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Fitting the Yield Curve

  • Moorad Choudhry
  • Didier Joannas
  • Richard Pereira
  • Rod Pienaar
Part of the Finance and Capital Markets Series book series (FCMS)

Abstract

In this chapter we consider some of the techniques used to actually fit the term structure. In theory we could use the bootstrapping approach described earlier. For a number of reasons, however, this does not produce accurate results, and so other methods are used instead. The term structure models described in the previous chapter defined the interest rate process under various assumptions about the nature of the stochastic process that drives these rates. However the zero-coupon curve derived by models such as those described by Vasicek (1977), Brennan and Schwartz (1979) and Cox, Ingersoll and Ross (1985) do not fit the observed market rates or spot rates implied by market yields, and generally market yield curves are found to contain more variable shapes than those derived using term structure models. Hence the interest rate models described in Chapter 7 are required to be calibrated to the market, and in practice they are calibrated to the market yield curve. This is carried out in two ways: either the model is calibrated to market instruments such as money market products and interest-rate swaps, which are used to construct the yield curve, or the yield curve is constructed from market instrument rates and the model is calibrated to this constructed curve. If the latter approach is preferred, there are a number of non-parametric methods that may be used. We consider these later.

Keywords

Interest Rate Cash Flow Discount Factor Term Structure Yield Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Selected Bibliography and References

  1. Anderson, N., Breedon, F., Deacon, M., Derry, A. and Murphy, M. Estimating and Interpreting the Yield Curve, Wiley 1996.Google Scholar
  2. Brennan, M. and Schwartz, E. ‘A continuous-time approach to the pricing of bonds’, Journal of Banking and Finance, 3, 1979, pp. 133–55.CrossRefGoogle Scholar
  3. Carleton, W. and Cooper, I. ‘Estimation and uses of the term structure of interest rates’, Journal of Finance, September 1976, pp. 1067–83.Google Scholar
  4. Choudhry, M. Bond Market Securities, FT Prentice Hall, 2001.Google Scholar
  5. Cox, J., Ingersoll, J. and Ross, S. ‘A theory of the term structure of interest rates’, Econometrica, 53, March 1985, pp. 385–407.CrossRefGoogle Scholar
  6. Deacon, M. and Derry, A. ‘Estimating the term structure of interest rates’, Bank of England Working Paper no. 24, July 1994.Google Scholar
  7. Gujarati, D. Basic Econometrics, 3rd edn, McGraw-Hill, 1995.Google Scholar
  8. James, J. and Webber, N. Interest Rate Modelling, Wiley, 2000.Google Scholar
  9. Jordan, J. and Mansi, S. ‘How well do constant-maturity treasuries approximate the on-the-run term structure?’, Journal of Fixed Income, 10, 2, September 2000, pp. 35–45.CrossRefGoogle Scholar
  10. Langetieg, T. C. ‘A multivariate model of the term structure’, Journal of Finance, 35, 1980, pp. 71–91.Google Scholar
  11. McCulloch, J. H. ‘Measuring the term structure of interest rates’, Journal of Business, January 1971, pp. 19–31.Google Scholar
  12. Nelson, C. and Siegel, A. ‘Parsimonious modelling of yield curves’, Journal of Business, 6, 1987, pp. 473–83.CrossRefGoogle Scholar
  13. Questa, G. Fixed Income Analysis for the Global Financial Market, Wiley, 1999.Google Scholar
  14. Steeley, J. M. ‘Estimating the gilt-edged term structure: basis splines and confidence intervals’, Journal of Business Finance and Accounting, 18, 1991, pp. 513–30.CrossRefGoogle Scholar
  15. Suits, D., Mason, A. and Chan, L. ‘Spline functions fitted by standard regression methods’, Review of Economics and Statistics, 60, 1978, pp. 132–9.CrossRefGoogle Scholar
  16. Tuckman, B. Fixed Income Securities, Wiley, 1996.Google Scholar
  17. Van Deventer, D. and Imai, K. Financial Risk Analytics, Irwin, 1997.Google Scholar
  18. Vasicek, O. ‘An equilibrium characterization of the term structure’, Journal of Financial Economics, 5, 1977, pp. 177–88.CrossRefGoogle Scholar
  19. Vasicek, O. and Fong, H. G. ‘Term structure modelling using exponential splines’, Journal of Finance, 37, 2, May 1982, pp. 339–48.CrossRefGoogle Scholar

Copyright information

© Moorad Choudhry, Didier Joannas, Richard Pereira and Rod Pienaar 2005

Authors and Affiliations

  • Moorad Choudhry
    • 1
  • Didier Joannas
    • 2
  • Richard Pereira
    • 3
  • Rod Pienaar
    • 4
  1. 1.KBC Financial ProductsUK
  2. 2.Hong KongChina
  3. 3.Nomura plcUK
  4. 4.UBS AGUK

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