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In this paper, we propose a new framework for modeling commodity forward curves. The proposed model describes the dynamics of fundamental driving factors simultaneously under physical ( P ) and risk-neutral ( Q ) probability measures. Our model is an extension of the forward curve model by Borovkova and Geman (2007), into several directions. It is a three-factor model, incorporating the synthetic spot price, based on liquidly traded futures, stochastic level of mean reversion and an analog of the stochastic convenience yield. We develop an innovative calibration mechanism based on the Kalman filtering technique and apply it to a large set of Brent oil futures. Additionally, we investigate properties of the time-dependent market price of risk in oil markets. We apply the proposed modeling framework to derivatives pricing, risk management and counterparty credit risk. Finally, we outline a way of adjusting the proposed model to account for negative oil futures prices observed recently due to coronavirus pandemic.

Using powerful technique of stochastic time change, we introduce a new two-factor commodity price model, where one of the fundamental factors is the activity rate. This factor implicitly introduces stochastic volatility into 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 and forward curve evolution 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.