Volatility of the short rate in the rational lognormal model
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.Download Info
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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
Note: received: January 1997; final version received: June 1997
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Web page: http://www.springerlink.com/content/101164/
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Related research
Keywords: Interest rate model; volatility; option value;Find related papers by 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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