A flexible model of term-structure dynamics of commodity prices: A comparative analysis with a two-factor Gaussian model

Abstract

This study compares two approaches to modeling a term structure of commodity prices. The first approach specifies the stochastic process of the underlying spot price and derives from the stipulated spot price dynamics valuation formulas of futures and other derivative contracts through no arbitrage. The second approach, as introduced by Smith [J. Appl. Econometr., 2005, 20, 405–422], is to model the dynamics of the entire futures curve directly by a set of common stochastic factors and to specify factor loadings by flexible functions of time-to-maturity and contract delivery month. Empirical applications of the models to four commodities (gold, crude oil, natural gas, and corn) reveal that the volatility of futures prices exhibits more complex dynamics than the pattern implied by the model stipulating a two-factor Gaussian process of the underlying spot price. Specifically, the flexible model of futures returns depicts the maturity effect and, particularly for the three consumption commodities, strong seasonal and cross-sectional variations invariance and covariance of concurrently traded contracts. Incorporating the depicted variance and covariance dynamics leads the flexible model of futures returns to suggest hedging strategies that are more effective than the strategies based on the conventional two-factor Gaussian model.