Volume 24, 2020
|Page(s)||963 - 1002|
|Published online||15 December 2020|
Estimating fast mean-reverting jumps in electricity market models
EDF Lab Paris-Saclay and Université Paris-Dauphine PSL, CNRS, Ceremade,
2 Olivier Féron, EDF Lab Paris-Saclay and FiME, Laboratoire de Finance des Marchés de l’Energie, 91120 Palaiseau, France.
3 Marc Hoffmann, Université Paris-Dauphine PSL, CNRS, Ceremade, 75016 Paris, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 5 November 2020
Based on empirical evidence of fast mean-reverting spikes, electricity spot prices are often modeled X + Zβ as the sum of a continuous Itô semimartingale X and a mean-reverting compound Poisson process Ztβ=∫0t ∫ℝxe−β(t−s)p̲(ds,dt) where p̲(ds,dt) is Poisson random measure with intensity λds ⊗dt. In a first part, we investigate the estimation of (λ, β) from discrete observations and establish asymptotic efficiency in various asymptotic settings. In a second part, we discuss the use of our inference results for correcting the value of forward contracts on electricity markets in presence of spikes. We implement our method on real data in the French, German and Australian market over 2015 and 2016 and show in particular the effect of spike modelling on the valuation of certain strip options. In particular, we show that some out-of-the-money options have a significant value if we incorporate spikes in our modelling, while having a value close to 0 otherwise.
Mathematics Subject Classification: 62M86 / 60J75 / 60G35 / 60F05
Key words: Financial statistics / discrete observations / electricity market modelling / derivatives pricing
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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