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A Stochastic Latent Moment Model for Electricity Price Formation


  • Angelica Gianfreda

    () (Free University of Bozen-Bolzano, Faculty of Economics and Management)

  • Derek Bunn

    () (London Business School, Energy Markets Group)


The wide range of models needed to support the various short-term operations for electricity generation demonstrates the importance of accurate specifications for the uncertainty in market prices. This is becoming increasingly challenging, since electricity hourly price densities exhibit a variety of shapes, with their characteristic features changing substantially within the day and over time, and the in ux of renewable power, wind and solar in particular, has amplified these effects. A general-purpose, analytically tractable representation of the stochastic price formation process would have considerable value for operations control and trading, but existing empirical approaches or the application of standard density functions are unsatisfactory. We develop a general four parameter stochastic model for hourly prices, in which the four moments of the density function are dynamically estimated as latent state variables and furthermore modelled as functions of several plausible exogenous drivers. This provides a transparent and credible model that is suffciently exible to capture the shape-shifting effects, particularly with respect to the wind and solar output variations causing dynamic switches in the upside and downside risks. Extensive testing on German wholesale price data, benchmarked against quantile regression and other models in out-of-sample backtesting, validated the approach and its analytical appeal.

Suggested Citation

  • Angelica Gianfreda & Derek Bunn, 2018. "A Stochastic Latent Moment Model for Electricity Price Formation," BEMPS - Bozen Economics & Management Paper Series BEMPS46, Faculty of Economics and Management at the Free University of Bozen.
  • Handle: RePEc:bzn:wpaper:bemps46

