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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.

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File URL: http://arxiv.org/pdf/1305.3988
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1305.3988.

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Date of creation: May 2013
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Handle: RePEc:arx:papers:1305.3988

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Web page: http://arxiv.org/

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  1. Olivier Bardou & Sandrine Bouthemy & Gilles Pagès, 2010. "When Are Swing Options Bang-Bang?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(06), pages 867-899.
  2. 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.
  3. Patrick Jaillet & Ehud I. Ronn & Stathis Tompaidis, 2004. "Valuation of Commodity-Based Swing Options," Management Science, INFORMS, vol. 50(7), pages 909-921, July.
  4. Nikolai Dokuchaev, 2010. "Controlled options: derivatives with added flexibility," Papers 1012.1412, arXiv.org, revised Oct 2011.
  5. René Carmona & Nizar Touzi, 2008. "Optimal Multiple Stopping And Valuation Of Swing Options," Mathematical Finance, Wiley Blackwell, vol. 18(2), pages 239-268.
  6. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
  7. John Schoenmakers, 2012. "A pure martingale dual for multiple stopping," Finance and Stochastics, Springer, vol. 16(2), pages 319-334, April.
  8. Christian Bender, 2011. "Dual pricing of multi-exercise options under volume constraints," Finance and Stochastics, Springer, vol. 15(1), pages 1-26, January.
  9. Amina Bouzguenda Zeghal & Mohamed Mnif, 2006. "Optimal Multiple Stopping And Valuation Of Swing Options In Lévy Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(08), pages 1267-1297.
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Cited by:
  1. Christian Bender & Nikolai Dokuchaev, 2014. "A First-Order BSPDE for Swing Option Pricing: Classical Solutions," Papers 1402.6444, arXiv.org.

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