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Volatility of the short rate in the rational lognormal model

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  • Lisa R. Goldberg

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

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    Abstract

    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.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 2 (1998)
    Issue (Month): 2 ()
    Pages: 199-211

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    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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    Related research

    Keywords: Interest rate model; volatility; option value;

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    Cited by:
    1. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, Elsevier, 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.

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