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Are American options European after all?

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  • Soren Christensen
  • Jan Kallsen
  • Matthias Lenga

Abstract

We call a given American option representable if there exists a European claim which dominates the American payoff at any time and such that the values of the two options coincide in the continuation region of the American option. This concept has interesting implications from a probabilistic, analytic, financial, and numeric point of view. Relying on methods from Jourdain and Martini (2001, 2002), Chrsitensen (2014) and convex duality, we make a first step towards verifying representability of American options.

Suggested Citation

  • Soren Christensen & Jan Kallsen & Matthias Lenga, 2020. "Are American options European after all?," Papers 2002.05571, arXiv.org.
    • Handle: RePEc:arx:papers:2002.05571
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    References listed on IDEAS

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    1. David C. Nachman, 1988. "Spanning and Completeness with Options," The Review of Financial Studies, Society for Financial Studies, vol. 1(3), pages 311-328.
    2. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    3. Sören Christensen, 2014. "A Method For Pricing American Options Using Semi-Infinite Linear Programming," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 156-172, January.
    4. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    5. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, February.
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    Cited by:

    1. Martin Larsson & Marvin S. Mueller & Josef Teichmann, 2020. "Stopper-Controller Games embedded in Single-Player Control Problems," Papers 2006.09493, arXiv.org.

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