# SFB 303 Discussion Paper No. B - 396

**Author**: Schloegl, Erik, and Lutz Schloegl

**Title**: A Tractable Term Structure Model with Endogenous Interpolation and Positive Interest Rates

**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 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.

**Keywords**: term structure of interest rates, fixed income derivatives, square root process, chi-square distribution

**JEL-Classification-Number**: G13

**Creation-Date**: November 1997

**URL**: ../1997/b/bonnsfb396.pdf"
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