Futures pricing in electricity markets based on stable CARMA spot models |
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| Affiliation: | 1. Center of Mathematics for Applications (CMA), University of Oslo, P.O. Box 1053, Blindern, N-0316 Oslo, Norway;2. Center for Mathematical Sciences, Technische Universität München, Boltzmannstrasse 3, D-85748 Garching, Germany;3. Institute of Mathematics, Universität Augsburg, Universitätsstrasse 14, D-86159 Augsburg, Germany;4. Department of Economics, University of Agder, Serviceboks 422, N-4604 Kristiansand, Norway;1. Centre for Advanced Study, Drammensveien 78, N-0271 Oslo, Norway;2. Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, N–0316 Oslo, Norway;3. School of Business and Law, University of Agder, Serviceboks 422, N-4604 Kristiansand, Norway;1. APG Asset Management, The Netherlands;2. Cardano, The Netherlands;3. Econometric Institute, Erasmus University Rotterdam, The Netherlands;4. Tinbergen Institute, The Netherlands;5. Erasmus Research Institute of Management, The Netherlands;1. Institute for Operations Research and Computational Finance, University of St. Gallen, Switzerland;2. Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway |
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| Abstract: | We present a new model for the electricity spot price dynamics, which is able to capture seasonality, low-frequency dynamics and extreme spikes in the market. Instead of the usual purely deterministic trend we introduce a non-stationary independent increment 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 L1-filter to find the states of the CARMA process. The procedure also involves the empirical and theoretical risk premia 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. Peak load contracts, on the other hand, show a clear positive risk premium, when they are close to delivery, while contracts in the longer end also have a negative premium. |
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