A Two-Factor Model of the Term Structure: An Approximate Analytical Solution

Stephen M. Schaefer and Eduardo S. Schwartz

Journal of Financial and Quantitative Analysis, 1984, vol. 19, issue 4, 413-424

Abstract: This paper develops an approximate analytical solution to a two state-variable model of the term structure similar to the one proposed by Brennan and Schwartz. Unlike the BS model, which was based on the consol rate and the short rate of interest, our model is based on the consol rate and the spread (i.e., the difference) between the consol rate and the short rate. This change, merely a redefinition of variables, is made to exploit an assumption, for which there is substantial empirical evidence, that these two variables (the consol rate and the spread) are orthogonal. Employing orthogonal state variables provides the key simplification in providing an approximate solution to the fundamental valuation equation.

Date: 1984
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