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A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures

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  • Klaus Sandmann
  • Dieter Sondermann

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: 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.

Suggested Citation

  • Klaus Sandmann & Dieter Sondermann, 1997. "A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 119-125, April.
    • Handle: RePEc:bla:mathfi:v:7:y:1997:i:2:p:119-125
    DOI: 10.1111/1467-9965.00027
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    References listed on IDEAS

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    1. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    2. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
    3. 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.
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