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Numerical Methods for the Pricing of Swing Options: A Stochastic Control Approach

Author

Listed:
  • Christophe Barrera-Esteve

    (Gaz de France - Direction de la Recherche)

  • Florent Bergeret

    (Gaz de France)

  • Charles Dossal

    (Ecole Polytechnique, Centre de Mathématiques Appliquées)

  • Emmanuel Gobet

    (ENSIMAG - INP Grenoble - Laboratoire de Modélisation et Calcul)

  • Asma Meziou

    (Ecole Polytechnique, Centre de Mathématiques Appliquées)

  • Rémi Munos

    (Ecole Polytechnique, Centre de Mathématiques Appliquées)

  • Damien Reboul-Salze

    (Gaz de France)

Abstract

In the natural gas market, many derivative contracts have a large degree of flexibility. These are known as Swing or Take-Or-Pay options. They allow their owner to purchase gas daily, at a fixed price and according to a volume of their choice. Daily, monthly and/or annual constraints on the purchased volume are usually incorporated. Thus, the valuation of such contracts is related to a stochastic control problem, which we solve in this paper using new numerical methods. Firstly, we extend the Longstaff–Schwarz methodology (originally used for Bermuda options) to our case. Secondly, we propose two efficient parameterizations of the gas consumption, one is based on neural networks and the other on finite elements. It allows us to derive a local optimal consumption law using a stochastic gradient ascent. Numerical experiments illustrate the efficiency of these approaches. Furthermore, we show that the optimal purchase is of bang-bang type.

Suggested Citation

  • Christophe Barrera-Esteve & Florent Bergeret & Charles Dossal & Emmanuel Gobet & Asma Meziou & Rémi Munos & Damien Reboul-Salze, 2006. "Numerical Methods for the Pricing of Swing Options: A Stochastic Control Approach," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 517-540, December.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:4:d:10.1007_s11009-006-0427-8
    DOI: 10.1007/s11009-006-0427-8
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    References listed on IDEAS

    as
    1. Thompson, Andrew C., 1995. "Valuation of Path-Dependent Contingent Claims with Multiple Exercise Decisions over Time: The Case of Take-or-Pay," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(2), pages 271-293, June.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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