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A dual approach to multiple exercise option problems under constraints

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  • N. Aleksandrov
  • B. Hambly

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, April.
    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, October.
    4. Christophe Barrera-Esteve & Florent Bergeret & Charles Dossal & Emmanuel Gobet & Asma Meziou & Rémi Munos & Damien Reboul-Salze, 2006. "Numerical Methods for the Pricing of Swing Options: A Stochastic Control Approach," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 517-540, December.
    5. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
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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. Tiziano De Angelis & Yerkin Kitapbayev, 2018. "On the Optimal Exercise Boundaries of Swing Put Options," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 252-274, February.
    3. Mr. Nikolay Aleksandrov & Mr. lajos Gyurko & Mr. Raphael A Espinoza, 2012. "Optimal Oil Production and the World Supply of Oil," IMF Working Papers 2012/294, International Monetary Fund.
    4. Christian Bender, 2011. "Dual pricing of multi-exercise options under volume constraints," Finance and Stochastics, Springer, vol. 15(1), pages 1-26, January.
    5. Christian Bender & John Schoenmakers & Jianing Zhang, 2011. "Dual representations for general multiple stopping problems," Papers 1112.2638, arXiv.org.
    6. Nadarajah, Selvaprabu & Secomandi, Nicola, 2023. "A review of the operations literature on real options in energy," European Journal of Operational Research, Elsevier, vol. 309(2), pages 469-487.
    7. Nicolas Essis-Breton & Patrice Gaillardetz, 2020. "Fast Lower and Upper Estimates for the Price of Constrained Multiple Exercise American Options by Single Pass Lookahead Search and Nearest-Neighbor Martingale," Papers 2002.11258, arXiv.org.

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