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Electricity intraday price modeling with marked Hawkes processes

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  • Thomas Deschatre
  • Pierre Gruet

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.

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  • Thomas Deschatre & Pierre Gruet, 2021. "Electricity intraday price modeling with marked Hawkes processes," Papers 2103.07407, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:2103.07407
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    References listed on IDEAS

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    1. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    2. Bacry, E. & Delattre, S. & Hoffmann, M. & Muzy, J.F., 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2475-2499.
    3. René Aïd & P. Gruet & H. Pham, 2016. "An optimal trading problem in intraday electricity markets," Post-Print hal-01609481, HAL.
    4. Xuefeng Gao & Xiang Zhou & Lingjiong Zhu, 2018. "Transform analysis for Hawkes processes with applications in dark pool trading," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 265-282, February.
    5. E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 65-77, January.
    6. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Modelling microstructure noise with mutually exciting point processes," Post-Print hal-01313995, HAL.
    7. Micha{l} Narajewski & Florian Ziel, 2019. "Estimation and simulation of the transaction arrival process in intraday electricity markets," Papers 1901.09729, arXiv.org, revised Dec 2019.
    8. Omar El Euch & Mathieu Rosenbaum, 2019. "The characteristic function of rough Heston models," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 3-38, January.
    9. Michał Narajewski & Florian Ziel, 2019. "Estimation and Simulation of the Transaction Arrival Process in Intraday Electricity Markets," Energies, MDPI, vol. 12(23), pages 1-16, November.
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    11. Edouard Jaeck & Delphine Lautier, 2016. "Volatility in electricity derivative markets: the Samuelson effect revisited," Post-Print hal-01488127, HAL.
    12. Jaeck, Edouard & Lautier, Delphine, 2016. "Volatility in electricity derivative markets: The Samuelson effect revisited," Energy Economics, Elsevier, vol. 59(C), pages 300-313.
    13. Kiesel, Rüdiger & Paraschiv, Florentina, 2017. "Econometric analysis of 15-minute intraday electricity prices," Energy Economics, Elsevier, vol. 64(C), pages 77-90.
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    Cited by:

    1. René Aid & Andrea Cosso & Huyên Pham, 2022. "Equilibrium price in intraday electricity markets," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 517-554, April.

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