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Erschienen in:
Estimation of the Number of Factors in a Multi-Factorial Heath-Jarrow-Morton Model in Power Markets Kapitel lesen Erstes Kapitel lesen

2024 | OriginalPaper | Buchkapitel

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

verfasst von : Riccardo Brignone, Luca Gonzato, Carlo Sgarra

Erschienen in: Quantitative Energy Finance

Verlag: Springer Nature Switzerland

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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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Vorheriges Kapitel Estimation of the Number of Factors in a Multi-Factorial Heath-Jarrow-Morton Model in Power Markets
Nächstes Kapitel Periodic Trawl Processes: Simulation, Statistical Inference and Applications in Energy Markets
Fußnoten
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
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
See e.g. [52] and the references therein for more details on the design of this experiment and definition of RMSE.
 
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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Metadaten
Titel
Hawkes Processes in Energy Markets: Modelling, Estimation and Derivatives Pricing
verfasst von
Riccardo Brignone
Luca Gonzato
Carlo Sgarra
Copyright-Jahr
2024
Buch
Quantitative Energy Finance

Print ISBN: 978-3-031-50596-6

Electronic ISBN: 978-3-031-50597-3

Copyright-Jahr: 2024

DOI
https://doi.org/10.1007/978-3-031-50597-3_2