Analysis of commodity prices with the particle filter

The behavior of commodities prices is fundamental to real-asset investment decisions, hedging, and pricing financial derivatives. Schwartz and Smith [Schwartz, E.S., Smith, J.E. (2000). Short term-variations and long-term dynamics in commodity prices. Management Science, 46, 893-911.] proposed a two-factor model for describing the stochastic processes of commodity prices, in which the two factors are short-term variations and equilibrium prices. These are both unobserved state variables that are estimated using the Kalman filter. The estimation is based on the observation of future prices for different maturities. The authors have carried out this process without incorporating jumps in the short-term variation of prices. Here we aim to demonstrate that the inclusion of jumps better explains the behavior of oil prices, and in fact creates difficulties in the estimation of state variables. This is because the variables become non-Gaussian so the Kalman filter is not recommended. Another methodology, called the particle filter, is more suitable in this case, and we describe its application in this article.