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Perpetual barrier options in jump-diffusion models

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  • Gapeev, Pavel V.

Abstract

We present a closed form solution to the perpetual American double barrier call option problem in a model driven by Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the inital 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

  • Gapeev, Pavel V., 2006. "Perpetual barrier options in jump-diffusion models," SFB 649 Discussion Papers 2006-058, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2006-058
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    References listed on IDEAS

    as
    1. 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.
    2. 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, July.
    3. Broadie, Mark & Detemple, Jerome, 1995. "American Capped Call Options on Dividend-Paying Assets," The Review of Financial Studies, Society for Financial Studies, vol. 8(1), pages 161-191.
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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; It^o-Tanaka-Meyer formula;
    All these keywords.

    JEL classification:

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

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