[Paper Review] A Self-Exciting Modelling Framework for Forward Prices in Power Markets

Giorgia Callegaro, Andrea Mazzoran+1 more|arXiv (Cornell University)|Oct 29, 2019

Stochastic processes and financial applications34 references4 citations

TL;DR

This paper proposes a Heath-Jarrow-Morton (HJM) framework for forward power prices using two self-exciting models—continuous branching processes with immigration (CBI) and Hawkes processes with exponential kernel—showing that Hawkes processes better capture jump clustering in forward prices than CBI models, as confirmed by goodness-of-fit tests on French power market data.

ABSTRACT

We propose and investigate two model classes for forward power price dynamics, based on continuous branching processes with immigration, and on Hawkes processes with exponential kernel, respectively. The models proposed exhibit jumps clustering features. Models of this kind have been already proposed for the spot price dynamics, but the main purpose of the present work is to investigate the performances of such models in describing the forward dynamics. We adopt a Heath-Jarrow-Morton approach in order to capture the whole forward curve evolution. By examining daily data in the French power market, we perform a goodness-of-fit test and we present our conclusions about the adequacy of these models in describing the forward prices evolution.

Motivation & Objective

• To investigate whether self-exciting dynamics, previously observed in spot prices, also emerge in forward power price movements.
• To extend existing self-exciting models—originally applied to spot prices—into a Heath-Jarrow-Morton (HJM) framework for full forward curve dynamics.
• To calibrate and test two model classes—CBI and Hawkes processes—on daily French power market data to assess their ability to describe forward price evolution.
• To evaluate the adequacy of these models through statistical goodness-of-fit tests on jump inter-arrival times.
• To determine whether self-exciting features in price jumps are observable at a daily frequency, not just intraday.

Proposed method

• Adopt a Heath-Jarrow-Morton (HJM) approach to model the full term structure of forward power prices, ensuring consistency across maturities.
• Model forward price dynamics using two classes: continuous branching processes with immigration (CBI), which are affine and exhibit mean-reverting jump clustering.
• Model forward price dynamics using Hawkes processes with exponential kernel, which are self-exciting and naturally capture clustering of jumps.
• Extract forward curves from quoted futures prices using optimization procedures to infer the underlying forward curve dynamics.
• Estimate model parameters via maximum likelihood or moment-based methods, using daily data from the French power market.
• Perform Kolmogorov-Smirnov (KS) goodness-of-fit tests on inter-jump durations: for CBI, test against the theoretical intensity-based distribution; for Hawkes, test against exponential distribution after time deformation.

Experimental results

Research questions

• RQ1 Can self-exciting jump clustering features, observed in spot electricity prices, also be detected in forward power price dynamics?
• RQ2 Do CBI-based models adequately describe the evolution of forward curves in power markets, particularly in terms of jump clustering?
• RQ3 Do Hawkes processes with exponential kernels provide a better fit to forward price dynamics than CBI models in the context of the HJM framework?
• RQ4 Is the self-exciting behavior of price jumps observable at a daily frequency, rather than only at intraday scales?
• RQ5 How do the inter-arrival times of jumps in forward prices compare to those of a Poisson process, and what does this imply about the underlying dynamics?

Key findings

• The hypothesis that forward price jumps follow a Poisson process is strongly rejected, indicating non-Poissonian, self-exciting dynamics.
• The CBI model is rejected by the goodness-of-fit test, with p-values of 0.041, 0.018, and 0.042 at maturities of 200, 400, and 700 days, respectively, indicating poor fit.
• The Hawkes model is not rejected by the test, with p-values of 0.23, 0.31, and 0.13 at the same maturities, suggesting it adequately captures the jump clustering behavior.
• The results confirm that self-exciting features are present in forward price dynamics and can be effectively modeled using Hawkes processes with exponential kernels.
• The forward curve dynamics in the French power market exhibit jump clustering that is better captured by Hawkes processes than by CBI processes.
• The study demonstrates that self-exciting dynamics in electricity prices are not limited to spot prices but extend meaningfully to forward markets at a daily frequency.