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Perpetual Barrier Options in Jump-Diffusion Models

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  • Pavel V. Gapeev
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    Abstract

    We present a closed form solution to the perpetual American double barrier call option problem in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial irregular optimal stopping problem to an integro-differential free-boundary problem and solving the latter by using continuous and smooth fit. The obtained solution of the nontrivial free-boundary problem gives the possibility to observe some special analytic properties of the value function at the optimal stopping boundaries.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-058.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 SFB649DP2006-058.

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    Length: 24 pages
    Date of creation: Sep 2006
    Date of revision:
    Handle: RePEc:hum:wpaper:sfb649dp2006-058

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    Related research

    Keywords: American double barrier options; optimal stopping problem; jump-diffusion model; integro-differential free-boundary problem; continuous and smooth fit; Ito-Tanaka-Meyer formula;

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    1. Rama Cont & Ekaterina Voltchkova, 2005. "Integro-differential equations for option prices in exponential Lévy models," Finance and Stochastics, Springer, vol. 9(3), pages 299-325, 07.
    2. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
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