrier from which one may define a stopping time which solves the Skorokhod embedding problem. This construction has the remarkable property, proved by Rost, that it minimizes the variance of the stopping time among all solutions. In this work, we prove a characterization of Root's barrier in terms of the solution to a variational inequality, and we give an alternative proof of the optimality property which has an important consequence for the construction of subhedging strategies in the financial context.

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    File URL: http://arxiv.org/pdf/1104.3583
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1104.3583.

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    Date of creation: Apr 2011
    Date of revision: Mar 2013
    Publication status: Published in Annals of Applied Probability 2013, Vol. 23, No. 3, 859-894
    Handle: RePEc:arx:papers:1104.3583

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    Web page: http://arxiv.org/

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    1. Haydyn Brown & David Hobson & L. C. G. Rogers, 2001. "Robust Hedging of Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 11(3), pages 285-314.
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    Cited by:
    1. Alexander M. G. Cox & Jiajie Wang, 2013. "Optimal robust bounds for variance options," Papers 1308.4363, arXiv.org.
    2. Y. Dolinsky & H. M. Soner, 2014. "Martingale optimal transport in the Skorokhod space," Papers 1404.1516, arXiv.org.

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