Forecasting Calendar Futures Spreads of Crude Oil Using Kalman Filter

The aim of this project is to forecast futures spreads of WTI Crude Oil. The motivation for this project springs from the fact that trading with calendar futures spreads is much more advantageous than trading with many other financial instruments. We make use of the fact that futures prices follow the mean-reverting process (Ornstein-Uhlenbeck process, OU). We develop a method, which was first proposed by Islyaev (2014) and the approach then extended by Sadik et al. (2020), that combines three linear Gaussian state space models, namely one factor model, one factor model with risk premium, and one factor model with seasonality. Thereafter, we directly model futures spreads. Kalman filter and the Maximum Likelihood Estimate (MLE) are used to estimate the model parameters. It is shown that this new approach, using the ratio between the nearest prices over spot prices as a latent variable and calendar futures spreads vector as the observed variable, is more accurate and robust than the indirect forecasting method which inputs both spot prices and futures prices as the latent variable and the observed variable respectively. Results on calibration and comparison for three models and two methods, as well as out-of-sample forecasting results are then presented and discussed.