Residual Model for Future Prices

Abstract

This paper presents a new factor model for the term structure of futures prices of commodities. This model fills a gap in the literature by providing not only flexibility on the deterministic drivers of the term structure’s (TS) curve but also a clear meaning of the stochastic factors implied by the model. These benefits allow the user of the model to predict, and to protect himself against, changes in the slope and concavity of the TS curve. In particular, these new factors are identified as the spot price, the slope and the concavity of the curve, and they directly tackle the phenomena defined as contango and backwardation movements. It is shown that the model provides a good fit for the term structure’s curve under the historical measure. Conditions on the processes of the factors are obtained under an equivalent measure which ensures an absence of arbitrage. Explicit expressions for the term structure of volatilities and correlations are also provided. The paper concludes with a set of derivatives inspired by the new factors which could be used to protect an investor against contango and backwardation movements.