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Barrier Option Hedging under Constraints: A Viscosity Approach

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  • Imen Bentahar
  • Bruno Bouchard
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    Abstract

    We study the problem of finding the minimal initial capital needed in order to hedge without risk a barrier option when the vector of proportions of wealth invested in each risky asset is constraint to lie in a closed convex domain. In the context of a Brownian diffusion model, we provide a PDE characterization of the super-hedging price. This extends the result of Broadie, Cvitanic and Soner (1998) and Cvitanic, Pham and Touzi (1999) which was obtained for plain vanilla options, and provides a natural numerical procedure for computing the corresponding super-hedging price. As a by-product, we obtain a comparison theorem for a class of parabolic PDE with relaxed Dirichet conditions involving a constraint on the gradient.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-022.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-022.

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    Length: 42 pages
    Date of creation: Mar 2006
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    Handle: RePEc:hum:wpaper:sfb649dp2006-022

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    Keywords: Super-replication; barrier options; portfolio constraints; viscosity solutions;

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    1. Uwe Wystup & Uwe Schmock & Steven E. Shreve, 2002. "Valuation of exotic options under shortselling constraints," Finance and Stochastics, Springer, Springer, vol. 6(2), pages 143-172.
    2. Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
    3. repec:wop:humbsf:1997-31 is not listed on IDEAS
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