Integrating Multiple Commodities in a Model of Stochastic Price Dynamics

Abstract

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 show in an application the economic significance of our approach. The spot price processes are assumed to be characterized by the weighted sum of latent factors. Employing an essentially-affine model structure we allow for rich dependencies among the latent factors and thus, the commodity prices. The co integrated behavior of the different spot price dynamics is explicitly taken into account. Within this framework we derive closed-form solutions of futures prices and apply the Kalman Filter methodology to estimate the model for crude oil, heating oil and gasoline futures contracts traded on the NYMEX. 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 which only impact subsets of the commodities considered. To demonstrate the economic consequences of our integrated approach, we evaluate the investment into 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.

Keywords: Commodities, Integrated Model, Futures, Kalman Filter, Crude Oil

JEL Classification: Q40, G13, C50