  Polynomial processes have the property that expectations of polynomial
functions (of degree $n$, say) of the future state of the process conditional
on the current state are given by polynomials (of degree $\leq n$) of the
current state. Here we explore the application of polynomial processes in the
context of structural models for energy prices. We focus on the example of
Alberta power prices, derive one- and two-factor models for spot prices. We
examine their performance in numerical experiments, and demonstrate that the
richness of the dynamics they are able to generate makes them well suited for
modelling even extreme examples of energy price behaviour.
