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Rough electricity: a new fractal multi-factor model of electricity spot prices

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  • Mikkel Bennedsen

    (Aarhus University and CREATES)

Abstract

We introduce a new mathematical model of electricity spot prices which accounts for the most important stylized facts of these time series: seasonality, spikes, stochastic volatility and mean reversion. Empirical studies have found a possible fifth stylized fact, fractality, and our approach explicitly incorporates this into the model of the prices. Our setup generalizes the popular Ornstein Uhlenbeck-based multi-factor framework of Benth et al. (2007) and allows us to perform statistical tests to distinguish between an Ornstein Uhlenbeck-based model and a fractal model. Further, through the multi-factor approach we account for seasonality and spikes before estimating - and making inference on - the degree of fractality. This is novel in the literature and we present simulation evidence showing that these precautions are crucial to accurate estimation. Lastly, we estimate our model on recent data from six European energy exchanges and we find statistical evidence of fractality in five out of six markets. As an application of our model, we show how, in these five markets, a fractal component improves short term forecasting of the prices.

Suggested Citation

  • 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.
    • Handle: RePEc:aah:create:2015-42
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    File URL: https://repec.econ.au.dk/repec/creates/rp/15/rp15_42.pdf
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/1433 is not listed on IDEAS
    2. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2015. "Hybrid scheme for Brownian semistationary processes," CREATES Research Papers 2015-43, Department of Economics and Business Economics, Aarhus University.
    3. Weron, Rafal & Przybyłowicz, Beata, 2000. "Hurst analysis of electricity price dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(3), pages 462-468.
    4. 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.
    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. 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.
    7. Erzgräber, Hartmut & Strozzi, Fernanda & Zaldívar, José-Manuel & Touchette, Hugo & Gutiérrez, Eugénio & Arrowsmith, David K., 2008. "Time series analysis and long range correlations of Nordic spot electricity market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6567-6574.
    8. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    9. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2015. "Hybrid scheme for Brownian semistationary processes," Papers 1507.03004, arXiv.org, revised May 2017.
    10. 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.
    11. Mikko S. Pakkanen, 2011. "Brownian Semistationary Processes And Conditional Full Support," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 579-586.
    12. 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.
    13. 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.
    14. Ole E. Barndorff-Nielsen & Fred Espen Benth & Almut E. D. Veraart, 2013. "Modelling energy spot prices by volatility modulated L\'{e}vy-driven Volterra processes," Papers 1307.6332, arXiv.org.
    15. Rypdal, Martin & Løvsletten, Ola, 2013. "Modeling electricity spot prices using mean-reverting multifractal processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 194-207.
    16. Thilo Meyer-Brandis & Peter Tankov, 2008. "Multi-Factor Jump-Diffusion Models Of Electricity Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 503-528.
    17. Ladislav KRISTOUFEK & Petra LUNACKOVA, 2013. "Long-term Memory in Electricity Prices: Czech Market Evidence," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 63(5), pages 407-424, November.
    18. Almut E. D. Veraart & Luitgard A. M. Veraart, 2012. "Modelling electricity day–ahead prices by multivariate Lévy semistationary processes," CREATES Research Papers 2012-13, Department of Economics and Business Economics, Aarhus University.
    19. T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 21-36.
    20. Helyette Geman & A. Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," Post-Print halshs-00144198, HAL.
    21. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    22. Norouzzadeh, P. & Dullaert, W. & Rahmani, B., 2007. "Anti-correlation and multifractal features of Spain electricity spot market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 333-342.
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    Cited by:

    1. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2015. "Hybrid scheme for Brownian semistationary processes," CREATES Research Papers 2015-43, Department of Economics and Business Economics, Aarhus University.
    2. Mikkel Bennedsen, 2016. "Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data," CREATES Research Papers 2016-21, Department of Economics and Business Economics, Aarhus University.
    3. Mikkel Bennedsen & Ulrich Hounyo & Asger Lunde & Mikko S. Pakkanen, 2016. "The Local Fractional Bootstrap," CREATES Research Papers 2016-15, Department of Economics and Business Economics, Aarhus University.
    4. Josselin Garnier & Knut Sølna, 2018. "Option pricing under fast-varying and rough stochastic volatility," Annals of Finance, Springer, vol. 14(4), pages 489-516, November.
    5. Mikkel Bennedsen & Ulrich Hounyo & Asger Lunde & Mikko S. Pakkanen, 2016. "The Local Fractional Bootstrap," Papers 1605.00868, arXiv.org, revised Oct 2017.
    6. Mikkel Bennedsen, 2016. "Semiparametric inference on the fractal index of Gaussian and conditionally Gaussian time series data," Papers 1608.01895, arXiv.org, revised Mar 2018.
    7. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2015. "Hybrid scheme for Brownian semistationary processes," Papers 1507.03004, arXiv.org, revised May 2017.

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    More about this item

    Keywords

    Energy markets; electricity prices; roughness; fractals; mean reversion; multi-factor modelling; forecasting.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • Q41 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Demand and Supply; Prices

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