Abstract
Investors such as insurance companies or pension funds have future liabilities and keep reserves in bonds. They face the risk of multiperiod interest rate changes and plan to buy bonds according to their estimations of future liabilities and interest rates. We use a discrete time model and show that the choice of the length of the bonds bought or sold determines a kinked payoff function. For investors who adopt a mean-variance strategy, hedging may be a common solution.
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References
BEEKMAN, J.A. and SHIU, E.S.W. (1988) Stochastic models for bond prices, function space integrals and immunization theory, Insurance: Mathematics and Economics 9, 163–173.
BIERWAG, G.O., KAUFMAN, G.G. and TOEVS, A. (1982) Single-factor duration models in a discrete general equilibrium framework, Journal of Finance 37, 325–338.
FELLER, W. (1966) An Introduction to Probability Theory and Its Application. John Wiley Sons, New York, 2nd Ed.
FISHER, L. and WEIL, R.L. (1971) Coping with the risk of interest-rate fluctuations: returns to bondholders from naive and optimal strategies, Journal of Business 44, 408–431.
GROVE, M.A. (1966) A model of the maturity profile of the balance sheet, Metroeconomica 18, 40–55.
GROVE, M.A. (1974) On ‘duration’ and the optimal maturity structure of the balance sheet, The Bell Journal of Economics and Management Science, 696–708.
GULTEKIN, N.B. and ROGALSKI, R.J. (1984) Alternative duration specifications and the measurement of basis risk: Empirical tests, Journal of Business 57, 241–246.
HICKS, J.R. (1946) Value and Capital. Clarendon Press, Oxford.
KHANG, C. (1983) A dynamic global portfolio immunization strategy in the world of multiple interest rate changes: A dynamic immunization and minimax theorem, Journal of Financial and Quantitative Analysis 18, 355–363.
KOCHERLAKOTA, R., ROSENBLOOM, E.S. and SHIU, E.S.W. (1988) Algorithms for cash-flow matching, Transactions of the Society of Actuaries 40, 37–44.
LANSTEIN, R. and SHARPE, W.F. (1978) Duration and security risk, Journal of Financial and Quantitative Analysis 13, 653–668.
MACAULAY, F.R. (1938) Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields and Stock Prices in the United States Since 1856. NBER, New York.
MACMIMM, R.D. and WITT, R.C. (1987) A financial theory of the insurance firm under uncertainty and regulatory constraints, The Geneva Papers of Risk and Insurance 12, 3–20.
SAMUELSON, P.A. (1945) The Effects of Interest Rate Increases on the Banking System, The American Economic Review 35, 16–27.
SHIU, E.S.W. (1987) On the Fisher—Weil immunization theorem, Insurance Mathematics and Economics 6, 250–265.
TILLEY, J.A. (1986) Control techniques for life insurance companies. In Controlling Interest Rate Risk: New Techniques and Applications for Money Management (ed. R.B. PLATT ) pp. 225–247, John Wiley Sons, New York.
WILKIE, A.D. (1985) Portfolio selection in the presence of fixed liabilities: A comment on the matching of assets to liabilities, Journal of the Institute of Actuaries 112, 229–277.
WISE, A.J. (1987) Matching and portfolio selection: Part 1, Journal of the Institute of Actuaries 114, 113–133. Part 2, 551–568.
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© 1995 Springer Science+Business Media Dordrecht
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Machnes, Y. (1995). Immunization and the Optimal Structure of the Balance Sheet. In: Janssen, J., Skiadas, C.H., Zopounidis, C. (eds) Advances in Stochastic Modelling and Data Analysis. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0663-6_3
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DOI: https://doi.org/10.1007/978-94-017-0663-6_3
Publisher Name: Springer, Dordrecht
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