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Laplace transforms and American options

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  • Roland Mallier
  • Ghada Alobaidi

Abstract

Laplace transform methods are used to study the valuation of American call and put options with constant dividend yield, and to derive integral equations giving the location of the optimal exercise boundary. In each case studied, the main result of this paper is a nonlinear Fredholm-type integral equation for the location of the free boundary. The equations differ depending on whether the dividend yield is less than or exceeds the risk-free rate. These integral equations contain a transform variable, so the solution of the equations would involve finding the free boundary that satisfies the equations for all values of this transform variable. Expressions are also given for the transform of the value of the option in terms of this free boundary.

Suggested Citation

  • Roland Mallier & Ghada Alobaidi, 2000. "Laplace transforms and American options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(4), pages 241-256.
    • Handle: RePEc:taf:apmtfi:v:7:y:2000:i:4:p:241-256
    DOI: 10.1080/13504860110060384
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    Cited by:

    1. Hyoseop Lee & Dongwoo Sheen, 2009. "Laplace transformation method for the Black-Scholes equation," Papers 0901.4604, arXiv.org, revised Apr 2009.
    2. Franck Moraux, 2009. "On perpetual American strangles," Post-Print halshs-00393811, HAL.
    3. Zhiqiang Zhou & Hongying Wu, 2018. "Laplace Transform Method for Pricing American CEV Strangles Option with Two Free Boundaries," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-12, September.

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