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Electricity Intraday Price Modelling with Marked Hawkes Processes

Electricity Intraday Price Modelling with Marked Hawkes Processes 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

Electricity Intraday Price Modelling with Marked Hawkes Processes

Deschatre, Thomas; Gruet, Pierre
Applied Mathematical Finance , Volume 29 (4): 34 – Jul 4, 2022
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34 pages

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...
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Publisher
Taylor & Francis
Copyright
© 2023 Informa UK limited, trading as Taylor & Francis Group
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2023.2180399
Publisher site
See Article on Publisher Site

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.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Jul 4, 2022

Keywords: Electricity intraday prices; microstructure noise; Hawkes processes; high-frequency statistics

References

  • An Optimal Trading Problem in Intraday Electricity Markets
  • Modelling Microstructure Noise with Mutually Exciting Point Processes
  • Some Limit Theorems for Hawkes Processes and Application to Financial Statistics
  • Hawkes Processes in Finance
  • Statistical Inference Across Time Scales
  • The Characteristic Function of Rough Heston Models
  • Transform Analysis for Hawkes Processes with Applications in Dark Pool Trading
  • Modeling Market Order Arrivals on the German Intraday Electricity Market with the Hawkes Process
  • A Cluster Process Representation of a Self-exciting Process
  • The Significance Probability of the Smirnov Two-sample Test
  • Volatility in Electricity Derivative Markets: The Samuelson Effect Revisited
  • Econometric Analysis of 15-minute Intraday Electricity Prices
  • Estimation and Simulation of the Transaction Arrival Process in Intraday Electricity Markets
  • On Lewis' Simulation Method for Point Processes
  • Spike Trains As (in) Homogeneous Poisson Processes Or Hawkes Processes: Non-parametric Adaptive Estimation and Goodness-of-fit Tests
  • Limit Theorems for Stochastic Processes