A tractable term structure model with endogenous interpolation and positive interest rates

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 contingent claims are derived in terms of a noncentral chi-square distribution whose noncentrality parameter is in turn noncentral chi-square distributed. Implementation details on this distribution are given in the appendix.