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Self-exciting jump processes with applications to energy markets

Author

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  • Heidar Eyjolfsson

    (University of Iceland)

  • Dag Tjøstheim

    (University of Bergen)

Abstract

In this paper, we discuss a class of mean-reverting, and self-exciting continuous-time jump processes. We give a short overview, with references, of the development of such processes, discuss maximum likelihood estimation, and put them into context with processes that have been proposed recently. More specifically, we introduce a class of SDE-governed intensity processes with varying jump intensity. We study Markovian aspects of this process, and analyse its stability properties. Finally, we consider parameter estimation of our model class with daily quotes of UK electricity prices over a specific period.

Suggested Citation

  • Heidar Eyjolfsson & Dag Tjøstheim, 2018. "Self-exciting jump processes with applications to energy markets," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 373-393, April.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:2:d:10.1007_s10463-016-0591-8
    DOI: 10.1007/s10463-016-0591-8
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    References listed on IDEAS

    as
    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Thibault Jaisson & Mathieu Rosenbaum, 2013. "Limit theorems for nearly unstable Hawkes processes," Papers 1310.2033, arXiv.org, revised Mar 2015.
    3. 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.
    4. Thilo Meyer-Brandis & Peter Tankov, 2008. "Multi-Factor Jump-Diffusion Models Of Electricity Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 503-528.
    5. Helyette Geman & A. Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," Post-Print halshs-00144198, HAL.
    6. Jean-Luc Prigent, 2001. "Option Pricing with a General Marked Point Process," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 50-66, February.
    7. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
    8. Emmanuel Bacry & Jean-Fran�ois Muzy, 2014. "Hawkes model for price and trades high-frequency dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1147-1166, July.
    9. repec:dau:papers:123456789/1433 is not listed on IDEAS
    10. Hélyette Geman & Andrea Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1225-1262, May.
    11. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    12. Konstantinos Fokianos & Dag Tjøstheim, 2012. "Nonlinear Poisson autoregression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1205-1225, December.
    13. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Post-Print hal-01313994, HAL.
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    Cited by:

    1. Song, Shiyu, 2024. "The valuation of arithmetic Asian options with mean reversion and jump clustering," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    2. Giorgia Callegaro & Andrea Mazzoran & Carlo Sgarra, 2019. "A Self-Exciting Modelling Framework for Forward Prices in Power Markets," Papers 1910.13286, arXiv.org.
    3. Nikolaus Graf von Luckner & Rüdiger Kiesel, 2021. "Modeling Market Order Arrivals on the German Intraday Electricity Market with the Hawkes Process," JRFM, MDPI, vol. 14(4), pages 1-31, April.

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