Abstract
It was nearly forty years ago when the eminent British actuary F.M. Redington published the paper “Review of the Principles of Life-Office Valuations,” in which he suggested the principle that there should be equal and parallel treatment in the valuation of assets and liabilities. His theory of immunization for insulating a portfolio against interest rate fluctuations follows as an immediate consequence of this principle. A deficiency in Redington’s model is the assumption that the asset and liability cash flows are fixed and certain. In this paper we show that his theory can be extended to the general case of interest-sensitive cash flows (SPDA, UL, MBS, etc.) by means of modern option-pricing theory.
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References
Bierwag, G.O. (1987). Duration Analysis: Managing Interest Rate Risk. Ballinger, Cambridge, Mass.
Bierwag, G.O., G.G. Kaufman and A.L. Toevs (1982). “Single-Factor Duration Models in a Discrete General Equilibrium Framework,” Journal of Finance 37, 325–338. Reprinted in Kaufman, Bierwag and Toevs (1983), 307–323.
Black, F., E. Derman and W. Toy (1990). “A One-Factor Model of Interest Rates and Its Applications to Treasury Bond Options,” Financial Analysts Journal (January-February), 33–39.
Black, F., and P. Karasinski (1991). “Bond and Option Pricing When Short Rates Are Lognormal,” Financial Analysts Journal (July-August), 52–59.
Black, F., and M. Scholes (1973). “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy 81, 637–659.
Borch, K. (1960). “The Safety Loading of Reinsurance Premiums,” Skandinavisk Aktuarietiaskrift, 163–184. Reprinted in Borch (1990), 61–81.
Borch, K. (1990). Economics of Insurance. Elsevier, Amsterdam.
Bühlmann, H. (1980). “An Economic Premium Principle,” ASTIN Bulletin 11, 52–60.
Bühlmann, H. (1984). “The General Economic Premium Principle,” ASTIN Bulletin 14, 13–21.
Dalang, R.C., A. Morton and W. Willinger (1990). “Equivalent Martingale Measures and No-Arbitrage in Stochastic Securities Market Models,” Stochastics and Stochastic Reports 29, 185–201.
Delbaen, F., and J. Haezendonck (1989). “A Martingale Approach to Premium Calculation Principles in an Arbitrage Free Market,” Insurance: Mathematics and Economics 8, 269–277.
Dothan, M.U. (1990). Prices in Financial Markets. Oxford University Press, New York.
Duffie, D. (1992). Dynamic Asset Pricing Theory. Princeton University Press, Princeton.
Dybvig, P.H., and S.A. Ross (1987). “Arbitrage.” In The New Palgrave: A Dictionary of Economics, Vol 1, edited by J. Eatwell, M. Milgate and P. Newman, Macmillan, London, 100–106. Reprinted in The New Palgrave: Finance, edited by J. Eatwell, M. Milgate and P. Newman, W.W. Norton, New York (1989), 57–71.
Fisher, L. (1980). “Evolution of the Immunization Concept.” In Leibowitz (1980), 21–26.
Fong, H. G., and O. Vasicek (1983). “Return Maximization for Immunized Portfolio.” In Kaufman, Bierwag and Toevs (1983), 227–238.
Fong, H. G., and O. Vasicek (1984). “A Risk Minimizing Strategy for Portfolio Immunization,” Journal of Finance 39, 1541–1546.
Granito, M.R. (1984). Bond Portfolio Immunization. Lexington Books, Lexington, Mass.
Griffin, M.W. (1990). “An Excess Spread Approach to Nonparticipating Insurance Products,” Transactions of the Society of Actuaries 42,231–248; Discussion 249–258.
Harrison, J.M., and D. Kreps (1979). “Martingales and Arbitrage in Multiperiod Securities Markets,” Journal of Economic Theory 20, 381–408.
Hawawini, G.A. (ed.) (1982). Bond Duration and Immunization: Early Developments and Recent Contributions. Garland Publishing, New York.
Hickman, J.C. (1971). “Investment Implications of the Actuarial Design of Life Insurance Products,” Journal of Risk and Insurance 38, 571–583.
Hicks, J.R. (1939). Value and Capital. Clarendon Press, Oxford.
Hiller, R.S., and C. Schaack (1990). “A Classification of Structured Bond Portfolio Modeling Techniques,” Journal of Portfolio Management (Fall), 37–48.
Ho, T.S.Y. (1992a). “Managing Illiquid Bonds and the Linear Path Space,” Journal of Fixed Income 2 no. 1, 80–94.
Ho, T.S.Y. (1992b). “Key Rate Durations: Measures of Interest Rate Risks,” Journal of Fixed Income 2 no. 2, 29–44.
Ho, T.S.Y., and S.-B. Lee (1986). “Term Structure Movements and Pricing Interest Rate Contingent Claims,” Journal of Finance 41, 1011–1029.
Huang, C.-F., and R.H. Litzenberger (1988). Foundations for Financial Economics. Elsevier, New York.
