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Volatility of the short rate in the rational lognormal model


  • Lisa R. Goldberg

    (BARRA, Inc., 1995 University Avenue, Berkeley, CA 94704, USA)


A recent article of Flesaker and Hughston introduces a one factor interest rate model called the rational lognormal model. This model has a lot to recommend it including guaranteed finite positive interest rates and analytic tractability. Consequently, it has received a lot of attention among practioners and academics alike. However, it turns out to have the undesirable feature of predicting that the asymptotic value of the short rate volatility is zero. This theoretical result is proved rigorously in this article. The outcome of an empirical study complementing the theoretical result is discussed at the end of the article. European call options are valued with the rational lognormal model and a comparably calibrated mean reverting Gaussian model. unsurprisingly, rational lognormal option values are considerably lower than the analogous mean reverting Gaussian option values. In other words, the volatility in the rational lognormal model declines so quickly that options are severely undervalued.

Suggested Citation

  • Lisa R. Goldberg, 1998. "Volatility of the short rate in the rational lognormal model," Finance and Stochastics, Springer, vol. 2(2), pages 199-211.
  • Handle: RePEc:spr:finsto:v:2:y:1998:i:2:p:199-211
    Note: received: January 1997; final version received: June 1997

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    References listed on IDEAS

    1. Jaime Cuevas Dermody & R. Tyrrell Rockafellar, 1991. "Cash Stream Valuation In the Face of Transaction Costs and Taxes," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 31-54.
    2. Bernard Bensaid & Jean-Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86.
    3. Lukasz Stettner, 2000. "Option Pricing in Discrete-Time Incomplete Market Models," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 305-321.
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    Cited by:

    1. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance,in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742 Elsevier.

    More about this item


    Interest rate model; volatility; option value;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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