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A critical empirical study of three electricity spot price models


  • Benth, Fred Espen
  • Kiesel, Rüdiger
  • Nazarova, Anna


We conduct an empirical analysis of three recently proposed and widely used models for electricity spot price process. The first model, called the jump-diffusion model, was proposed by Cartea and Figueroa (2005), and is a one-factor mean-reversion jump-diffusion model, adjusted to incorporate the most important characteristics of electricity prices. The second model, called the threshold model, was proposed by Roncoroni (2002) and further developed by Geman and Roncoroni (2006), and is an exponential Ornstein–Uhlenbeck process driven by a Brownian motion and a state-dependent compound Poisson process. It is designed to capture both statistical and pathwise properties of electricity spot prices. The third model, called the factor model, was proposed by Benth et al. (2007). It is an additive linear model, where the price dynamics is a superposition of Ornstein–Uhlenbeck processes driven by subordinators to ensure positivity of the prices. It separates the modelling of spikes and base components. We calibrate all three models to German spot price data. Besides employing techniques similar to those used in the original papers we adopt the prediction-based estimating function technique (Sørensen, 2000) and the filtering technique (Meyer-Brandis and Tankov, 2008). We critically compare the properties and the estimation of the three models and discuss several shortcomings and possible improvements. Besides analysing the spot price behaviour, we compute forward prices and risk premia for all three models for various German forward data and identify the key forward price drivers.

Suggested Citation

  • Benth, Fred Espen & Kiesel, Rüdiger & Nazarova, Anna, 2012. "A critical empirical study of three electricity spot price models," Energy Economics, Elsevier, vol. 34(5), pages 1589-1616.
  • Handle: RePEc:eee:eneeco:v:34:y:2012:i:5:p:1589-1616
    DOI: 10.1016/j.eneco.2011.11.012

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    References listed on IDEAS

    1. Alvaro Cartea & Marcelo Figueroa, 2005. "Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 313-335.
    2. Benth, Fred Espen & Cartea, Álvaro & Kiesel, Rüdiger, 2008. "Pricing forward contracts in power markets by the certainty equivalence principle: Explaining the sign of the market risk premium," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2006-2021, October.
    3. Helyette Geman & A. Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," Post-Print halshs-00144198, HAL.
    4. repec:dau:papers:123456789/1433 is not listed on IDEAS
    5. Hélyette Geman & Andrea Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1225-1262, May.
    6. 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.
    7. Michael Sørensen, 2000. "Prediction-based estimating functions," Econometrics Journal, Royal Economic Society, vol. 3(2), pages 123-147.
    8. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    9. Fred Espen Benth & Jan Kallsen & Thilo Meyer-Brandis, 2007. "A Non-Gaussian Ornstein-Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(2), pages 153-169.
    10. Helyette Geman & Stelios Kourouvakalis, 2008. "A Lattice-Based Method for Pricing Electricity Derivatives Under the Threshold Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(5-6), pages 531-567.
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    Cited by:

    1. Inderfurth, Karl & Kelle, Peter & Kleber, Rainer, 2013. "Dual sourcing using capacity reservation and spot market: Optimal procurement policy and heuristic parameter determination," European Journal of Operational Research, Elsevier, vol. 225(2), pages 298-309.
    2. Benth, Fred Espen & Biegler-König, Richard & Kiesel, Rüdiger, 2013. "An empirical study of the information premium on electricity markets," Energy Economics, Elsevier, vol. 36(C), pages 55-77.
    3. Weron, Rafał & Zator, Michał, 2015. "A note on using the Hodrick–Prescott filter in electricity markets," Energy Economics, Elsevier, vol. 48(C), pages 1-6.
    4. repec:eee:eneeco:v:63:y:2017:i:c:p:301-313 is not listed on IDEAS
    5. Bannör, Karl & Kiesel, Rüdiger & Nazarova, Anna & Scherer, Matthias, 2016. "Parametric model risk and power plant valuation," Energy Economics, Elsevier, vol. 59(C), pages 423-434.
    6. Olga Y. Uritskaya & Vadim M. Uritsky, 2015. "Predictability of price movements in deregulated electricity markets," Papers 1505.08117,
    7. Nowotarski, Jakub & Tomczyk, Jakub & Weron, Rafał, 2013. "Robust estimation and forecasting of the long-term seasonal component of electricity spot prices," Energy Economics, Elsevier, vol. 39(C), pages 13-27.
    8. Asger Lunde & Anne Floor Brix & Wei Wei, 2013. "A Generalized Schwartz Model for Energy Spot Prices - Estimation using a Particle MCMC Method," CREATES Research Papers 2015-46, Department of Economics and Business Economics, Aarhus University.
    9. Rainer Kleber & Karl Inderfurth & Peter Kelle, 2014. "Combined sourcing and inventory management using capacity reservation and spot market," FEMM Working Papers 140005, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    10. Mikkel Bennedsen, 2015. "Rough electricity: a new fractal multi-factor model of electricity spot prices," CREATES Research Papers 2015-42, Department of Economics and Business Economics, Aarhus University.
    11. Jakub Nowotarski & Jakub Tomczyk & Rafal Weron, 2013. "Modeling and forecasting of the long-term seasonal component of the EEX and Nord Pool spot prices," HSC Research Reports HSC/13/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    12. Uritskaya, Olga Y. & Uritsky, Vadim M., 2015. "Predictability of price movements in deregulated electricity markets," Energy Economics, Elsevier, vol. 49(C), pages 72-81.
    13. Densing, M., 2013. "Dispatch planning using newsvendor dual problems and occupation times: Application to hydropower," European Journal of Operational Research, Elsevier, vol. 228(2), pages 321-330.
    14. Stübinger, Johannes & Endres, Sylvia, 2017. "Pairs trading with a mean-reverting jump-diffusion model on high-frequency data," FAU Discussion Papers in Economics 10/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    15. repec:eee:eneeco:v:65:y:2017:i:c:p:375-388 is not listed on IDEAS
    16. Weron, Rafał, 2014. "Electricity price forecasting: A review of the state-of-the-art with a look into the future," International Journal of Forecasting, Elsevier, vol. 30(4), pages 1030-1081.
    17. Locatelli, Giorgio & Invernizzi, Diletta Colette & Mancini, Mauro, 2016. "Investment and risk appraisal in energy storage systems: A real options approach," Energy, Elsevier, vol. 104(C), pages 114-131.
    18. Ballester, Cristina & Furió, Dolores, 2015. "Effects of renewables on the stylized facts of electricity prices," Renewable and Sustainable Energy Reviews, Elsevier, vol. 52(C), pages 1596-1609.
    19. G P Girish & Aviral Kumar Tiwari, 2016. "A comparison of different univariate forecasting models forSpot Electricity Price in India," Economics Bulletin, AccessEcon, vol. 36(2), pages 1039-1057.


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