Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-15T13:46:34.706Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  06 April 2009

Stephen M. Schaefer  and
Eduardo S. Schwartz
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 19 , Issue 4 , December 1984 , pp. 413 - 424
Copyright
Copyright © School of Business Administration, University of Washington 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Ayres, H. R., and Barry, J. Y.. “The Equilibrium Yield Curve for Government Securities.” Financial Analysts Journal, (05/06 1979), pp. 31–39.CrossRefGoogle Scholar
[2]Ayres, H. R., and Barry, J. Y.. “A Theory of the U.S. Treasury Market Equilibrium.” Management Science, Vol. 26 (06 1980), pp. 539–569.Google Scholar
[3]Brennan, M. J., and Schwartz, E. S.. “A Continuous Time Approach to the Pricing of Bonds.” Journal of Banking and Finance, Vol. 3 (07 1979), pp. 133–155.CrossRefGoogle Scholar
[4]Brennan, M. J., and Schwartz, E. S.. “Conditional Predictions of Bond Prices and Returns.” Journal of Finance, Vol. 35 (05 1980), pp. 405–416.CrossRefGoogle Scholar
[5]Brennan, M. J., and Schwartz, E. S.. “An Equilibrium Model of Bond Pricing and a Test of Market Efficiency.” Journal of Financial and Quantitative Analysis, Vol. 17 (09 1982), pp. 301–329.CrossRefGoogle Scholar
[6]Carslaw, H. S., and Jaeger, J. C.. Conduction of Heat in Solids, Oxford University Press (1959).Google Scholar
[7]Cox, J. C; Ingersoll, J. E.; and Ross, S. A.. “A Theory of the Term Structure of Interest Rates.” Research Paper No. 468, Graduate School of Business, Stanford University (1978).Google Scholar
[8]McKee, S., and Mitchell, A. R.. “Alternative Direction Methods for Parabolic Equation in Two Space Dimensions with Mixed Derivatives.” Computer Journal, Vol. 13 (02 1970), pp. 81–86.CrossRefGoogle Scholar
[9]Nelson, J., and Schaefer, S. M.. “The Dynamics of the Term Structure and Alternative Portfolio Immunization Strategies.” In Innovations in Bond Portfolio Management: Duration Analysis and Immunization Bierwag, G. O., Kaufman, G. G., and Toevs, A., eds. Greenwich, CT: JAI Press (1983).Google Scholar
[10]Richard, S. F. “An Arbitrage Model of the Term Structure of Interest Rates.” Journal of Financial Economics, Vol. 6 (03 1978), pp. 33–57.CrossRefGoogle Scholar
[11]Schaefer, S. M. “Discussion.” Journal of Finance, Vol. 35 (05 1980), pp. 417–419.Google Scholar
[12]Vasicek, O. A. “An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics, Vol. 5 (–11 1977), pp. 177–188.CrossRefGoogle Scholar