The GARCH-copula model for gaugeing time conditional dependence in the risk management of electricity derivatives

Sammanfattning: In the risk management of electricity derivatives, time to delivery can be divided into a time grid, with the assumption that within each cell of the grid, volatility is more or less constant. This setup however does not take in to account dependence between the different cells in the time grid. This thesis tries to develop a way to gauge the dependence between electricity derivatives at the different places in the time grid and different delivery periods. More specifically, the aim is to estimate the size of the ratio of the quantile of the sum of price changes against the sum of the marginal quantiles of the price changes. The approach used is a combination of Generalised Autoregressive Conditional Heteroscedasticity (GARCH) processes and copulas. The GARCH process is used to filter out heteroscedasticity in the price data. Copulas are fitted to the filtered data using pseudo maximum likelihood and the fitted copulas are evaluated using a goodness of fit test. GARCH processes alone are found to be insufficient to capture the dynamics of the price data. It is found that combining GARCH with Autoregressive Moving Average processes provides better fit to the data. The resulting dependence is the found to be best captured by elliptical copulas. The estimated ratio is found to be quite small in the cases studied. The use of the ARMA-GARCH filtering gives in general a better fit for copulas when applied to financial data. A time dependency in the dependence can also be observed.