Electricity Intraday Price Modelling with Marked Hawkes Processes

Abstract

We consider a two-dimensional marked Hawkes process with increasing baseline intensity 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 modelled 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. [2013a. ‘Modelling Microstructure Noise with Mutually Exciting Point Processes.’ Quantitative Finance 13 (1): 65–77. doi:10.1080/14697688.2011.647054.] 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.