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A finite dimensional approximation for pricing moving average options

Author

Listed:
  • Marie Bernhart

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique, EDF - EDF)

  • Peter Tankov

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Xavier Warin

    (EDF - EDF, FiME Lab - Laboratoire de Finance des Marchés d'Energie - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CREST - EDF R&D - EDF R&D - EDF - EDF)

Abstract

We propose a method for pricing American options whose pay-off depends on the moving average of the underlying asset price. The method uses a finite dimensional approximation of the infinite-dimensional dynamics of the moving average process based on a truncated Laguerre series expansion. The resulting problem is a finite-dimensional optimal stopping problem, which we propose to solve with a least squares Monte Carlo approach. We analyze the theoretical convergence rate of our method and present numerical results in the Black-Scholes framework.

Suggested Citation

  • Marie Bernhart & Peter Tankov & Xavier Warin, 2010. "A finite dimensional approximation for pricing moving average options," Working Papers hal-00554216, HAL.
    • Handle: RePEc:hal:wpaper:hal-00554216
    Note: View the original document on HAL open archive server: https://hal.science/hal-00554216
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    References listed on IDEAS

    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Gapeev, Pavel V. & Reiß, Markus, 2006. "An optimal stopping problem in a diffusion-type model with delay," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 601-608, March.
    3. Bernard Lapeyre & Emmanuel Temam, 2001. "Competitive Monte Carlo methods for the pricing of Asian options," Post-Print hal-01667057, HAL.
    4. Dai, Min & Li, Peifan & Zhang, Jin E., 2010. "A lattice algorithm for pricing moving average barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 542-554, March.
    5. Mark Broadie & Menghui Cao, 2008. "Improved lower and upper bound algorithms for pricing American options by simulation," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 845-861.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Enrico Biffis & Beniamin Goldys & Cecilia Prosdocimi & Margherita Zanella, 2015. "A pricing formula for delayed claims: Appreciating the past to value the future," Papers 1505.04914, arXiv.org, revised Jul 2022.
    2. Xavier Warin, 2012. "Hedging Swing contract on gas markets," Papers 1208.5303, arXiv.org.

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    More about this item

    Keywords

    American options; indexed swing options; moving average; finite-dimensional approximation; Laguerre polynomial; least squares Monte Carlo;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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