  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.
