Dynamics of Commodity Prices. A Potential Function Approach with Numerical Implementation

In the present analysis a nonlinear model is discussed in order to capture the presence of several forces acting in commodity markets and the difficulty to disentangle their relative price impacts. Global commodity markets have experienced significant price swings in recent years. Analysts offer two explanations: market forces and speculative expectations, not mutually exclusive. Commodity prices seem to indicate that various factors are acting in a very complex way. We start from one specific feature: price clustering phenomenon, which is the tendency to concentrate in a number of attraction regions, preferring some values over others. Commodities are in the process of becoming mainstream. The mean-reverting class of diffusion models are not able to model the phenomenon of multiple attraction regions. In the potential function approach the price is modelled as a diffusion process governed by a potential function. A fundamental step is to fit the multimodal density of the invariant distribution. We postulate a parametric form of the distribution in the framework of finite mixture models and Expectation-Maximization algorithm. The procedure for identifying and estimating potential function and diffusion parameter is provided. Applications to crude oil and soybean prices capture the essential characteristics of the data remarkably well. An underlying assumption is that potential function and long-term volatility do not change with time. New market conditions and new attraction regions can form, changing the shape of the potential and the magnitude of long-term volatility. We investigate changes in shape of the potential, which reflects new price equilibrium levels (attraction regions) and hence new market conditions. The model allows to generate copies of the observed price series with the same invariant distribution, useful for applications requiring a large number of independent price trajectories. A goodness-of-fit test for the SDE model is provided. A numerical implementation of the analysis is provided.