IDEAS home Printed from https://ideas.repec.org/p/boc/bocoec/275.html
   My bibliography  Save this paper

An Alternative Strategy for Estimation of a Nonlinear Model of the Term Structure of Interest Rates

Author

Listed:
  • Christopher F. Baum

    () (Boston College)

  • Olin Liu

    () (International Monetary Fund)

Abstract

This paper develops and tests a nonlinear general equilibrium model of the term structure of interest rates based on the framework of Cox, Ingersoll and Ross (CIR, 1985). The contributions of this paper to the literature are both theoretical and empirical. The theoretical advantages of the general equilibrium model developed in this paper over the CIR model are (a) the risk premium is endogenously derived as a nonlinear function of the instantaneous interest rate. The nonlinear model shows that the term premium need not be strictly increasing in maturity as in CIR's model; it can be either increasing or humped, a result that is consistent with recent findings by Fama (1984) and McCulloch (1987). A partial differential equation for valuing the discount bond price is presented, and a closed-form expression is derived. In an empirical application of the model, we develop a strategy for estimation which permits analysis of the model's temporal stability. Our model, like that of CIR, expresses the underlying stochastic process as a highly nonlinear function of two fundamental, time-invariant parameters. Many researchers have found that general equilibrium models such as CIR's provide quite poor explanations of the evolution of the term structure of interest rates. As an alternative strategy to that of fitting the fundamental parameters, we employ nonlinear system estimation of the unrestricted reduced-form parameters with a moving-window strategy in order to capture the term structure volatility caused by factors other than the instantaneous interest rate. We purposefully do not impose any law of motion on the estimated volatilities. This methodology is shown to have strong predictive power for the observed term structure of interest rates, both in-sample and out-of-sample.

Suggested Citation

  • Christopher F. Baum & Olin Liu, 1994. "An Alternative Strategy for Estimation of a Nonlinear Model of the Term Structure of Interest Rates," Boston College Working Papers in Economics 275., Boston College Department of Economics.
  • Handle: RePEc:boc:bocoec:275
    as

    Download full text from publisher

    File URL: http://fmwww.bc.edu/EC-P/wp275.pdf
    File Function: full text
    Download Restriction: no

    References listed on IDEAS

    as
    1. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    2. Richard, Scott F., 1978. "An arbitrage model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 33-57, March.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. David K. Backus & Stanley E. Zin, 1993. "Long-memory inflation uncertainty: evidence from the term structure of interest rates," Proceedings, Federal Reserve Bank of Cleveland, pages 681-708.
    5. Fama, Eugene F., 1984. "Term premiums in bond returns," Journal of Financial Economics, Elsevier, vol. 13(4), pages 529-546, December.
    6. Brennan, Michael J. & Schwartz, Eduardo S., 1982. "An Equilibrium Model of Bond Pricing and a Test of Market Efficiency," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(03), pages 301-329, September.
    7. Sundaresan, Mahadevan, 1984. " Consumption and Equilibrium Interest Rates in Stochastic Production Economies," Journal of Finance, American Finance Association, vol. 39(1), pages 77-92, March.
    8. David K. Backus, 1993. "Long-Memory Inflation Uncertainty: Evidence from the Term Structure of Interest Rates," Working Papers 93-04, New York University, Leonard N. Stern School of Business, Department of Economics.
    9. David K. Backus & Stanley E. Zin, 1993. "Long-memory inflation uncertainty: evidence from the term structure of interest rates," Proceedings, Federal Reserve Bank of Cleveland, pages 681-708.
    10. Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
    11. McCulloch, J Huston, 1971. "Measuring the Term Structure of Interest Rates," The Journal of Business, University of Chicago Press, vol. 44(1), pages 19-31, January.
    12. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    13. Longstaff, Francis A., 1989. "A nonlinear general equilibrium model of the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 23(2), pages 195-224, August.
    14. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    15. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    16. Hull, John & White, Alan, 1990. "Valuing Derivative Securities Using the Explicit Finite Difference Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(01), pages 87-100, March.
    17. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    18. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    term structure of interest rates; risk premium;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:boc:bocoec:275. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F Baum). General contact details of provider: http://edirc.repec.org/data/debocus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.