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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 - Ecole Polytechnique - X - École polytechnique - 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. 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.
    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. 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.
    4. 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.
    5. Bernard Lapeyre & Emmanuel Temam, 2001. "Competitive Monte Carlo methods for the pricing of Asian options," Post-Print hal-01667057, HAL.
    6. 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.
    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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