Estimating fast mean-reverting jumps in electricity market models

¹ EDF Lab Paris-Saclay and Université Paris-Dauphine PSL, CNRS, Ceremade, 75016 Paris, France.
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: hoffmann@ceremade.dauphine.fr

Received: 12 November 2019
Accepted: 5 November 2020

Abstract

Based on empirical evidence of fast mean-reverting spikes, electricity spot prices are often modeled X + Z^β as the sum of a continuous Itô semimartingale X and a mean-reverting compound Poisson process Z_t^β=∫₀^t ∫_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.