Co-integrated Commodity Forward Pricing Model

Commodities pricing needs a specific approach as they are often linked to each other and so are expectedly doing their prices. They are called co-integrated when at least one stationary linear combination exists between them. Though widespread in economic literature, and even if many equilibrium relations and co-movements exist in economy, this principle of co-movement is not developed in derivatives field. Present study focuses on the following problem: How can the price of a forward agreement on a commodity be simulated, when it is co-integrated with other ones? Theoretical analysis is developed from Gibson-Schwartz model and analytical solution is given for short maturities contracts and under risk-neutral conditions. Application has been made to crude oil and heating oil energy commodities and result confirms the applicability of proposed method.