Using powerful technique of stochastic time change, we introduce a new two-factor commodity price model, where one of the fundamental factors is the stochastic activity rate in the market. This factor is responsible for stochastic volatility in the model. The model is developed under both physical and risk neutral probability measures, which allows for a wide range of applications ranging from derivatives pricing to risk management.

We derive forward prices within the model’s framework and develop an ingenious calibration procedure, which allows us to filter out the activity rate from daily observed price data. We apply the model to the rich dataset of daily crude oil and natural gas spot and futures prices and demonstrate its versatility and excellent fit to the historical forward curves.