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Perpetual Barrier Options in Jump-Diffusion Models

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  • Pavel V. Gapeev

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.

Suggested Citation

  • Pavel V. Gapeev, 2006. "Perpetual Barrier Options in Jump-Diffusion Models," SFB 649 Discussion Papers SFB649DP2006-058, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    • Handle: RePEc:hum:wpaper:sfb649dp2006-058
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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2006-058.pdf
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    References listed on IDEAS

    as
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    8. 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.
    9. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
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    More about this item

    Keywords

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

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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