Volatility of the Short Rate in the Rational Lognormal Model

Finance and Stochastics (1998)

Posted: 20 Apr 1998

See all articles by Lisa R. Goldberg

Lisa R. Goldberg

University of California, Berkeley; Aperio Group

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 practitioners 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.

JEL Classification: E43, G12, G13

Suggested Citation

Goldberg, Lisa R., Volatility of the Short Rate in the Rational Lognormal Model. Finance and Stochastics (1998), Available at SSRN: https://ssrn.com/abstract=77108

Lisa R. Goldberg (Contact Author)

University of California, Berkeley ( email )

Department of Statistics
367 Evans Hall
Berkeley, CA 94720-3860
United States

Aperio Group ( email )

3 Harbor Drive
Suite 315
Sausalito, CA 94965
United States

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