Gaussian factor models futures and forward prices

Email: hyndman{at}mathstat.concordia.ca Received on 31 July 2006. Accepted on 19 March 2007. We completely characterize the futures price and forward priceof a risky asset (commodity) paying a stochastic dividend yield(convenience yield). The asset (commodity) price is modelledas an exponential affine function of a Gaussian factors process,while the interest rate and dividend yield are affine functionsof the factors process. The characterization we provide is basedon the method of stochastic flows. We believe this method leadsto simpler and more clear-cut derivations of the futures priceand forward price formulae than alternative methods. Hedginga long-term forward contract with shorter term futures contractsand bonds is also examined.