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Least Squares Monte Carlo and Approximate Linear Programming with an Energy Real Option Application

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  • Nadarajah, Selvaprabu
  • Secomandi, Nicola

Abstract

Least squares Monte Carlo (LSM) is an approximate dynamic programming technique commonly used for the valuation of high dimensional financial and real options, but has broader applicability. It is known that the regress-later version of this method is an approximate linear programming (ALP) relaxation that implicitly provides a potential solution to a familiar ALP deficiency. We provide numerical backing for the usefulness of this solution using a numerical study dealing with merchant ethanol production, an energy real option application, based on an ALP heuristic that we propose. When both methodologies are applicable, our research supports the use of regress-later LSM rather than this ALP technique to approximately solve intractable Markov decision processes. Our findings motivate additional research to obtain even better methods than the regress-later version of LSM.

Suggested Citation

  • Nadarajah, Selvaprabu & Secomandi, Nicola, 2020. "Least Squares Monte Carlo and Approximate Linear Programming with an Energy Real Option Application," Foundations and Trends(R) in Technology, Information and Operations Management, now publishers, vol. 14(1-2), pages 178-202, October.
    • Handle: RePEc:now:fnttom:0200000096-10
    DOI: 10.1561/0200000096-10
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    References listed on IDEAS

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    1. Nadarajah, Selvaprabu & Margot, François & Secomandi, Nicola, 2017. "Comparison of least squares Monte Carlo methods with applications to energy real options," European Journal of Operational Research, Elsevier, vol. 256(1), pages 196-204.
    2. 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.
    3. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    4. James E. Smith, 2005. "Alternative Approaches for Solving Real-Options Problems," Decision Analysis, INFORMS, vol. 2(2), pages 89-102, June.
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