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Pricing American currency options in an exponential Levy model

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  • Marc Chesney
  • M. Jeanblanc
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    Abstract

    In this article the problem of the American option valuation in a Levy process setting is analysed. The perpetual case is first considered. Without possible discontinuities (i.e. with negative jumps in the call case), known results concerning the currency option value as well as the exercise boundary are obtained with a martingale approach. With possible discontinuities of the underlying process at the exercise boundary (i.e. with positive jumps in the call case), original results are derived by relying on first passage time and overshoot associated with a Levy process. For finite life American currency calls, the formula derived by Bates or Zhang, in the context of a negative jump size, is tested. It is basically an extension of the one developed by Mac Millan and extended by Barone-Adesi and Whaley. It is shown that Bates' model generates pretty good results only when the process is continuous at the exercise boundary.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000249336
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 11 (2004)
    Issue (Month): 3 ()
    Pages: 207-225

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    Handle: RePEc:taf:apmtfi:v:11:y:2004:i:3:p:207-225

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    Web page: http://www.tandfonline.com/RAMF20

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    Related research

    Keywords: American options; perpetual options; exercise boundary; incomplete markets; jump diffusion model; Laplace transform; stopping times; Levy exponent; overshoot;

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    Cited by:
    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. Pauline Barrieu & N. Bellamy, 2007. "Optimal hitting time and perpetual option in a non-Lévy model: application to real options," LSE Research Online Documents on Economics 5099, London School of Economics and Political Science, LSE Library.
    3. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.

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