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Futures pricing in electricity markets based on stable CARMA spot models

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  • Fred Espen Benth
  • Claudia Kluppelberg
  • Gernot Muller
  • Linda Vos

Abstract

We present a new model for the electricity spot price dynamics, which is able to capture seasonality, low-frequency dynamics and the extreme spikes in the market. Instead of the usual purely deterministic trend we introduce a non-stationary independent increments process for the low-frequency dynamics, and model the large fluctuations by a non-Gaussian stable CARMA process. The model allows for analytic futures prices, and we apply these to model and estimate the whole market consistently. Besides standard parameter estimation, an estimation procedure is suggested, where we fit the non-stationary trend using futures data with long time until delivery, and a robust $L^1$-filter to find the states of the CARMA process. The procedure also involves the empirical and theoretical risk premiums which -- as a by-product -- are also estimated. We apply this procedure to data from the German electricity exchange EEX, where we split the empirical analysis into base load and peak load prices. We find an overall negative risk premium for the base load futures contracts, except for contracts close to delivery, where a small positive risk premium is detected. The peak load contracts, on the other hand, show a clear positive risk premium, when they are close to delivery, while the contracts in the longer end also have a negative premium.

Suggested Citation

  • Fred Espen Benth & Claudia Kluppelberg & Gernot Muller & Linda Vos, 2012. "Futures pricing in electricity markets based on stable CARMA spot models," Papers 1201.1151, arXiv.org.
    • Handle: RePEc:arx:papers:1201.1151
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    References listed on IDEAS

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    1. Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
    2. Hendrik Bessembinder & Michael L. Lemmon, 2002. "Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets," Journal of Finance, American Finance Association, vol. 57(3), pages 1347-1382, June.
    3. Paschke, Raphael & Prokopczuk, Marcel, 2010. "Commodity derivatives valuation with autoregressive and moving average components in the price dynamics," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2742-2752, November.
    4. Kolos, Sergey P. & Ronn, Ehud I., 2008. "Estimating the commodity market price of risk for energy prices," Energy Economics, Elsevier, vol. 30(2), pages 621-641, March.
    5. P. Brockwell, 2001. "Lévy-Driven Carma Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 113-124, March.
    6. 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.
    7. Claudia Kluppelberg & Thilo Meyer-Brandis & Andrea Schmidt, 2010. "Electricity spot price modelling with a view towards extreme spike risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 963-974.
    8. 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.
    9. Brockett, Patrick L. & Tucker, Howard G., 1977. "A conditional dichotomy theorem for stochastic processes with independent increments," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 13-27, March.
    10. repec:bla:jfinan:v:59:y:2004:i:4:p:1877-1900 is not listed on IDEAS
    11. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0601, December.
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    Cited by:

    1. Almut E. D. Veraart & Luitgard A. M. Veraart, 2013. "Risk premia in energy markets," CREATES Research Papers 2013-02, Department of Economics and Business Economics, Aarhus University.

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