We propose a new model for the description and forecast of gross prices of electricity in the liberalized Italian energy market via an additive two-factor model. We show the characteristics of spot prices and the presence of self-correlations in the price increments. Further, we show the presence of several jumps in the Italian electricity market, many of which appear clustered over short time periods. The two-factor model we propose is driven by both Hawkes and fractional Brownian processes. We examine the system in detail from a modeling point of view. We then perform a calibration procedure, discussing the seasonality, spikes and an estimate of the Hurst coefficient. After calibrating and validating the model, we consider its forecasting performance via a class of adequate evaluation metrics.