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Filtering and parameter estimation for electricity markets

University of British Columbia

The growing complexity of energy markets requires the introduction of in creasingly sophisticated tools for the analysis of market structures and for the modeling of the dynamics of spot market and forward prices. In order for market participants to use these markets in an efficient way, it is important to employ good mathematical models of these markets. This has proved to be particularly difficult for electricity, where markets are complex, and ex hibit a number of unique features, mainly due to the problems involved in storing electricity. In this thesis we propose three models for electricity prices. All are multifactor models, that is, as well as an observable spot price they assume the existence of an unobservable long term mean’ process. The introduction of such additional processes helps to explain the relation between spot and futures prices. In the first part of the thesis we introduce a two factor Gaus sian model for prices. Using the Kalman filter, and based on both spot and forward prices, we successfully estimate parameters for simulated data. We then estimate parameters for the German EEX market, and compare our fitted model with the observed prices. We find that this model does capture some features of the EEX market, but it fails to exhibit the price spikes which are a prominent feature of true spot prices. We therefore introduce a second model, which includes jumps. The inclusion of jumps has the potential to give a better explanation of the behavior of electricity prices, but it creates difficulties in the estimation of parameters. This is because as the model noise is non-Gaussian the Kalman filter cannot be applied satisfactorily. We implement the particle filter adopting the Liu & West approach for the jump model. This method allows us to identify the hidden process in the model, and to estimate a small number of parameters. The third model is a new model for electricity prices based on the inverse Box-Cox transformation. This model is non-linear with Gaussian noise, and can generate price spikes using fewer parameters than a multi-factor jump-diffusion model. In this context, we successfully applied the Unscented Kalman filter to estimate the parameters.

Text

2010-03-10

Attribution-NonCommercial-NoDerivs 3.0 Unported

http://hdl.handle.net/2429/21736

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/3.0/