Electricity intraday price modeling with marked Hawkes processes

TL;DR

This paper introduces a 2D marked Hawkes process model with increasing baseline intensity to accurately capture the dynamics of electricity intraday prices, including market activity, jump sizes, and microstructure noise, with practical estimation and theoretical insights.

Contribution

It extends Hawkes process modeling by incorporating increasing baseline intensity and random jump sizes, providing analytic formulas and empirical validation for electricity market prices.

Findings

Model fits German electricity data well

Captures microstructure noise via signature plot

Shows convergence to Brownian motion with increasing volatility

Abstract

We consider a 2-dimensional marked Hawkes process with increasing baseline intensity in order to model prices on electricity intraday markets. This model allows to represent different empirical facts such as increasing market activity, random jump sizes but above all microstructure noise through the signature plot. This last feature is of particular importance for practitioners and has not yet been modeled on those particular markets. We provide analytic formulas for first and second moments and for the signature plot, extending the classic results of Bacry et al. (2013) in the context of Hawkes processes with random jump sizes and time dependent baseline intensity. The tractable model we propose is estimated on German data and seems to fit the data well. We also provide a result about the convergence of the price process to a Brownian motion with increasing volatility at macroscopic scales, highlighting the Samuelson effect.