Log-Normal Interest Rate Models: Stability and Methodology

Posted: 5 Jun 1997

See all articles by Klaus Sandmann

Klaus Sandmann

University of Bonn - The Bonn Graduate School of Economics

Dieter Sondermann

University of Bonn - Institute of Statistics

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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.

JEL Classification: E43, G13

Suggested Citation

Sandmann, Klaus and Sondermann, Dieter, Log-Normal Interest Rate Models: Stability and Methodology. Mathematical Finance, Vol. 7, No. 2, pp. 119-125, April 1997, Available at SSRN: https://ssrn.com/abstract=8350

Klaus Sandmann (Contact Author)

University of Bonn - The Bonn Graduate School of Economics ( email )

Adenauerallee 24-26
Bonn, D-53113
Germany

Dieter Sondermann

University of Bonn - Institute of Statistics ( email )

Adenauerallee 24-26
53113 Bonn, 53113
Germany

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