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A non-Gaussian Ornstein–Uhlenbeck model for pricing wind power futures

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  • Fred Espen Benth
  • Anca Pircalabu

Abstract

The recent introduction of wind power futures written on the German wind power production index has brought with it new interesting challenges in terms of modelling and pricing. Some particularities of this product are the strong seasonal component embedded in the underlying, the fact that the wind index is bounded from both above and below and also that the futures are settled against a synthetically generated spot index. Here, we consider the non-Gaussian Ornstein–Uhlenbeck type processes proposed by Barndorff-Nielsen and Shephard in the context of modelling the wind power production index. We discuss the properties of the model and estimation of the model parameters. Further, the model allows for an analytical formula for pricing wind power futures. We provide an empirical study, where the model is calibrated to 37 years of German wind power production index that is synthetically generated assuming a constant level of installed capacity. Also, based on 1 year of observed prices for wind power futures with different delivery periods, we study the market price of risk. Generally, we find a negative risk premium whose magnitude decreases as the length of the delivery period increases. To further demonstrate the benefits of our proposed model, we address the pricing of European options written on wind power futures, which can be achieved through Fourier techniques.

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  • Fred Espen Benth & Anca Pircalabu, 2018. "A non-Gaussian Ornstein–Uhlenbeck model for pricing wind power futures," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(1), pages 36-65, January.
    • Handle: RePEc:taf:apmtfi:v:25:y:2018:i:1:p:36-65
    DOI: 10.1080/1350486X.2018.1438904
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    Cited by:

    1. Fred Espen Benth, 2021. "Pricing of Commodity and Energy Derivatives for Polynomial Processes," Mathematics, MDPI, vol. 9(2), pages 1-30, January.
    2. Christensen, Troels Sønderby & Pircalabu, Anca & Høg, Esben, 2019. "A seasonal copula mixture for hedging the clean spark spread with wind power futures," Energy Economics, Elsevier, vol. 78(C), pages 64-80.
    3. Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes," Papers 2011.09147, arXiv.org.
    4. Rowińska, Paulina A. & Veraart, Almut E.D. & Gruet, Pierre, 2021. "A multi-factor approach to modelling the impact of wind energy on electricity spot prices," Energy Economics, Elsevier, vol. 104(C).
    5. Zdeněk Zmeškal & Dana Dluhošová & Karolina Lisztwanová & Antonín Pončík & Iveta Ratmanová, 2023. "Distribution Prediction of Decomposed Relative EVA Measure with Levy-Driven Mean-Reversion Processes: The Case of an Automotive Sector of a Small Open Economy," Forecasting, MDPI, vol. 5(2), pages 1-19, May.
    6. Thomaidis, Nikolaos S. & Christodoulou, Theodoros & Santos-Alamillos, Francisco J., 2023. "Handling the risk dimensions of wind energy generation," Applied Energy, Elsevier, vol. 339(C).
    7. Lingohr, Daniel & Müller, Gernot, 2021. "Conditionally independent increment processes for modeling electricity prices with regard to renewable power generation," Energy Economics, Elsevier, vol. 103(C).
    8. Rønn-Nielsen, Anders & Stehr, Mads, 2022. "Extremes of Lévy-driven spatial random fields with regularly varying Lévy measure," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 19-49.
    9. Kanamura, Takashi & Homann, Lasse & Prokopczuk, Marcel, 2021. "Pricing analysis of wind power derivatives for renewable energy risk management," Applied Energy, Elsevier, vol. 304(C).
    10. Roberto Baviera & Pietro Manzoni, 2024. "Fast and General Simulation of L\'evy-driven OU processes for Energy Derivatives," Papers 2401.15483, arXiv.org, revised Sep 2024.
    11. Li, Wei & Paraschiv, Florentina, 2022. "Modelling the evolution of wind and solar power infeed forecasts," Journal of Commodity Markets, Elsevier, vol. 25(C).
    12. Grochowicz, Aleksander & Benth, Fred Espen & Zeyringer, Marianne, 2024. "Spatio-temporal smoothing and dynamics of different electricity flexibility options for highly renewable energy systems—Case study for Norway," Applied Energy, Elsevier, vol. 356(C).
    13. Yuji Yamada & Takuji Matsumoto, 2023. "Construction of Mixed Derivatives Strategy for Wind Power Producers," Energies, MDPI, vol. 16(9), pages 1-26, April.
    14. Nicola Cufaro Petroni & Piergiacomo Sabino, 2019. "Fast Pricing of Energy Derivatives with Mean-reverting Jump-diffusion Processes," Papers 1908.03137, arXiv.org, revised Mar 2020.
    15. Markus Hess, 2021. "A new approach to wind power futures pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1235-1252, December.
    16. Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Gamma Related Ornstein-Uhlenbeck Processes and their Simulation," Papers 2003.08810, arXiv.org.
    17. Piergiacomo Sabino, 2020. "Exact Simulation of Variance Gamma related OU processes: Application to the Pricing of Energy Derivatives," Papers 2004.06786, arXiv.org.
    18. Takuji Matsumoto & Yuji Yamada, 2023. "Improving the Efficiency of Hedge Trading Using Higher-Order Standardized Weather Derivatives for Wind Power," Energies, MDPI, vol. 16(7), pages 1-22, March.
    19. Lingohr, Daniel & Müller, Gernot, 2019. "Stochastic modeling of intraday photovoltaic power generation," Energy Economics, Elsevier, vol. 81(C), pages 175-186.
    20. Fugui Dong & Xiaohui Ding & Lei Shi, 2019. "Wind Power Pricing Game Strategy under the China’s Market Trading Mechanism," Energies, MDPI, vol. 12(18), pages 1-17, September.

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