Log-Elliptical Tail Distributions of Power Prices – Evidence from Germany and France

Abstract

Electricity price distributions exhibit high volatility, positive and negative price spikes and consequently fat tails. As risk management is mainly concerned with extreme outcomes that exceed a defined safety threshold value, the exceedances, we can focus on the tails of the distributions. With Augmented Dickey-Fuller-, Durbin-Watson-, and Autoregressive Conditional Heteroskedasticity Lagrange multiplier tests we show for daily German and French power prices that the log exceedances in the expected Pareto tails of electricity price distributions can be assumed as stationary, independent and identically distributed. We can therefore assume, that the prerequisites of the applied peak over threshold extreme value theory and statistical inference are fulfilled. With the further results of the here suitable Andersen-Darling test we conclude, that for daily German and French power prices it can be justified to recommend the log logistic or the lognormal distribution as alternatives in power price risk management.