Log-Normal Interest Rate Models: Stability and Methodology
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 instrument on the Euromoney market, nameley the Eurodollar future contract. The purpose of this paper is twofold: First to show that the problems with lognormal models result from modelling the wrong rate, namely the continuously compounded rate. If instead one models the effective annual rate these problems disappear. Second to give a survey on recent work on lognormal term structure models for effective or nominal forward rates.
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- Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- Sandmann,Klaus & Sondermann,Dieter, . "A term structure model and the pricing of interest rate options," Discussion Paper Serie B 129, University of Bonn, Germany.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
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