A Note on the Stability of Lognormal 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: rates explode and 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 instruments on the Euromoney market, namely the Eurodollar futures contract.
The purpose of this note is to show that the problems with lognormal models result from modeling the wrong rate, namely the continuously compounded rate. If instead one models the effective annual rate these problems disappear.