Abstract

We extend the popular Gibson and Schwartz (1990) and Schwartz and Smith (2000) two-factor models for the spot price of a commodity to include stochastic volatility and correlation. This generalization is based on the Wishart variance-covariance matrix process. For both of the extended models we present the joint characteristic functions of the two state variables. The original models are known to fit the term-structure of implied volatility in futures and options markets very well. However, the extended models are also able to match volatility smiles observed in these markets. Regarding the analysis of financial time series, the assumption of a constant correlation between the state variables is known to be too restrictive. Introducing time-varying correlation via the Wishart process allows us to study its empirical behaviour in commodity markets through the use of filtering techniques.

Speaker

Lorenz Schneider (Emlyon Business School)