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

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Author Info

  • D. Sondermann
  • Sandmann, K.

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)

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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 263.

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Date of creation: Oct 1994
Date of revision:
Handle: RePEc:bon:bonsfb:263

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

Related research

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

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References

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  1. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
  2. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  3. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
  4. Rady, Sven, 1994. "The Direct Approach to Debt Option Pricing," Munich Reprints in Economics 3404, University of Munich, Department of Economics.
  5. K. Sandmann & Sandmann, K., 1995. "The Direct Approach to Debt Option Pricing," Discussion Paper Serie B 212, University of Bonn, Germany.
  6. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
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Cited by:
  1. Goldys, B. & M. Musiela & D. Sondermann, 1996. "Lognormality of Rates and Term Structure Models," Discussion Paper Serie B 394, University of Bonn, Germany.
  2. Ram Bhar & Carl Chiarella & Hing Hung & Wolfgang Runggaldier, 2004. "The Volatility of the Instantaneous Spot Interest Rate Implied by Arbitrage Pricing - A Dynamic Bayesian Approach," Finance 0409002, EconWPA.
  3. Albanese, Claudio, 2007. "Callable Swaps, Snowballs And Videogames," MPRA Paper 5229, University Library of Munich, Germany, revised 01 Oct 2007.
  4. Ciurlia, Pierangelo & Gheno, Andrea, 2008. "A model for pricing real estate derivatives with stochastic interest rates," MPRA Paper 9924, University Library of Munich, Germany.

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