Commodity derivatives pricing with cointegration and stochastic covariances

Empirically, cointegration and stochastic covariances, including stochastic volatilities, are statistically significant for commodity prices and energy products. To capture such market phenomena, we develop a continuous‐time dynamics of cointegrated assets with a stochastic covariance matrix and derive the joint characteristic function of asset returns in closed‐form. The proposed model offers an endogenous explanation for the stochastic mean‐reverting convenience yield. The time series of spot and futures prices of WTI crude oil and gasoline shows cointegration relationship under both physical and risk‐neutral measures. The proposed model also allows us to fit the observed term structure of futures prices and calibrate the market‐implied cointegration relationship. We apply it to value options on a single commodity and on multiple commodities.