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    1. Koopman, Siem Jan & Ooms, Marius & Carnero, M. Angeles, 2007. "Periodic Seasonal Reg-ARFIMAGARCH Models for Daily Electricity Spot Prices," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 16-27, March.
    2. Karakatsani, Nektaria V. & Bunn, Derek W., 2008. "Forecasting electricity prices: The impact of fundamentals and time-varying coefficients," International Journal of Forecasting, Elsevier, vol. 24(4), pages 764-785.
    3. Matsumoto, Ken'ichi & Voudouris, Vlasios & Stasinopoulos, Dimitrios & Rigby, Robert & Di Maio, Carlo, 2012. "Exploring crude oil production and export capacity of the OPEC Middle East countries," Energy Policy, Elsevier, vol. 48(C), pages 820-828.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Haldrup, Niels & Nielsen, Morten Orregaard, 2006. "A regime switching long memory model for electricity prices," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 349-376.
    6. Knittel, Christopher R. & Roberts, Michael R., 2005. "An empirical examination of restructured electricity prices," Energy Economics, Elsevier, vol. 27(5), pages 791-817, September.
    7. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    8. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the "t"-distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174.
    9. Patrick Jaillet & Ehud I. Ronn & Stathis Tompaidis, 2004. "Valuation of Commodity-Based Swing Options," Management Science, INFORMS, vol. 50(7), pages 909-921, July.
    10. De Vany, Arthur S. & Walls, W. David, 1999. "Cointegration analysis of spot electricity prices: insights on transmission efficiency in the western US," Energy Economics, Elsevier, vol. 21(5), pages 435-448, October.
    11. Panagiotelis, Anastasios & Smith, Michael, 2008. "Bayesian density forecasting of intraday electricity prices using multivariate skew t distributions," International Journal of Forecasting, Elsevier, vol. 24(4), pages 710-727.
    12. Len Umantsev & Victor Chernozhukov, 2001. "Conditional value-at-risk: Aspects of modeling and estimation," Empirical Economics, Springer, vol. 26(1), pages 271-292.
    13. Weron, Rafal & Misiorek, Adam, 2008. "Forecasting spot electricity prices: A comparison of parametric and semiparametric time series models," International Journal of Forecasting, Elsevier, vol. 24(4), pages 744-763.
    14. Jae Ho Kim & Warren B. Powell, 2011. "Optimal Energy Commitments with Storage and Intermittent Supply," Operations Research, INFORMS, vol. 59(6), pages 1347-1360, December.
    15. Ketterer, Janina C., 2014. "The impact of wind power generation on the electricity price in Germany," Energy Economics, Elsevier, vol. 44(C), pages 270-280.
    16. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    17. Paraschiv, Florentina & Erni, David & Pietsch, Ralf, 2014. "The impact of renewable energies on EEX day-ahead electricity prices," Energy Policy, Elsevier, vol. 73(C), pages 196-210.
    18. M. C. Jones & Arthur Pewsey, 2009. "Sinh-arcsinh distributions," Biometrika, Biometrika Trust, vol. 96(4), pages 761-780.
    19. Kay Giesecke & Baeho Kim & Jack Kim & Gerry Tsoukalas, 2014. "Optimal Credit Swap Portfolios," Management Science, INFORMS, vol. 60(9), pages 2291-2307, September.
    20. Caporin, Massimiliano & Preś, Juliusz & Torro, Hipolit, 2012. "Model based Monte Carlo pricing of energy and temperature Quanto options," Energy Economics, Elsevier, vol. 34(5), pages 1700-1712.
    21. Karakatsani Nektaria V & Bunn Derek W., 2010. "Fundamental and Behavioural Drivers of Electricity Price Volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-42, September.
    22. repec:dau:papers:123456789/11500 is not listed on IDEAS
    23. Haldrup Niels & Nielsen Morten Ø., 2006. "Directional Congestion and Regime Switching in a Long Memory Model for Electricity Prices," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-24, September.
    24. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    25. Alvaro Escribano & J. Ignacio Peña & Pablo Villaplana, 2011. "Modelling Electricity Prices: International Evidence," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 73(5), pages 622-650, October.
    26. Tryggvi Jónsson & Pierre Pinson & Henrik Madsen & Henrik Aalborg Nielsen, 2014. "Predictive Densities for Day-Ahead Electricity Prices Using Time-Adaptive Quantile Regression," Energies, MDPI, Open Access Journal, vol. 7(9), pages 1-25, August.
    27. Serinaldi, Francesco, 2011. "Distributional modeling and short-term forecasting of electricity prices by Generalized Additive Models for Location, Scale and Shape," Energy Economics, Elsevier, vol. 33(6), pages 1216-1226.
    28. Huisman, Ronald, 2008. "The influence of temperature on spike probability in day-ahead power prices," Energy Economics, Elsevier, vol. 30(5), pages 2697-2704, September.
    29. Clò, Stefano & Cataldi, Alessandra & Zoppoli, Pietro, 2015. "The merit-order effect in the Italian power market: The impact of solar and wind generation on national wholesale electricity prices," Energy Policy, Elsevier, vol. 77(C), pages 79-88.
    30. Johannes Mauritzen, 2013. "Dead Battery? Wind Power, the Spot Market, and Hydropower Interaction in the Nordic Electricity Market," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1).
    31. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554.
    32. Kristiansen, Tarjei, 2012. "Forecasting Nord Pool day-ahead prices with an autoregressive model," Energy Policy, Elsevier, vol. 49(C), pages 328-332.
    33. 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.
    34. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
    35. 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.
    36. Woo, C.K. & Horowitz, I. & Moore, J. & Pacheco, A., 2011. "The impact of wind generation on the electricity spot-market price level and variance: The Texas experience," Energy Policy, Elsevier, vol. 39(7), pages 3939-3944, July.
    37. Bunn, Derek W. & Gianfreda, Angelica, 2010. "Integration and shock transmissions across European electricity forward markets," Energy Economics, Elsevier, vol. 32(2), pages 278-291, March.
    38. Chung-Li Tseng & Graydon Barz, 2002. "Short-Term Generation Asset Valuation: A Real Options Approach," Operations Research, INFORMS, vol. 50(2), pages 297-310, April.
    39. Mulder, Machiel & Scholtens, Bert, 2013. "The impact of renewable energy on electricity prices in the Netherlands," Renewable Energy, Elsevier, vol. 57(C), pages 94-100.
    40. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew "t"-distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389.
    41. Dennis Frestad & Fred Espen Benth & Steen Koekebakker, 2010. "Modeling Term Structure Dynamics in the Nordic Electricity Swap Market," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2), pages 53-86.
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    More about this item


    Electricity Prices; Density Estimation; Skewness; Quantiles; Risk;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • 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
    • Q47 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy Forecasting

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