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Stochastic Modeling of Wind Derivatives in Energy Markets

Author

Listed:
  • Fred Espen Benth

    (Department of Mathematics, University of Oslo, 0316 Blindern, Norway)

  • Luca Di Persio

    (Department of Computer Science, University of Verona, 37134 Verona, Italy)

  • Silvia Lavagnini

    (Department of Mathematics, University of Oslo, 0316 Blindern, Norway)

Abstract

We model the logarithm of the spot price of electricity with a normal inverse Gaussian (NIG) process and the wind speed and wind power production with two Ornstein–Uhlenbeck processes. In order to reproduce the correlation between the spot price and the wind power production, namely between a pure jump process and a continuous path process, respectively, we replace the small jumps of the NIG process by a Brownian term. We then apply our models to two different problems: first, to study from the stochastic point of view the income from a wind power plant, as the expected value of the product between the electricity spot price and the amount of energy produced; then, to construct and price a European put-type quanto option in the wind energy markets that allows the buyer to hedge against low prices and low wind power production in the plant. Calibration of the proposed models and related price formulas is also provided, according to specific datasets.

Suggested Citation

  • Fred Espen Benth & Luca Di Persio & Silvia Lavagnini, 2018. "Stochastic Modeling of Wind Derivatives in Energy Markets," Risks, MDPI, vol. 6(2), pages 1-21, May.
    • Handle: RePEc:gam:jrisks:v:6:y:2018:i:2:p:56-:d:146703
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    References listed on IDEAS

    as
    1. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Financial markets for weather," World Scientific Book Chapters, in: Modeling and Pricing in Financial Markets for Weather Derivatives, chapter 1, pages 1-13, World Scientific Publishing Co. Pte. Ltd..
    2. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Modeling and Pricing in Financial Markets for Weather Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8457, January.
    3. Fred Espen Benth & Jūratė Šaltytė-Benth, 2004. "The Normal Inverse Gaussian Distribution And Spot Price Modelling In Energy Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 177-192.
    4. Villanueva, D. & Feijóo, A., 2010. "Wind power distributions: A review of their applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 14(5), pages 1490-1495, June.
    5. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
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    Cited by:

    1. 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.
    2. Roberto Baviera & Pietro Manzoni, 2024. "Fast and General Simulation of L\'evy-driven OU processes for Energy Derivatives," Papers 2401.15483, arXiv.org.
    3. Thomaidis, Nikolaos S. & Christodoulou, Theodoros & Santos-Alamillos, Francisco J., 2023. "Handling the risk dimensions of wind energy generation," Applied Energy, Elsevier, vol. 339(C).
    4. Yeny E. Rodríguez & Miguel A. Pérez-Uribe & Javier Contreras, 2021. "Wind Put Barrier Options Pricing Based on the Nordix Index," Energies, MDPI, vol. 14(4), pages 1-14, February.
    5. Piergiacomo Sabino, 2021. "Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein-Uhlenbeck Type," Papers 2103.13252, arXiv.org.
    6. Giovanni Masala & Marco Micocci & Andrea Rizk, 2022. "Hedging Wind Power Risk Exposure through Weather Derivatives," Energies, MDPI, vol. 15(4), pages 1-30, February.
    7. Yuji Yamada & Takuji Matsumoto, 2023. "Construction of Mixed Derivatives Strategy for Wind Power Producers," Energies, MDPI, vol. 16(9), pages 1-26, April.
    8. Shinji Kuno & Kenji Tanaka & Yuji Yamada, 2022. "Effectiveness and Feasibility of Market Makers for P2P Electricity Trading," Energies, MDPI, vol. 15(12), pages 1-24, June.
    9. Riccardo De Blasis & Giovanni Batista Masala & Filippo Petroni, 2021. "A Multivariate High-Order Markov Model for the Income Estimation of a Wind Farm," Energies, MDPI, vol. 14(2), pages 1-16, January.
    10. Yuji Yamada & Takuji Matsumoto, 2021. "Going for Derivatives or Forwards? Minimizing Cashflow Fluctuations of Electricity Transactions on Power Markets," Energies, MDPI, vol. 14(21), pages 1-28, November.
    11. Piergiacomo Sabino, 2021. "Normal Tempered Stable Processes and the Pricing of Energy Derivatives," Papers 2105.03071, arXiv.org.
    12. 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.
    13. Christa Cuchiero & Luca Di Persio & Francesco Guida & Sara Svaluto-Ferro, 2022. "Measure-valued processes for energy markets," Papers 2210.09331, arXiv.org.
    14. Roman V. Ivanov, 2023. "The Semi-Hyperbolic Distribution and Its Applications," Stats, MDPI, vol. 6(4), pages 1-21, October.
    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. Laura Casula & Guglielmo D'Amico & Giovanni Masala & Filippo Petroni, 2020. "Performance estimation of a wind farm with a dependence structure between electricity price and wind speed," The World Economy, Wiley Blackwell, vol. 43(10), pages 2803-2822, October.
    17. Nicola Cufaro Petroni & Piergiacomo Sabino, 2020. "Tempered stable distributions and finite variation Ornstein-Uhlenbeck processes," Papers 2011.09147, arXiv.org.
    18. Laura Casula & Guglielmo D’Amico & Giovanni Masala & Filippo Petroni, 2020. "Performance estimation of photovoltaic energy production," Letters in Spatial and Resource Sciences, Springer, vol. 13(3), pages 267-285, December.
    19. Kanamura, Takashi & Homann, Lasse & Prokopczuk, Marcel, 2021. "Pricing analysis of wind power derivatives for renewable energy risk management," Applied Energy, Elsevier, vol. 304(C).
    20. Piergiacomo Sabino & Nicola Cufaro Petroni, 2022. "Fast simulation of tempered stable Ornstein–Uhlenbeck processes," Computational Statistics, Springer, vol. 37(5), pages 2517-2551, November.

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