Journal of Energy Markets

Integrating multiple commodities in a model of stochastic price dynamics

Raphael Paschke, Marcel Prokopczuk


In this paper we develop a multi-factor model for the joint dynamics of related commodity spot prices in continuous time. We contribute to the existing literature by simultaneously considering various commodity markets in a single, consistent model and, through its application, demonstrate the economic significance of our approach. Employing an essential affine model structure, we allow for rich dependencies among the latent factors and, thus, the commodity prices. The cointegrated behavior of the different spot price dynamics is explicitly taken into account.We apply the Kalman filter methodology to estimate the model for crude oil, heating oil and gasoline futures contracts. Empirically, we are able to identify a common non-stationary equilibrium factor, driving the long-term price behavior, and stationary factors affecting all three markets in a common way. Additionally, we identify factors that only impact on subsets of the commodities considered. To demonstrate the economic consequences of our integrated approach, we evaluate the investment in a refinery from a financial management perspective and compare the results with an approach neglecting the co-movement of prices. This negligence leads to radical changes in the project's assessment.

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