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Valuation of power plants by utility indifference and numerical computation

Author

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  • Arnaud Porchet
  • Nizar Touzi
  • Xavier Warin

Abstract

This paper presents a real option valuation model of a power plant, which accounts for physical constraints and market incompleteness. Switching costs, minimum on-off times, ramp rates, or non-constant heat rates are important characteristics that can lead, if neglected, to overestimated values. The existence of non-hedgeable uncertainties is also a feature of energy markets that can impact assets value. We use the utility indifference approach to define the value of the physical asset. We derive the associated mixed optimal switching-control problem and provide a characterization of its solution by means of a coupled system of reflected Backward Stochastic Differential Equations (BSDE). We relate this system to a system of variational inequalities, and we provide a numerical comparative study by implementing BSDE simulation algorithms, and PDE finite differences schemes. Copyright Springer-Verlag 2009

Suggested Citation

  • Arnaud Porchet & Nizar Touzi & Xavier Warin, 2009. "Valuation of power plants by utility indifference and numerical computation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 47-75, August.
    • Handle: RePEc:spr:mathme:v:70:y:2009:i:1:p:47-75
    DOI: 10.1007/s00186-008-0231-z
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    References listed on IDEAS

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    Citations

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    Cited by:

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    2. Yunhong Li & Zuo Quan Xu & Xun Yu Zhou, 2023. "Robust utility maximization with intractable claims," Papers 2304.06938, arXiv.org, revised Jul 2023.
    3. Nadarajah, Selvaprabu & Secomandi, Nicola, 2023. "A review of the operations literature on real options in energy," European Journal of Operational Research, Elsevier, vol. 309(2), pages 469-487.
    4. Elberg, Christina & Hagspiel, Simeon, 2015. "Spatial dependencies of wind power and interrelations with spot price dynamics," European Journal of Operational Research, Elsevier, vol. 241(1), pages 260-272.
    5. Giorgia Callegaro & Luciano Campi & Valeria Giusto & Tiziano Vargiolu, 2017. "Utility indifference pricing and hedging for structured contracts in energy markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 265-303, April.
    6. de Angelis, Tiziano & Ferrari, Giorgio & Hamadène, Saïd, 2018. "A Note on a New Existence Result for Reflected BSDES with Interconnected Obstacles," Center for Mathematical Economics Working Papers 591, Center for Mathematical Economics, Bielefeld University.
    7. Yunhong Li & Zuo Quan Xu & Xun Yu Zhou, 2023. "Robust utility maximisation with intractable claims," Finance and Stochastics, Springer, vol. 27(4), pages 985-1015, October.
    8. Zhehao Huang & Zhenghui Li & Zhenzhen Wang, 2020. "Utility Indifference Valuation for Defaultable Corporate Bond with Credit Rating Migration," Mathematics, MDPI, vol. 8(11), pages 1-26, November.

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