Volatility of the short rate in the rational lognormal model

Lisa R. Goldberg
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Lisa R. Goldberg: BARRA, Inc., 1995 University Avenue, Berkeley, CA 94704, USA

Finance and Stochastics, 1998, vol. 2, issue 2, 199-211

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.

Keywords: Interest rate model; volatility; option value (search for similar items in EconPapers)
JEL-codes: E43 G13 (search for similar items in EconPapers)
Date: 1998-02-12
Note: received: January 1997; final version received: June 1997
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Citations: View citations in EconPapers (1)

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