Hostname: page-component-84b7d79bbc-lrf7s Total loading time: 0 Render date: 2024-07-25T19:54:58.806Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of Models for the Term Structure of Interest Rates with Application to German Market Data

Published online by Cambridge University Press:  10 June 2011

A.J.G. Cairns  and
D.J. Pritchard
A.J.G. Cairns
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, U.K. E-mail: A.Cairns@ma.hw.ac.uk Internet: www.ma.hw.ac.uk/~andrewc/
D.J. Pritchard
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, U.K. E-mail: D.J.Pritchard@ma.hw.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper discusses the use of parametric models for description of the term structure of interest rates and their uses. We extend earlier work of Cairns (1998), Chaplin (1998) and Feldman et al. (1998), by presenting new theoretical results and also by demonstrating that the same model can be applied to countries other than the United Kingdom. First, we prove that the process of fitting a yield curve to price data has a unique optimal solution in both zero-coupon-bond and low-coupon-bond markets. Furthermore, an alternative method of curve fitting to those proposed previously is shown to have a unique solution in all markets.

The restricted-exponential model has previously been applied to U.K. data (Cairns, 1998). Here, we consider its wider application in European bond markets. In particular, we analyse German market data and conclude that the same model applies equally well to both countries.

Keywords

Term StructureMultiple MaximaRestricted-Exponential ModelLikelihood FunctionPosterior DistributionBayesian Estimator
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 7 , Issue 3 , 01 August 2001 , pp. 467 - 507
Copyright
Copyright © Institute and Faculty of Actuaries 2001

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

REFERENCES

Anderson, N. & Sleath, J. (1999). New estimates of the U.K. real and nominal yield curves. Bank of England Quarterly Bulletin, 39, 384–392.Google Scholar
Baxter, M. & Rennie, A. (1996). Financial calculus. CUP. Cambridge.CrossRefGoogle Scholar
Bjørk, T. & Christensen, B.J. (1999). Interest rate dynamics and consistent forward rate curves. Mathematical Finance, 9, 323–348.CrossRefGoogle Scholar
Cairns, A.J.G. (1998). Descriptive bond-yield and forward-rate models for the British government securities' market. B.A.J. 4, 265–321.Google Scholar
Cairns, A.J.G. (2000). A discussion of parameter and model uncertainty in insurance. Insurance: Mathematics and Economics, 27, 313–330.Google Scholar
Cairns, A.J.G. (2002). Interest-rate models. Princeton University Press. (to appear)Google Scholar
Chaplin, G.B. (1998). A review of term-structure models and their applications. B.A.J. 4, 323–349.Google Scholar
Dalquist, M. & Svensson, L.E.O. (1996). Estimating the term structure of interest rates for monetary policy analysis. Scandinavian Journal of Economics, 98, 163–183.CrossRefGoogle Scholar
Deacon, M. & Derry, A. (1994). Estimating the term structure of interest rates. Bank of England Working Paper Series, Number 24.Google Scholar
Dobbie, G.M. & Wilkie, A.D. (1978). The FT-Actuaries Fixed Interest Indices. J.I.A. 105, 15–27 and T.F.A. 36, 203–213.Google Scholar
Feldman, K.S., Bergman, B., Cairns, A.J.G., Chaplin, G.B., Gwilt, G.D., Lockyer, P.R. & Turley, F. B. (1998). Report of the fixed interest working group. B.A.J. 4, 213–263.Google Scholar
Fisher, M., Nychka, D. & Zervos, D. (1995). Fitting the term structure of interest rates with smoothing splines. Finance and Economic Discussion Series, 95–1, Federal Reserve Board.Google Scholar
Flesaker, B. & Hughston, L.P. (1996). Positive interest. Risk, 9(1), 46–49.Google Scholar
Heath, D., Jarrow, R. & Morton, A. (1992). Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation. Econometrica, 60, 77–105.CrossRefGoogle Scholar
Jarrow, R. (1996). Modelling fixed income securities and interest rate options. McGraw-Hill.Google Scholar
Lorimier, S. (1995). Interest rate term structure estimation based on the optimal degree of smoothness of the forward rate curve. Ph.D. Thesis, Universiteit Antwerpen, Depertement Wiskunde-Informatica.Google Scholar
Mastronikola, K. (1991). Yield curves for gilt-edged stocks: a new model. Discussion paper number 49. Bank of England.Google Scholar
McCulloch, J.H. (1971). Measuring the term structure of interest rates. Journal of Business, 44, 19–31.CrossRefGoogle Scholar
McCulloch, J.H. (1975). The tax-adjusted yield curve. Journal of Finance, 30, 811–830.Google Scholar
Mills, T.C. (1993). The econometric modelling of financial time series. CUP.Google Scholar
Nelson, C.R. & Siegel, A.F. (1987). Parsimonious modeling of yield curves. Journal of Business, 60, 473–489.CrossRefGoogle Scholar
Poston, T. & Stewart, I.M. (1978). Catastrophe theory and its applications. Pitman.Google Scholar
Rebonato, R. (1998). Interest-rate option models, second edition. Wiley.Google Scholar
Silvey, S.D. (1970). Statistical inference. Chapman and Hall.Google Scholar
Svensson, L.E.O. (1994). Estimating and interpreting forward interest rates: Sweden 1992–1994. Working paper of the International Monetary Fund, 94.114.Google Scholar
Vasicek, O.E. (1977). An equilibrium characterisation of the term structure. Journal of Financial Economics, 5, 177–188.CrossRefGoogle Scholar
Vasicek, O.E. & Fong, H.G. (1982). Term structure modelling using exponential splines. Journal of Finance, 37, 339–348.CrossRefGoogle Scholar
Waggoner, D. (1997). Spline methods for extracting interest rate curves from coupon bond prices. Working paper, No 97–10, Federal Reserve Bank of Atlanta.Google Scholar
Wei, W.W.S. (1990). Time series analysis. Addison-Wesley.Google Scholar
Wilkie, A.D. (1995). More on a stochastic asset model for actuarial use. B.A.J. 1, 777–964.Google Scholar
Wiseman, J. (1994). The exponential yield curve model. J.P. Morgan, 16 December.Google Scholar