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Hawkes Processes in Energy Markets: Modelling, Estimation and Derivatives Pricing

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Quantitative Energy Finance

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Abstract

The purpose of the present contribution is to illustrate the extensive use of Hawkes processes in modeling price dynamics in energy markets and to show how they can be applied for derivatives pricing. After a review of the literature devoted to the subject and on the exact simulation of Hawkes processes, we introduce a simple, yet useful, Hawkes-based model for energy spot prices. We present the model under the historical measure and illustrate a structure preserving change of measure, allowing to specify a risk-neutral dynamics. Then, we propose an effective estimation methodology based on particle filtering. Finally, we show how to perform exotic derivatives pricing both through exact simulation and characteristic function inversion techniques.

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Notes

  1. 1.

    In other words, we exclude from our review those methods which are expectantly slow since based on repeated implementation of computationally intensive numerical techniques such as, for example, root finding algorithms (as in [64]), or numerical integration (as in [59]).

  2. 2.

    A partial solution to this problem is given by increasing the value of the parameter \(\bar {k}\) in Algorithm 3, which controls the function L.

  3. 3.

    See e.g. [52] and the references therein for more details on the design of this experiment and definition of RMSE.

  4. 4.

    We performed several experiments and we found that, for the log–likelihood computation in step 1, \(N=100\) and \(M=10^4\) are enough to fully represent the spectrum of reasonable starting points. A higher number of particles N is only needed to control the Monte Carlo variance of the likelihood estimator, but not to increase its level. Therefore, we increase N only for the subsequent optimization in order to stabilize the inferential procedure.

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Acknowledgements

The authors express their gratitude to an anonymous referee, who read very carefully a previous version of this chapter and provided significant suggestions, helpful in substantially improving the manuscript.

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Authors and Affiliations

  1. Department of Quantitative Finance, Institute for Economic Research, University of Freiburg, Freiburg im Breisgau, Germany

    Riccardo Brignone

  2. Department of Statistics and Operations Research, University of Vienna, Vienna, Austria

    Luca Gonzato

  3. Department of Mathematics, Università degli studi di Bari “Aldo Moro”, Bari, Italy

    Carlo Sgarra

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  1. Riccardo Brignone
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  2. Luca Gonzato
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  3. Carlo Sgarra
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Correspondence to Carlo Sgarra .

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Editors and Affiliations

  1. Department of Mathematics, University of Oslo, Oslo, Norway

    Fred Espen Benth

  2. Department of Mathematics, Imperial College London, London, UK

    Almut E. D. Veraart

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Brignone, R., Gonzato, L., Sgarra, C. (2024). Hawkes Processes in Energy Markets: Modelling, Estimation and Derivatives Pricing. In: Benth, F.E., Veraart, A.E.D. (eds) Quantitative Energy Finance. Springer, Cham. https://doi.org/10.1007/978-3-031-50597-3_2

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