  We present a new model for the electricity spot price dynamics, which is able
to capture seasonality, low-frequency dynamics and the extreme spikes in the
market. Instead of the usual purely deterministic trend we introduce a
non-stationary independent increments process for the low-frequency dynamics,
and model the large fluctuations by a non-Gaussian stable CARMA process. The
model allows for analytic futures prices, and we apply these to model and
estimate the whole market consistently. Besides standard parameter estimation,
an estimation procedure is suggested, where we fit the non-stationary trend
using futures data with long time until delivery, and a robust $L^1$-filter to
find the states of the CARMA process. The procedure also involves the empirical
and theoretical risk premiums which -- as a by-product -- are also estimated.
We apply this procedure to data from the German electricity exchange EEX, where
we split the empirical analysis into base load and peak load prices. We find an
overall negative risk premium for the base load futures contracts, except for
contracts close to delivery, where a small positive risk premium is detected.
The peak load contracts, on the other hand, show a clear positive risk premium,
when they are close to delivery, while the contracts in the longer end also
have a negative premium.
