A self-exciting modeling framework for forward prices in power markets

We propose and investigate two model classes for forward power price dynamics, based on continuous branching processes with immigration, and on Hawkes processes with exponential kernel, respectively. The models proposed exhibit jumps clustering features. Models of this kind have been already proposed for the spot price dynamics, but the main purpose of the present work is to investigate the performances of such models in describing the forward dynamics. We adopt a Heath–Jarrow–Morton approach in order to capture the whole forward curve evolution. By examining daily data in the French power market, we perform a goodness-of-fit test and we present our conclusions about the adequacy of these models in describing the forward prices evolution.