On EKF and UKF in Polynomial Diffusion Models for Commodity Futures

Often commodity futures are priced using two latent state variables representing the short and long-term factors. These latent variables then are being modelled as Ornstein-Uhlenbeck processes. In this study, we use the polynomial diffusion model for commodity spot price with two state variables, introduced in Filipović and Larsson (2016). The Schwartz-Smith’s two-factor model, Schwartz and Smith (2000), represents a particular case of this model with the polynomial of degree one in the logarithmic scale. In this paper, the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) were developed for estimating the model parameters jointly with latent state variables under the polynomial diffusion framework for polynomials of degree from one to four. The comparative analysis of the models’ performance has been carried out using WTI Crude Oil futures data in terms of RMSE criterion applied to in-sample and out-of-sample forecasts.