Three-Factor Commodity Forward Curve Model and Its Joint P and Q Dynamics

Abstract

In this paper, we propose a new framework for modelling 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 an extension of the forward curve model by Borovkova and Geman (2007), into several directions. It is a three-factor model, incorpo- rating the synthetic spot price, based on liquidly traded futures, stochastic level of mean reversion and an analogue of the stochastic convenience yield. We develop an innovative calibration mechanism based on the Kalman ltering technique and apply it to a large set of Brent oil futures. Addition- ally, we investigate properties of the time-dependent market price of risk in oil markets. We apply the proposed modelling 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.