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

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  • 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 modelÕs 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.

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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 275..

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Length: 44 pages
Date of creation: 01 Oct 1994
Date of revision:
Handle: RePEc:boc:bocoec:275

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Keywords: term structure of interest rates; risk premium;

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References

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  1. 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 637-54, May-June.
  2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  3. Fama, Eugene F., 1984. "Term premiums in bond returns," Journal of Financial Economics, Elsevier, vol. 13(4), pages 529-546, December.
  4. 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.
  5. 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.
  6. 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.
  7. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  8. 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.
  9. 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.
  10. 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 363-84, March.
  11. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
  12. 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.
  13. 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.
  14. 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.
  15. 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 1209-27, July.
  16. 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.
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