| Summary: | 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.
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