Approximating Functional of Local Martingale Under the Lack of Uniqueness of Black-Scholes PDE
AbstractWhen 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1102.2285.
Date of creation: Feb 2011
Date of revision: Sep 2012
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-02-19 (All new papers)
- NEP-CFN-2011-02-19 (Corporate Finance)
- NEP-CIS-2011-02-19 (Confederation of Independent States)
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