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A First-Order BSPDE for Swing Option Pricing

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  • Christian Bender
  • Nikolai Dokuchaev

Abstract

We study an optimal control problem related to swing option pricing in a general non-Markovian setting in continuous time. As a main result we show that the value process solves a first-order non-linear backward stochastic partial differential equation. Based on this result we can characterize the set of optimal controls and derive a dual minimization problem.

Suggested Citation

  • Christian Bender & Nikolai Dokuchaev, 2013. "A First-Order BSPDE for Swing Option Pricing," Papers 1305.3988, arXiv.org.
  • Handle: RePEc:arx:papers:1305.3988
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    File URL: http://arxiv.org/pdf/1305.3988
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    References listed on IDEAS

    as
    1. Christian Bender, 2011. "Dual pricing of multi-exercise options under volume constraints," Finance and Stochastics, Springer, vol. 15(1), pages 1-26, January.
    2. John Schoenmakers, 2012. "A pure martingale dual for multiple stopping," Finance and Stochastics, Springer, vol. 16(2), pages 319-334, April.
    3. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268.
    4. Patrick Jaillet & Ehud I. Ronn & Stathis Tompaidis, 2004. "Valuation of Commodity-Based Swing Options," Management Science, INFORMS, vol. 50(7), pages 909-921, July.
    5. 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.
    6. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
    7. Nikolai Dokuchaev, 2010. "Controlled options: derivatives with added flexibility," Papers 1012.1412, arXiv.org, revised Oct 2011.
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    Cited by:

    1. Nikolai Dokuchaev, 2016. "First Order BSPDEs: examples in higher dimension," Papers 1603.06825, arXiv.org, revised Dec 2016.
    2. Christian Bender & Nikolai Dokuchaev, 2014. "A First-Order BSPDE for Swing Option Pricing: Classical Solutions," Papers 1402.6444, arXiv.org, revised Nov 2014.

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