In this article, we construct a stochastic model for electricity spot prices, derive a pricing formula for electricity forward contracts, and specify risk premia inherent in such contracts. Our spot price model accounts for seasonality, mean‐reversion, and time‐varying jump intensity. Empirically, the model with a sinusoidal seasonal function, different mean‐reversion rates for the diffusion and jumps, and constant volatility is most appropriate among six different models for the United States market. The modeling approach leads us to investigate the stochastic risk premium due to both the diffusion and the jump components explicitly. The empirical results reveal that both risk premia are time‐varying and state‐dependent. The diffusion risk premium is negatively correlated with the diffusion level and fluctuates about zero, and the jump risk premium is negatively correlated with the jump level and always negative. In magnitude, the jump risk premium is much larger than the diffusion risk premium. © 2014 Wiley Periodicals, Inc. Jrl Fut Mark 35:776–793, 2015