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General Duality For Perpetual American Options

Author

Listed:
  • AURÉLIEN ALFONSI

    (CERMICS, project-team Mathfi, École des Ponts, ParisTech, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne-la-vallée, France;
    Institut für Mathematik, MA 7-4, TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany)

  • BENJAMIN JOURDAIN

    (CERMICS, project-team Mathfi, École des Ponts, ParisTech, 6-8 avenue Blaise Pascal, Cité Descartes, Champs sur Marne, 77455 Marne-la-vallée, France)

Abstract

In this paper, we investigate the generalization of the Call-Put duality equality obtained in Alfonsi and Jourdain (preprint, 2006, available at ) for perpetual American options when the Call-Put payoff (y - x)+ is replaced by ϕ(x,y). It turns out that the duality still holds under monotonicity and concavity assumptions on ϕ. The specific analytical form of the Call-Put payoff only makes calculations easier but is not crucial unlike in the derivation of the Call-Put duality equality for European options. Last, we give some examples for which the optimal strategy is known explicitly.

Suggested Citation

  • Aurélien Alfonsi & Benjamin Jourdain, 2008. "General Duality For Perpetual American Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 545-566.
    • Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:06:n:s0219024908004920
    DOI: 10.1142/S0219024908004920
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    References listed on IDEAS

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    1. Aur'elien Alfonsi & Benjamin Jourdain, 2006. "A Call-Put Duality for Perpetual American Options," Papers math/0612648, arXiv.org.
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    Cited by:

    1. Gapeev Pavel V. & Rodosthenous Neofytos, 2013. "Perpetual American options in a diffusion model with piecewise-linear coefficients," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 1-21, March.

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