Mathematical Modelling of Derivative on the Nordic Power Market

Per Hansson and Erik Lindström

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2000:E13

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Abstract

This is a Master's thesis with the aim to model power derivatives on the Nordic power market. Almost three quarters of the trading on Nord Pool consist of derivatives. We have focused on futures and forwards in this thesis.

We mainly use two techniques for modelling, beginning with a black-box model where we look at the sets of data and from that, try to find a well-describing model. The statistical tools applied work with no information about the structure of the data and all knowledge is based on the data. Starting with the identification of a number of trends in the data, we primarily work with two methods for detrending, the EP-method and the Hough transform. We filter the detrended process for outliers and then continue with the analysis of the remaining process by using non-linear heteroscedastic models such as AR-GARCH to capture the dynamics of the process. The result is that heteroscedastic models are successful when modelling detrended price data. The remaining residuals are Gaussian and uncorrelated according to the Bera-Jarque test.

The second technique is called grey-box, where we work from the assumption that we have some knowledge of the process generating the data. We start with a simple model to see whether our assumptions about the model are correct. From there we use stochastic differential equations to mathematically express the relation between the price and external signals. Using GMM-estimation we are able to do a long-term prediction of the price that do well in comparison with differentiation.

Taking into consideration that consumption and supply varies over time, a grey-box model is a more suitable model for long-term predictions.

The result from the prediction can then be used in portfolio optimisation. We end with an introduction to portfolio optimisation and arbitrage theory, and show possible arbitrage opportunities on the Nordic power market.