Hostname: page-component-89b8bd64d-4ws75 Total loading time: 0 Render date: 2026-05-10T04:49:44.586Z Has data issue: false hasContentIssue false
  • English
  • Français

Descriptive Bond-Yield and Forward-Rate Models for the British Government Securities' Market: [forms Part Of: Report of the Fixed-Interest Working Group, B.A.J. 4, II Pg.213–383]

Published online by Cambridge University Press:  10 June 2011

A.J.G. Cairns
A.J.G. Cairns
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh, EH14 4AS, U.K. Tel: +44(0)131-451-3202; Fax: +44(0)131-451-3249; E-mail: a.cairns@ma.hw.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper discusses possible approaches to the construction of gilt yield indices published by the Financial Times. The existing method, described by Dobbie & Wilkie (1978) splits bonds into high, medium and low-coupon bands and fits separate yield curves to each. This method has been identified as susceptible to ‘catastrophic’ jumps when the least-squares fit jumps from one set of parameters to another set of quite different values. This problem is a result of non-linearities in the least-squares formula which can give rise to more than one local minimum. A desire to remove the risk of catastrophic changes prompted this research, which is being carried out as part of the work of the Fixed Interest Working Group.

Recent changes in the taxation of bonds has, further, prompted the need for a review of the yield indices. Significantly, since the announcement of the new tax regime, the old coupon effect has been removed. This has made the use of a single forward-rate curve appropriate for the first time.

A particular form of forward-rate curve is proposed as the basis for a revision of the gilt yield indices. This curve appears to give a significantly better fit than the present yield–curve model. It is also argued that the risk of catastrophic jumps has been reduced significantly.

Keywords

Yield CurveForward-Rate CurveCatastrophic JumpsLeast SquaresMaximum LikelihoodForward-Inflation Curve

Information

Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 4 , Issue 2 , 01 June 1998 , pp. 265 - 321
Copyright
Copyright © Institute and Faculty of Actuaries 1998

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Anderson, N., Breedon, F., Deacon, M., Derry, A. & Murphy, G. (1996). Estimating and interpreting the yield curve. Wiley, Chichester.Google Scholar
Bjørk, T. & Christensen, B. J. (1997). Forward rate models and invariant manifolds. Preprint, Stockholm School of Economics.Google Scholar
Cairns, A.J.G. (1995). Uncertainty in the modelling process. Transactions of the 25th International Congress of Actuaries, Brussels, 1, 67–94. (Correct version at http://www.ma.hw.ac.uk/~andrewc/papers/ajgc3.ps).Google Scholar
Chaplin, G.B. (1998). A review of term structure models and their applications. B.A.J. 4, 323–349.Google Scholar
Clarkson, R.S. (1979). A mathematical model for the gilt-edged market. J.I.A. 106, 85–132.Google Scholar
Cox, J.C., Ingersoll, J.E. & Ross, S.A. (1985). A theory of the term-structure of interest rates. Econometrica, 53, 385–407.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, 15–26 and T.F.A. 36, 203–213.Google Scholar
Feldman, K.S. (1977). The gilt-edged market reformulated J.I.A. 104, 227–240.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.AJ. 4, 213–383.Google Scholar
Gwilt, G.D. (1982). Presidential address. T.F.A. 38, 1–17.Google Scholar
Heath, D.C., Jarrow, R.A. & 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
Ho, S.Y. & Lee, S.-B. (1986). Term structure movements and pricing interest rate contingent claims. Journal of Finance, 41, 1011–1029.CrossRefGoogle Scholar
Hull, J. & White, A., (1990). Pricing interest rate derivative securities. The Review of Financial Studies, 3, 573–592.CrossRefGoogle 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
McCutcheon, J.J. & Scott, W.F. (1986). An introduction to the mathematics of finance. Heinemann, Oxford.Google Scholar
Mastroniola, K. (1991). Yield curves for gilt-edged stocks: a new model. Discussion Paper Number 49. Bank of England.Google Scholar
Neave, H.R. (1978). Statistics tables. George Allen and Unwin, London.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, London.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, 33 pages.CrossRefGoogle Scholar
Vasicek, O.A. (1977). An equilibrium characterisation of the term structure. Journal of Financial Economics, 5, 177–188.CrossRefGoogle Scholar
Wei, W.W.S. (1990). Time series analysis. Addison-Wesley, Redwood City.Google Scholar
Wiseman, J. (1994). The exponential yield curve model. J.P. Morgan, 16 December.Google Scholar