# SFB 303 Discussion Paper No. B-263

**Author:** Sondermann, Dieter, and K. Sandmann

**Title:** On the Stability of
Lognormal Interest Rate Models and the Pricing of Eurodollar Futures

**Abstract:** 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)

**Keywords:** Eurodollar Futures, Term Structure Models, Log-Normal
Interest Rate

**JEL-Classification-Number:** G13

**Creation-Date:** October
1994

**URL:**
../1994/b/bonnsfb263.pdf
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