Abstract
Building on the influential Gibson and Schwartz (1990) and Schwartz and Smith (2000) two-factor models for commodity spot prices, this paper extends the framework to incorporate stochastic volatility and time-varying correlation through a Wishart variance-covariance matrix process. This generalization provides joint characteristic functions for both the state variables and their variance-covariance matrices, offering a richer description of the dynamics of volatility and correlation in commodity markets. While the original models are well known for tractably capturing the term structure of futures prices and implied volatility, the extended versions further account for volatility smiles and relax the restrictive assumption of constant correlation, facilitating empirical analysis via filtering techniques.