A mean reverting process for pricing treasury bills and futures contracts

An analytically tractable, discrete‐time single‐factor model is developed for valuing treasury bills and futures contracts. It uses a multiplicative binomial foward process that creates neither negative nor implausibly large positive interest factors, and which can incorporate different possible degrees of mean reversion. The paper derives explicit formulae for bill prices, futures prices, their conditional variances and risk premia in a setting that relates the evolution of the term structure more closely to both model and data than do other similar works. In contrast to other term‐structure constrained models, this paper emphasizes that in a one‐factor model the martingale probabilities cannot be treated independently of the perturbation functions. The paper's empirical methods also differ from the customary approaches. Instead of comparing differences between model‐predicted and observed prices, the paper applies ARCH methodology to test model‐predicted ratios of conditional variances to risk premia. Our tests find influences exogenous to the model, but these factors do not seem capable of being explained with two‐factor models using only interest rates.