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Nonlinearity in the Term Structure

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  • Dong Heon Kim

Abstract

This paper uses the flexible approach of Hamilton (2001) to investigate the nature of nonlinearities in the term structure. The paper reports clear evidence of nonlinearity, in contrast to the affine term structure model and consistent with recent claims in the literature. We find that there is a threshold effect of volatility on the interest rate but this effect does not capture the entire nature of the nonlinearity. The quadratic term structure model recently proposed performs better for capturing the nonlinearity than the threshold model but the former model seems to miss some aspect of nonlinearity for short-term rates. However, our flexible nonlinear model which incorporates the threshold effect and the convexity of volatility into the quadratic model, generally performs well for all interest rates. The paper suggests that this model is a promising representation of nonlinearities and out-of-sample forecasts support the claim of nonlinearities

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 Far Eastern Meetings with number 440.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:feam04:440

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Keywords: Nonlinearity; Term Structure; Affine model; Quadratic model; Flexible nonlinear model;

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  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 1209-27, July.
  2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  3. David Backus & Silverio Foresi & Abon Mozumdar & Liuren Wu, 1998. "Predictable Changes in Yields and Forward Rates," NBER Working Papers 6379, National Bureau of Economic Research, Inc.
  4. David K. Backus, 2001. "Affine Term Structure Models and the Forward Premium Anomaly," Journal of Finance, American Finance Association, vol. 56(1), pages 279-304, 02.
  5. 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.
  6. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
  7. Hamilton, James Douglas & Kim, Dong Heon, 2000. "A Re-examination of the Predictability of Economic Activity Using the Yield Spread," University of California at San Diego, Economics Working Paper Series qt69v8p1m9, Department of Economics, UC San Diego.
  8. James D. Hamilton, 2000. "What is an Oil Shock?," NBER Working Papers 7755, National Bureau of Economic Research, Inc.
  9. Chen, Ren-Raw & Scott, Louis O, 1992. "Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 613-36.
  10. Pierluigi Balduzzi & Sanjiv Ranjan Das & Silverio Foresi, 1997. "The Central Tendency: A Second Factor in Bond Yields," NBER Working Papers 6325, National Bureau of Economic Research, Inc.
  11. Eric Ghysels & Serena Ng, 1998. "A Semiparametric Factor Model Of Interest Rates And Tests Of The Affine Term Structure," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 535-548, November.
  12. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02.
  13. 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.
  14. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
  15. Kim, Dong Heon & Denise R Osborn & Marianne Sensier, 2003. "Nonlinearity in the Fed's Monetary Policy Rule," Royal Economic Society Annual Conference 2003 121, Royal Economic Society.
  16. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
  17. Gong, Fangxiong & Remolona, Eli M, 1997. "Two Factors along the Yield Curve," The Manchester School of Economic & Social Studies, University of Manchester, vol. 65(0), pages 1-31, Supplemen.
  18. Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 85-107, March.
  19. Hamilton, James D, 2001. "A Parametric Approach to Flexible Nonlinear Inference," Econometrica, Econometric Society, vol. 69(3), pages 537-73, May.
  20. Christian M. Dahl, 2002. "An investigation of tests for linearity and the accuracy of likelihood based inference using random fields," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 263-284, 06.
  21. Longstaff, Francis A & Schwartz, Eduardo S, 1992. " Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-82, September.
  22. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-62.
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Cited by:
  1. Denise R. Osborn & Dong Heon Kim & Marianne Sensier, 2005. "Nonlinearity in the Fed's monetary policy rule," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(5), pages 621-639.

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