Risk premiums between spot and forward prices play a key role in energy markets. This paper derives analytic expressions for such risk premiums when spot prices are modeled by Lévy semistationary processes. We focus particularly on electricity prices. In an empirical study based on electricity spot prices and futures from the European Energy Exchange market, we investigate the behavior of electricity risk premiums from a statistical perspective. Furthermore, we demonstrate how a suitable model for electricity futures prices can be formulated, obtaining promising empirical results.