An Analytically Tractable Interest Rate Model that Precludes Negative Interest Rates

Antoon Pelsser
Department of Finance, Erasmus University Rotterdam
Pelsser@finbel.few.eur.nl

Abstract

In this paper we analyse the one-factor squared Gaussian interest rate model. In this model the interest rates are always positive and the model has a rich analytical structure. We provide explicit analytical expressions for the prices of discount bonds, and show how the model can be fitted analytically to the initial yield-curve. Also an explicit expression in terms of normal distribution functions for the prices of options on discount bonds is given. Finally, we show how the model can be implemented efficiently using a trinomial tree algorithm. Hence, concerning analytical and numerical tractability, the model has the same properties as the Hull-White model, with the additional advantage that interest rates never become negative.