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Dual representations for general multiple stopping problems

  • Christian Bender
  • John Schoenmakers
  • Jianing Zhang
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    In this paper, we study the dual representation for generalized multiple stopping problems, hence the pricing problem of general multiple exercise options. We derive a dual representation which allows for cashflows which are subject to volume constraints modeled by integer valued adapted processes and refraction periods modeled by stopping times. As such, this extends the works by Schoenmakers (2010), Bender (2011a), Bender (2011b), Aleksandrov and Hambly (2010), and Meinshausen and Hambly (2004) on multiple exercise options, which either take into consideration a refraction period or volume constraints, but not both simultaneously. We also allow more flexible cashflow structures than the additive structure in the above references. For example some exponential utility problems are covered by our setting. We supplement the theoretical results with an explicit Monte Carlo algorithm for constructing confidence intervals for the price of multiple exercise options and exemplify it by a numerical study on the pricing of a swing option in an electricity market.

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    File URL: http://arxiv.org/pdf/1112.2638
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    Paper provided by arXiv.org in its series Papers with number 1112.2638.

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    Date of creation: Dec 2011
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    Handle: RePEc:arx:papers:1112.2638
    Contact details of provider: Web page: http://arxiv.org/

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    2. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    3. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
    4. 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.
    5. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    6. repec:spr:compst:v:71:y:2010:i:3:p:503-533 is not listed on IDEAS
    7. N. Aleksandrov & B. Hambly, 2010. "A dual approach to multiple exercise option problems under constraints," Mathematical Methods of Operations Research, Springer, vol. 71(3), pages 503-533, June.
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