On the Stability of Log-Normal Interest Rate Models and the Pricing of Eurodollar Futures

The lognormal distribution assumption for the term structure of interest is the most natural way to exclude negative spot and forward rates. However, imposing this assumption on the continuously compounded interest rate has a serious drawback: expected rollover returns are infinite even if the rollover period is arbitrarily short. As a consequence such models cannot price one of the most widely used hedging instrument on the Euromoney market, namely the Eurofuture contract. The purpose of this paper is to show that the problem with lognormal models result from modelling the wrong rate, namely the continuously compounded rate. If instead one models the effective annual rate the problem disappears, i.e. the expected rollover returns are finite. The paper studies the resulting dynamics of the continuously compounded rate which is neither normal nor lognormal. (Completely revised version october 1994)