Polynomial processes for power prices

TL;DR

This paper explores polynomial processes for modeling energy prices, specifically Alberta power prices, demonstrating their ability to capture complex and extreme price behaviors through one- and two-factor models.

Contribution

It introduces polynomial processes into energy price modeling, deriving new models and showing their effectiveness in capturing complex price dynamics.

Findings

Polynomial models effectively capture extreme price behaviors.

Models demonstrate strong performance in numerical experiments.

Polynomial processes provide a flexible framework for energy price modeling.

Abstract

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.