A discrete time model for pricing treasury bills, forward, and futures contracts.

Abstract

This paper develops a discrete time model for valuing treasury bills and either forward or futures contracts written against them. It provides formulae for bill prices, forward prices, futures prices, and their conditional variances and risk premiums. The interest rate process is described by a multlphcatwe binomial random walk whose features conform to some principal characteristics of observed processes. Initial forward rates are constrained to match mltmlly observed term structure data. This paper uses a discrete time multlplicatlve binomial model of the spot interest rate process to derive pricing formulae for treasury bills, and forward and futures contracts written against them. All results are developed under assumptions of zero arbitrage profits. The model ~s constrained to match the initial term structure of interest rates, and uses an empirically plausible interest rate process. The model explicitly states the theoretical and empirical Importance of initially estimated forward rates, bond maturity dates, and forward and futures contract delivery dates. We find pricing formulae and time dependent expressions for the condltlonal variance and conditional risk premiums of bill prices, forward prices and futures prices. Finally, we use a property of binomial processes to relate conditional variances and risk premiums, and hence provide theoretical support for relations used m the empirical literature (ENGLE [1982], ENGLE, LILIEN and ROBINS [1987])