We introduce a three-factor model of electricity spot prices, consisting of a determinis-
tic seasonality and trend function as well as short- and long-term stochastic components,
and derive a formula for futures prices. The long-term component is modelled as a L ́evy
process with increments belonging to the class of generalised hyperbolic distributions. We de-
scribe the short-term factor by L ́evy semistationary processes: we start from a CARMA(2,1),
i.e. a continous-time ARMA model, and generalise it by adding a short-memory stochastic
volatility. We further modify the model by including the information about the wind energy
production as an exogenous variable. We fit our models to German and Austrian data in-
cluding spot and futures prices as well as the wind energy production and total load data.
Empirical studies reveal that taking into account the impact of the wind energy generation on
the prices improves the goodness of fit.