We present a new model for pricing electricity swaps. Two general factors affect all contracts but unique risk factors affect each contract. General factors are average swap prices and deterministic trend-seasonal components, and unique factors are forward premiums. Innovations follow MNIG distributions. We estimate the model with data from the European Energy Exchange. The model outperforms four competitors, both in in-sample valuation and in out-of-sample forecasting, and in fitting the term structure of volatilities by market segments. Competitor models are (i) diffusion spot prices, (ii) jump-diffusion spot prices with time dependent volatility, (iii) HJM-based and (iv) Levy multifactor model with NIG distributions. Value-at-Risk measures based on normality strongly underestimate tail risk whereas our model gives estimates that are more accurate.