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A dual approach to multiple exercise option problems under constraints

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  • N. Aleksandrov

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  • B. Hambly

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Abstract

This paper considers the pricing of multiple exercise options in discrete time. This type of option can be exercised up to a finite number of times over the lifetime of the contract. We allow multiple exercise of the option at each time point up to a constraint, a feature relevant for pricing swing options in energy markets. It is shown that, in the case where an option can be exercised an equal number of times at each time point, the problem can be reduced to the case of a single exercise possibility at each time. In the general case there is not a solution of this type. We develop a dual representation for the problem and give an algorithm for calculating both lower and upper bounds for the prices of such multiple exercise options. Copyright Springer-Verlag 2010

Suggested Citation

  • N. Aleksandrov & B. Hambly, 2010. "A dual approach to multiple exercise option problems under constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 503-533, June.
  • Handle: RePEc:spr:mathme:v:71:y:2010:i:3:p:503-533
    DOI: 10.1007/s00186-010-0310-9
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    References listed on IDEAS

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    1. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268.
    2. Patrick Jaillet & Ehud I. Ronn & Stathis Tompaidis, 2004. "Valuation of Commodity-Based Swing Options," Management Science, INFORMS, vol. 50(7), pages 909-921, July.
    3. N. Meinshausen & B. M. Hambly, 2004. "Monte Carlo Methods For The Valuation Of Multiple-Exercise Options," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 557-583.
    4. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
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    Cited by:

    1. Aleksandrov, Nikolay & Espinoza, Raphael & Gyurkó, Lajos, 2013. "Optimal oil production and the world supply of oil," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1248-1263.
    2. Christian Bender, 2011. "Dual pricing of multi-exercise options under volume constraints," Finance and Stochastics, Springer, vol. 15(1), pages 1-26, January.
    3. Christian Bender & John Schoenmakers & Jianing Zhang, 2011. "Dual representations for general multiple stopping problems," Papers 1112.2638, arXiv.org.

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