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Immunization under stochastic models of the term structure

Published online by Cambridge University Press:  20 April 2012

Extract

1.1. The purpose of this paper is to survey some new results concerning the term structure of interest rates and discuss actuarial applications. The term structure of interest rates exhibits the relationship among the yields on default free debt instruments of different maturities. Although there is a considerable volume of literature dealing with the determinants of the term structure the analysis has until recently been presented for the most part in a deterministic (i.e. non-stochastic) framework. This constrasts with the treatment of capital assets where equilibrium prices have been obtained under the assumption that returns on these assets are random variables.

Type
Research Article
Copyright
Copyright © Institute and Faculty of Actuaries 1978

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References

REFERENCES

(1) Vasicek, O. A. An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5 (November 1977).CrossRefGoogle Scholar
(2) Cox, J. C., Ingersoll, J. E. & Ross, S.A. A Theory of the Term Structure of Interest Ratesand the Valuation of Interest-Dependent Claims. (Paper presented at the Western Finance Association Meetings, Anaheim, California, June 1977).Google Scholar
(3) Brennan, M. J. & Schwartz, E. S. Savings Bonds, Retractable Bonds and Callable Bonds. Journal of Financial Economics, 5, 6788 (1977).CrossRefGoogle Scholar
(4) Richard, S. F. An Analytical Model of the Term Structure of Interest Rates. (Working Paper, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania, December 1976).Google Scholar
(5) Redington, F. M. Review of the Principles of Life Office Valuations. J.I.A., 78, 286.Google Scholar
(6) Shedden, A. D. A Practical Approach to Applying Immunization Theory. T.F.A., 35, 313.Google Scholar
(7) Fisher, L. & Weil, R. L. Coping with the Risk of Interest Rate Fluctuations. Journal of Business 44, 408.CrossRefGoogle Scholar
(9) Bierwag, G. O. Immunization Duration and the Term Structure of Interest Rates. Journal of Financial and Quantitative Analysis (forthcoming).Google Scholar
(9) Cox, J. C., Ingersoll, J. E. & Ross, S. A. Duration and the Measurement of Basis Risk. (Mimeograph, Graduate School of Business, University of Chicago, Illinois, July 1977).Google Scholar
(10) McKean, H. P. JR., Stochastic Integrals. Academic Press, New York, 1969.Google Scholar
(11) Black, F. & Scholes, M. J., The Pricing of Options and Corporate Liabilities. Journal of Political Economy 81, 637.CrossRefGoogle Scholar
(12) Beekman, J. A. A new Collective Risk Model. T.S.A. XXV, 573.Google Scholar
(13) Feller, W. Two Singular Diffusion Problems. Annals of Mathematics 54, 173.CrossRefGoogle Scholar
(14) Jackson, C. J. Stochastic Models of a Risk Business Operating Under the Influence of Investment and Insurance Risks. (Ph.D. thesis, Graduate School of Business, University of Wisconsin-Madison, 1971).Google Scholar
(15) Cox, D. R. & Mular, H. D. The Theory of Stochastic Processes. Methuen, London, 1965.Google Scholar