Gaussian factor models futures and forward prices

Abstract

We completely characterize the futures price and forward price of a risky asset (commodity) paying a stochastic dividend yield (convenience yield). The asset (commodity) price is modelled as an exponential affine function of a Gaussian factors process, while the interest rate and dividend yield are affine functions of the factors process. The characterization we provide is based on the method of stochastic flows. We believe this method leads to simpler and more clear-cut derivations of the futures price and forward price formulae than alternative methods. Hedging a long-term forward contract with shorter term futures contracts and bonds is also examined.