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Modelling electricity prices: a time change approach

Author

Listed:
  • Lingfei Li
  • Rafael Mendoza-Arriaga
  • Zhiyu Mo
  • Daniel Mitchell
Abstract
To capture mean reversion and sharp seasonal spikes observed in electricity prices, this paper develops a new stochastic model for electricity spot prices by time changing the Jump Cox-Ingersoll-Ross (JCIR) process with a random clock that is a composite of a Gamma subordinator and a deterministic clock with seasonal activity rate. The time-changed JCIR process is a time-inhomogeneous Markov semimartingale which can be either a jump-diffusion or a pure-jump process, and it has a mean-reverting jump component that leads to mean reversion in the prices in addition to the smooth mean-reversion force. Furthermore, the characteristics of the time-changed JCIR process are seasonal, allowing spikes to occur in a seasonal pattern. The Laplace transform of the time-changed JCIR process can be efficiently computed by Gauss--Laguerre quadrature. This allows us to recover its transition density through efficient Laplace inversion and to calibrate our model using maximum likelihood estimation. To price electricity derivatives, we introduce a class of measure changes that transforms one time-changed JCIR process into another time-changed JCIR process. We derive a closed-form formula for the futures price and obtain the Laplace transform of futures option price in terms of the Laplace transform of the time-changed JCIR process, which can then be efficiently inverted to yield the option price. By fitting our model to two major electricity markets in the US, we show that it is able to capture both the trajectorial and the statistical properties of electricity prices. Comparison with a popular jump-diffusion model is also provided.

Suggested Citation

  • Lingfei Li & Rafael Mendoza-Arriaga & Zhiyu Mo & Daniel Mitchell, 2016. "Modelling electricity prices: a time change approach," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1089-1109, July.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:7:p:1089-1109
    DOI: 10.1080/14697688.2015.1125521
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/607 is not listed on IDEAS
    2. Helyette Geman, 2005. "Commodities and Commodity Derivatives. Modeling and Pricing for Agriculturals, Metals and Energy," Post-Print halshs-00144182, HAL.
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    Cited by:

    1. Deschatre, Thomas & Féron, Olivier & Gruet, Pierre, 2021. "A survey of electricity spot and futures price models for risk management applications," Energy Economics, Elsevier, vol. 102(C).
    2. Hilden, Mikael & Huuki, Hannu & Kivisaari, Visa & Kopsakangas-Savolainen, Maria, 2018. "The importance of transnational impacts of climate change in a power market," Energy Policy, Elsevier, vol. 115(C), pages 418-425.
    3. Moreno, Manuel & Novales, Alfonso & Platania, Federico, 2019. "Long-term swings and seasonality in energy markets," European Journal of Operational Research, Elsevier, vol. 279(3), pages 1011-1023.
    4. Bonaldo, Cinzia & Caporin, Massimiliano & Fontini, Fulvio, 2022. "The relationship between day-ahead and future prices in electricity markets: An empirical analysis on Italy, France, Germany, and Switzerland," Energy Economics, Elsevier, vol. 110(C).
    5. Figueiredo, Raquel & Nunes, Pedro & Brito, Miguel C., 2017. "The feasibility of solar parking lots for electric vehicles," Energy, Elsevier, vol. 140(P1), pages 1182-1197.
    6. Zhang, Xi & Strbac, Goran & Teng, Fei & Djapic, Predrag, 2018. "Economic assessment of alternative heat decarbonisation strategies through coordinated operation with electricity system – UK case study," Applied Energy, Elsevier, vol. 222(C), pages 79-91.
    7. Narayana, Mahinsasa & Sunderland, Keith M. & Putrus, Ghanim & Conlon, Michael F., 2017. "Adaptive linear prediction for optimal control of wind turbines," Renewable Energy, Elsevier, vol. 113(C), pages 895-906.
    8. Aithal, Avinash & Li, Gen & Wu, Jianzhong & Yu, James, 2018. "Performance of an electrical distribution network with Soft Open Point during a grid side AC fault," Applied Energy, Elsevier, vol. 227(C), pages 262-272.
    9. Zhigang Tong & Allen Liu, 2018. "Analytical pricing of discrete arithmetic Asian options under generalized CIR process with time change," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-21, March.
    10. Zhigang Tong & Allen Liu, 2017. "Analytical pricing formulas for discretely sampled generalized variance swaps under stochastic time change," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-24, June.
    11. Thomas Deschatre & Olivier F'eron & Pierre Gruet, 2021. "A survey of electricity spot and futures price models for risk management applications," Papers 2103.16918, arXiv.org, revised Jul 2021.
    12. Wild, Phillip, 2017. "Determining commercially viable two-way and one-way ‘Contract-for-Difference’ strike prices and revenue receipts," Energy Policy, Elsevier, vol. 110(C), pages 191-201.
    13. Morvaj, Boran & Evins, Ralph & Carmeliet, Jan, 2017. "Decarbonizing the electricity grid: The impact on urban energy systems, distribution grids and district heating potential," Applied Energy, Elsevier, vol. 191(C), pages 125-140.

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