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A Review of Term-Structure Models and Their Applications: [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

G.B. Chaplin
G.B. Chaplin
Affiliation:
ABN Amro Bank N.V., 199 Bishopgate, London EC2M 3TY, U.K. Tel: +44(0)171-678-3965; E-mail: [email protected]
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Abstract

The literature on ‘Term-Structure Models’ is extensive with many contributions from financial economists over the last twenty years. This paper reviews examples of term-structure models from different categories (‘equilibrium’, ‘evolutionary’ and ‘descriptive’) with particular emphasis on their intended application. The Vasicek (one-factor equilibrium), Richard (two-factor), and Hull & White (evolutionary) models are discussed in some detail.

The paper reviews a particular class of descriptive polynomial models which is flexible and in widespread use both in the academic and the practitioner community. The model is cast in terms of forward rates, applied to the gilt market, and techniques are used to determine how many terms in the polynomial expansion are statistically required in order to describe the market accurately. The model is a linear model of forward and spot rates and is stable; this allows the calculation of risk measures for each bond which give a superior approach, in principle, to portfolio hedging.

Selection of model should be driven by its application. If the objective is a reasonably accurate description of the curve and, by implication, an accurate indication of yields which can be obtained in the market, then a model which fits the market accurately is preferable. The ‘descriptive’ approach is therefore most appropriate in this context.

Keywords

One-Factor and Two-Factor ModelsForward RatesSpot (Zero Coupon) RatesTerm-StructureEquilibriumEvolutionary and Descriptive ModelsRepo RatesParameter Significance and EstimationModel Risk Measures
Type
Sessional meetings: papers and abstracts of discussions
Information
British Actuarial Journal , Volume 4 , Issue 2 , 01 June 1998 , pp. 323 - 383
Copyright
Copyright © Institute and Faculty of Actuaries 1998

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References

REFERENCES

Babbs, S. (1991). A Family of Ito process models for the term-structure of interest rates. Midland Montagu Capital Markets.Google Scholar
Baxter, M. & Renile, A. (1996). Financial calculus. CUP.CrossRefGoogle Scholar
Boylb, P.P. (1980). Recent models of the term-structure of interest rates with actuarial applications. Transactions of the International Congress of Actuaries.Google Scholar
Brennan, M.J. & Schwarz, E.S. (1979). A continuous time approach to the pricing of bonds. Journal of Banking and Finance, 3, 133–155.CrossRefGoogle Scholar
Cattell, R.B. (1965). Factor analysis: an introduction to fundamentals … Biometrics 21: 190–215, 405–435.CrossRefGoogle Scholar
Chaplin, G.B. (1987). A two-factor model of the term-structure with closed form solutions for bond and option prices. University of Waterloo Working Paper in Actuarial Science.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
Dobbie, C.M. & Wilkie, A.D. (1978). The F.T.-Actuaries Fixed Interest Indices. J.I.A., 105, 15–26, and T.F.A. 36, 203–213.Google Scholar
Dothan, M.U. (1990). Prices in financial markets. OUP.Google Scholar
Harman, H. H. (1975). Modern factor analysis. Chicago UP.Google Scholar
Heath, D.C., Jarrow, R.A. & Morton, A. (1992a). Bond pricing and the term-structure of interest rates: a new methodology. Econometrica, 60, 77–105.CrossRefGoogle Scholar
Heath, O.C., Jarrow, R.A. & Morton, A. (1992b). Easier done than said. Risk, Oct 1992, 77.CrossRefGoogle Scholar
Ho, T.S.Y. & Lee, S.-B. (1986). Term-structure movements and pricing of interest rate contingent claims. Journal of Finance, 41, 1011–1029.CrossRefGoogle Scholar
Hull, J.C. & White, A. (1990). Pricing interest-rate-derivative securities. Review of Financial Studies, 3, 573–592.CrossRefGoogle Scholar
Hull, J.C. (1993). Options, futures and other derivative securities. Prentice Hall.Google Scholar
Jamashidian, F. (1989). An exact bond option formula. Journal of Finance, 35, 71–97.Google Scholar
Karki, J. & Reyes, C. (1993). Model relationships. Risk, 7, 12.Google Scholar
Kendall, M. Sir & Stuart, A. (1977–1983). The advanced theory of statistics. Charles Griffin & Co.Google Scholar
Leong, K. (1992). Model choice. Risk, 5, no. 11.Google Scholar
Nelson, C.R. & Siegel, A.F. (1987). Parsimonious modelling of yield curves. Journal of Business, 60, 473–489.CrossRefGoogle Scholar
Richard, S. (1978). An arbitrage model of the term-structure of interest rates. Journal of Financial Economics, 6, 33–57.CrossRefGoogle Scholar
Shaeffer, S. & Schwarz, E.S. (1984). A two-factor model of the term-structure: an approximate analytic solution. Journal of Financial and Quantitative Analysis, 19, 4, 413–424.Google Scholar
Sharp, K.P. (1988). Stochastic models of interest rates. Transactions of the 23rd International Congress of Actuaries, 247–261.Google Scholar
Svensson, L.E.O. (1994). Estimating and interpreting forward rates: Sweden 1992–1994. IMF working paper, 94.113, 33 pages.CrossRefGoogle Scholar
Tilley, J.A. & Mueller, M. (1991). Managing interest rate risk for long liabilities. Proceedings of the 2nd AFIR Colloquium, 1.Google Scholar
Tucker, L.R., Koopman, R.F. & Linn, R.L. (1969). Evaluation of factor analytic research procedures by means of simulated correlation matrices. Psychometrica, 34, 421–459.CrossRefGoogle Scholar
Vasicek, O.A. (1977). An equilibrium characterization of the term-structure of interest rates. Journal of Financial Economics, 5, 177–188.CrossRefGoogle Scholar
Vetzal, K.R. (1994). A survey of stochastic continuous time models of the term-structure of interest rates. Insurance: Mathematics and Economics, 14, 139–161.Google Scholar
Wilkie, A.D. (1995). More on a stochastic asset model for actuarial use. B.A.J. 1, 777–964.Google Scholar