Even though commodity pricing models have been successful in fitting the term structure of futures prices and its dynamics, they do not generate accurate true distributions of spot prices. This paper develops a new approach to calibrate these models using not only observations of oil futures...

We conduct a comprehensive analysis of unspanned stochastic volatility in commodity markets in general and the crude-oil market in particular. We present model-free results that strongly suggest the presence of unspanned stochastic volatility in the crude-oil market. We then develop a tractable...