A branching process approach to power markets

Highlights: • A new model for power prices including the jumps clustering features • Some explicit valuation formulas for the basic derivatives contracts in the modeling framework proposed • A risk premium analysis for the model introduced with a comparison with previous models • A statistical analysis supporting the modeling approach proposed -- Abstract: We propose and investigate a market model for power prices, including most basic features exhibited by previous models and taking into account self-exciting properties. The model proposed extends Hawkes-type models by introducing a twofold integral representation property. A Random Field approach was already exploited by Barndorff-Nielsen et al., who adopted the Ambit Field framework for describing the power price dynamics. The novelty contained in our approach consists of combining the basic features of both Branching Processes and Random Fields in order to get a realistic and parsimonious model setting. We shall provide some closed-form evaluation formulae for forward contracts. We discuss the risk premium behavior, by pointing out that in the present framework, a very realistic description arises. We outline a possible methodology for parameters estimation. We illustrate by graphical representation the main achievements of this approach.