A Square-Root Interest Rate Model Fitting Discrete Initial Term Structure Data

Abstract

This paper presents the one- and the multifactor versions of a term structure model in which the factor dynamics are given by Cox/Ingersoll/Ross (CIR) type "square root" diffusions with piecewise constant parameters. The model is fitted to initial term structures given by a finite number of data points, interpolating endogenously. Closed form and near--closed form solutions for a large class of fixed income derivatives are derived in terms of a compound noncentral chi-square distribution. An implementation of the model is discussed where the initial term structure of volatility is fitted via cap prices.

JEL Classification: E43, G12, G13