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Exercise regions of American options on several assets

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  • Stephane Villeneuve

    (Equipe d'Analyse et de Math\' ematiques AppliquÊes, UniversitÊ de Marne-la-VallÊe, 2 rue de la Butte Verte, F-93166 Noisy-le-Grand Cedex, France Manuscript)

Abstract

In this paper, we study the nonemptiness and the shape of the exercise region of American options written on several assets. Our contribution is threefold. First, we state an analytic theorem which characterizes the nonemptiness of the exercise region. Second, we study a particular class of payoff functions for which we explicitly identify the shape and the asymptotic behavior near maturity of the associated exercise region. Finally, we present additional results which complement the Broadie and Detemple results concerning the valuation of various types of American options on several assets.

Suggested Citation

  • Stephane Villeneuve, 1999. "Exercise regions of American options on several assets," Finance and Stochastics, Springer, vol. 3(3), pages 295-322.
    • Handle: RePEc:spr:finsto:v:3:y:1999:i:3:p:295-322
    Note: received: June 1997; final version received: July 1998
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    Citations

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    Cited by:

    1. Louberge, Henri & Villeneuve, Stephane & Chesney, Marc, 2002. "Long-term risk management of nuclear waste: a real options approach," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 157-180, November.
    2. Décamps, Jean-Paul & Mariotti, Thomas & Villeneuve, Stéphane, 2000. "Investment Timing under Incomplete Information," IDEI Working Papers 115, Institut d'Économie Industrielle (IDEI), Toulouse, revised Apr 2004.
    3. Rombouts, Jeroen V.K. & Stentoft, Lars, 2011. "Multivariate option pricing with time varying volatility and correlations," Journal of Banking & Finance, Elsevier, vol. 35(9), pages 2267-2281, September.
    4. Len Patrick Dominic M. Garces & Gerald H. L. Cheang, 2021. "A numerical approach to pricing exchange options under stochastic volatility and jump-diffusion dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 21(12), pages 2025-2054, December.
    5. Th'eo Durandard & Matteo Camboni, 2024. "Comparative Statics for Optimal Stopping Problems in Nonstationary Environments," Papers 2402.06999, arXiv.org, revised Jul 2024.
    6. Leonardo Kanashiro Felizardo & Elia Matsumoto & Emilio Del-Moral-Hernandez, 2022. "Solving the optimal stopping problem with reinforcement learning: an application in financial option exercise," Papers 2208.00765, arXiv.org.
    7. Damien Lamberton & Giulia Terenzi, 2019. "Properties of the American price function in the Heston-type models," Working Papers hal-02088487, HAL.
    8. Stephane Villeneuve & Antonino Zanette, 2002. "Parabolic ADI Methods for Pricing American Options on Two Stocks," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 121-149, February.
    9. Tiziano De Angelis, 2020. "Stopping spikes, continuation bays and other features of optimal stopping with finite-time horizon," Papers 2009.01276, arXiv.org, revised Jan 2022.
    10. Christensen, Sören & Crocce, Fabián & Mordecki, Ernesto & Salminen, Paavo, 2019. "On optimal stopping of multidimensional diffusions," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2561-2581.
    11. Ken-ichi Mitsui & Yoshio Tabata, 2005. "Wavelet based Multi-grid analysis, Wavelet Galerkin method and their Applications to American option: A Survey," Discussion Papers in Economics and Business 05-26, Osaka University, Graduate School of Economics.
    12. Alessandro Milazzo, 2024. "On the Monotonicity of the Stopping Boundary for Time-Inhomogeneous Optimal Stopping Problems," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 336-358, October.
    13. Jerome Detemple & Yerkin Kitapbayev, 2021. "Optimal Power Investment and Pandemics: A Micro-Economic Analysis," Energies, MDPI, vol. 14(4), pages 1-25, February.
    14. Min Dai & Zuo Quan Xu, 2009. "Optimal Redeeming Strategy of Stock Loans," Papers 0906.0702, arXiv.org.
    15. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2005. "Investment Timing Under Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 30(2), pages 472-500, May.
    16. Anne Mackay & Marie-Claude Vachon, 2023. "On an Optimal Stopping Problem with a Discontinuous Reward," Papers 2311.03538, arXiv.org, revised Nov 2023.
    17. Erik Ekström & Martin Vannestål, 2019. "American Options And Incomplete Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-14, September.
    18. BOBTCHEFF Catherine, 2008. "Real Options and Technology Choice under Bertrand Competition," LERNA Working Papers 08.16.260, LERNA, University of Toulouse.
    19. Masahiko Egami & Tadao Oryu, 2010. "Options on Multiple Assets in a Mean-Reverting Model," Discussion papers e-10-005, Graduate School of Economics Project Center, Kyoto University.
    20. Nishihara, Michi, 2014. "Preemptive investment game with alternative projects," Economic Modelling, Elsevier, vol. 43(C), pages 124-135.
    21. Bobtcheff, Catherine & Villeneuve, Stéphane, 2010. "Technology choice under several uncertainty sources," European Journal of Operational Research, Elsevier, vol. 206(3), pages 586-600, November.

    More about this item

    Keywords

    Optimal stopping; free boundary problems; American options;
    All these keywords.

    JEL classification:

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

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