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An Approximate Dynamic Programming Approach to Benchmark Practice-Based Heuristics for Natural Gas Storage Valuation

Author

Listed:
  • Guoming Lai

    (McCombs School of Business, The University of Texas at Austin, Austin, Texas 78712)

  • François Margot

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Nicola Secomandi

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

Abstract

The valuation of the real option to store natural gas is a practically important problem that entails dynamic optimization of inventory trading decisions with capacity constraints in the face of uncertain natural gas price dynamics. Stochastic dynamic programming is a natural approach to this valuation problem, but it does not seem to be widely used in practice because it is at odds with the high-dimensional natural gas price evolution models that are widespread among traders. According to the practice-based literature, practitioners typically value natural gas storage heuristically. The effectiveness of the heuristics discussed in this literature is currently unknown because good upper bounds on the value of storage are not available. We develop a novel and tractable approximate dynamic programming method that, coupled with Monte Carlo simulation, computes lower and upper bounds on the value of storage, which we use to benchmark these heuristics on a set of realistic instances. We find that these heuristics are extremely fast to execute but significantly suboptimal compared to our upper bound, which appears to be fairly tight and much tighter than a simpler perfect information upper bound; computing our lower bound takes more time than using these heuristics, but our lower bound substantially outperforms them in terms of valuation. Moreover, with periodic reoptimizations embedded in Monte Carlo simulation, the practice-based heuristics become nearly optimal, with one exception, at the expense of higher computational effort. Our lower bound with reoptimization is also nearly optimal, but exhibits a higher computational requirement than these heuristics. Besides natural gas storage, our results are potentially relevant for the valuation of the real option to store other commodities, such as metals, oil, and petroleum products.

Suggested Citation

  • Guoming Lai & François Margot & Nicola Secomandi, 2010. "An Approximate Dynamic Programming Approach to Benchmark Practice-Based Heuristics for Natural Gas Storage Valuation," Operations Research, INFORMS, vol. 58(3), pages 564-582, June.
  • Handle: RePEc:inm:oropre:v:58:y:2010:i:3:p:564-582
    DOI: 10.1287/opre.1090.0768
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    References listed on IDEAS

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    1. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    2. D. P. Kennedy, 1994. "The Term Structure Of Interest Rates As A Gaussian Random Field," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 247-258, July.
    3. 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.
    4. Nicola Secomandi, 2008. "An Analysis of the Control-Algorithm Re-solving Issue in Inventory and Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 10(3), pages 468-483, December.
    5. Byers, Joe Wayne, 2006. "Commodity storage valuation: A linear optimization based on traded instruments," Energy Economics, Elsevier, vol. 28(3), pages 275-287, May.
    6. Alan Brace & Dariusz G¸atarek & Marek Musiela, 1997. "The Market Model of Interest Rate Dynamics," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 127-155, April.
    7. Matt Thompson & Matt Davison & Henning Rasmussen, 2009. "Natural gas storage valuation and optimization: A real options application," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(3), pages 226-238, April.
    8. Patrick Jaillet & Ehud I. Ronn & Stathis Tompaidis, 2004. "Valuation of Commodity-Based Swing Options," Management Science, INFORMS, vol. 50(7), pages 909-921, July.
    9. David B. Brown & James E. Smith & Peng Sun, 2010. "Information Relaxations and Duality in Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 58(4-part-1), pages 785-801, August.
    10. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    11. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    12. James E. Smith & Kevin F. McCardle, 1999. "Options in the Real World: Lessons Learned in Evaluating Oil and Gas Investments," Operations Research, INFORMS, vol. 47(1), pages 1-15, February.
    13. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
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