Multi-Factor Function-on-Function Regression of Bond Yields on WTI Commodity Futures Term Structure Dynamics

Abstract: In the analysis of commodity futures, it is commonly assumed that futures prices are driven by two latent factors: short-term fluctuations and long-term equilibrium price levels. In this study, we extend this framework by introducing a novel state-space functional regression model that incorporates yield curve dynamics. Our model offers a distinct advantage in capturing the interdependencies between commodity futures and the yield curve. Through a comprehensive empirical analysis of WTI crude oil futures, using US Treasury yields as a functional predictor, we demonstrate the superior accuracy of the functional regression model compared to the Schwartz-Smith two-factor model, particularly in estimating the short-end of the futures curve. Additionally, we conduct a stress testing analysis to examine the impact of both temporary and permanent shocks to US Treasury yields on futures price estimation.