Abstract
Energy commodities and their futures naturally show cointegrated price movements. However, there is empirical evidence that the prices of futures with different maturities might have, e.g., different jump behaviours in different market situations. Observing commodity futures over time, there is also evidence for different states of the underlying volatility of the futures. In this paper, we therefore allow for cointegration of the term structure within a multi-factor model, which includes seasonality, as well as joint and individual jumps in the price processes of futures with different maturities. The seasonality in this model is realized via a deterministic function, and the jumps are represented with thinned-out compound Poisson processes. The model also includes a regime-switching approach that is modelled through a Markov chain and extends the class of geometric models. We show how the model can be calibrated to empirical data and give some practical applications.
Highlights
The physical and the financial markets of energy commodities have converged over time.This is shown in multiple studies, e.g., Adams and Glück (2015), Benth and Koekebakker (2015), Carmona (2015), Döttling and Heider (2014) and Silvennoinen and Thorp (2013)
The model of Paschke and Prokopczuk (2009) considers cointegration in a commodity futures context. This model is based on the class of geometric models and uses cointegration to model prices of different commodities while including jumps
The aim of this paper is to find and discuss a suitable model for a considered commodity and its futures prices that is able to incorporate cointegration of the term structure
Summary
The physical and the financial markets of energy commodities have converged over time. Panagiotidis and Rutledge (2007) document that there exists a cointegrating relationship between the gas and oil price in the spot and futures markets None of these papers try to model the joint evolution of the forward curves. For some commodities such as natural gas and electricity, anticipated cyclical factors affecting demand generate corresponding cyclical patterns in the levels of futures prices Another observation (pertinent to the approach in our paper) is the appearance of qualitatively different dynamical behaviour at different times, possibly corresponding to unanticipated changes in market conditions. The model of Paschke and Prokopczuk (2009) considers cointegration in a commodity futures context This model is based on the class of geometric models and uses cointegration to model prices of different commodities while including jumps.
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