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Approximating Functional of Local Martingale Under the Lack of Uniqueness of Black-Scholes PDE

  • Qingshuo Song
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    When the underlying stock price is a strict local martingale process under an equivalent local martingale measure, Black-Scholes PDE associated with an European option may have multiple solutions. In this paper, we study an approximation for the smallest hedging price of such an European option. Our results show that a class of rebate barrier options can be used for this approximation. Among of them, a specific rebate option is also provided with a continuous rebate function, which corresponds to the unique classical solution of the associated parabolic PDE. Such a construction makes existing numerical PDE techniques applicable for its computation. An asymptotic convergence rate is also studied when the knocked-out barrier moves to infinity under suitable conditions.

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    File URL: http://arxiv.org/pdf/1102.2285
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    Paper provided by arXiv.org in its series Papers with number 1102.2285.

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    Date of creation: Feb 2011
    Date of revision: Sep 2012
    Handle: RePEc:arx:papers:1102.2285
    Contact details of provider: Web page: http://arxiv.org/

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    1. Erhan Bayraktar & Hao Xing, 2009. "On the uniqueness of classical solutions of Cauchy problems," Papers 0908.1086, arXiv.org, revised Sep 2009.
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