Title: Oscillating Ornstein-Uhlenbeck processes in electricity markets: Modelling and statistical inference
Authors: Jeannette Woerner - TU Dortmund (Germany) [presenting]
Daniel Kobe - TU Dortmund (Germany)
Abstract: Recently there have been proposed many models for electricity spot prices trying to capture the characteristic features of seasonalities and spikes in the prices. A common approach is to remove the seasonalities first and then divide the remaining random part in a stochastic process accounting for the normal variations of the prices and one modelling the spikes, e.g. with a combination of Ornstein-Uhlenbeck processes with different speed of mean reversion. We now propose to generalize the underlying stochastic process in such a way that we can include the seasonalities into our stochastic process and also reproduce the oscillating behaviour of the empirical autocorrelation function of the prices. We consider oscillating Ornstein-Uhlenbeck processes which belong to the class of continuous-time moving average processes. We show that a linear combination of the oscillating Ornstein-Uhlenbeck processes together with an Ornstein-Uhlenbeck process well fits the autocorrelation function of electricity spot prices and reproduces the spikes. Furthermore, we derive an explicit formula for the forward price, which is a generalization of a previous formula. In a similar way this formula may be used for option pricing. Finally, we show, how we may infer the model parameters using empirical moments.