Jacob, D.P., G. Lord and J.A. Tilley (1987). “A Generalized Framework for Pricing Contingent Cash Flows,” Financial Management 16 no. 3, 5–14.
Jamshidian, F. (1991). “Forward Induction and Construction of Yield Curve Diffusion Models,” Journal of Fixed Income 1, 62–74.
Kaufman G.G., G.O. Bierwag and A. Toevs (eds.) (1983). Innovations in Bond Portfolio Management: Duration Analysis and Immunization. JAI Press Inc., Greenwich, Conn.
Kocherlakota, R., E.S. Rosenbloom and E.S.W. Shiu (1988). “Algorithms for Cash-Flow Matching,” Transactions of the Society of Actuaries 40,477–484.
Kocherlakota, R., E.S. Rosenbloom and E.S.W. Shiu (1990). “Cash-Flow Matching and Linear Programming Duality,” Transactions of the Society of Actuaries 42, 281–293.
Koopmans, K.C. (1942). The Risk of Interest Fluctuations in Life Insurance Companies. Perm Mutual Life Insurance Company, Philadelphia.
Leibowitz, M.L. (ed,) (1980). Pros & Cons of Immunization: Proceedings of a Seminar on the Roles and Limits of Bond Immunization. Salomon Brothers, New York.
Lidstone, G.J. (1893). “On the Approximate Calculation of the Values of Increasing Annuities and Assurances,” Journal of the Institute of Actuaries 31, 68–72.
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. National Bureau of Economic Research, New York. Partially reprinted in Leibowitz (1980) and Hawawini (1982).
Mitchell, R.B. (1974). From Actuarius to Actuary. Society of Actuaries, Chicago.
Montrucchio, L., and L. Peccati (1991). “A Note on Shiu-Fisher-Weil Immunization Theorem,” Insurance: Mathematics and Economics 10, 125–131.
Noris, P.D., and S. Epstein (1989). “Finding the Immunizing Investment for Insurance Liabilities: The Case of the SPDA.” In Fixed-Income Portfolio Strategies, edited by F.J. Fabozzi, Probus, Chicago (1989), Chapter 7, 97–141.
Pedersen, H.W., E.S.W. Shiu and A.E. Thorlacius (1989). “Arbitrage-Free Pricing of Interest-Rate Contingent Claims,” Transactions of the Society of Actuaries 41, 231–265; Discussion 267–279.
Redington, F.M. (1952). “Review of the Principles of Life-Office Valuations,” Journal of the Institute of Actuaries 78, 286–315; Discussion 316–340. Reprinted in Leibowitz (1980), Hawawini (1982) and Redington (1986).
Redington, F.M. (1982). “The Phase of Transition-An Historical Essay,” Journal of the Institute of Actuaries 109, 83–96. Reprinted in Redington (1986), 492–506.
Redington, F.M. (1986). A Ramble through the Actuarial Countryside: The Collected Papers, Essays & Speeches of Frank Mitchell Redington, MA. Institute of Actuaries Students’ Society, Staple Inn, London.
Reitano, R.R. (1991a). “Multivariate Duration Analysis,” Transactions of the Society of Actuaries 43, 335–376; Discussion 377–391.
Reitano, R.R. (1991b). “Multivariate Immunization Theory,” Transactions of the Society of Actuaries 43, 393–428; Discussion 429–441.
Richard, S. (1991). “Valuation Challenges: Mortgage-Backed Securities and Collateralized Mortgage Obligations.” In Understanding Securitized Investments and Their Use in Portfolio Management, edited by K.M. Eades, D.R. Harrington and R.S. Harris, Association for Investment Management and Research, Charlottesville, Virginia, 20–29.
Samuelson, P.A. (1945). “The Effect of Interest Rate Increases on the Banking System,” American Economic Review 35, 16–27.
Shiu, E.S.W. (1988). “Immunization of Multiple Liabilities,” Insurance: Mathematics and Economics 7, 219–224.
Shiu, E.S.W. (1990). “On Redington’s Theory of Immunization,” Insurance: Mathematics and Economics 9, 171–175.
Society of Actuaries Committee on Life Insurance Company Valuation Principles (1987). The Valuation Actuary Handbook. Society of Actuaries, Itasca, Illinois.
Sonderman, D. (1991). “Reinsurance in Arbitrage-Free Markets,” Insurance: Mathematics and Economics 10, 191–202.
Tilley, J.A. (1988). “The Application of Modern Techniques to the Investment of Insurance and Pension Funds,” Transactions of the 23rd International Congress of Actuaries, Helsinki R, 301–326.
Tilley, J.A. (1992). “An Actuarial Layman’s Guide to Building Stochastic Interest Rate Generators,” Transactions of the Society of Actuaries 44, to appear.
Tilley, J.A., P.D. Noris, J.J. Buff and G. Lord (1985). Discussion of “Options on Bonds and Applications to Product Pricing,” Transactions of the Society of Actuaries 37, 134–145.
Vanderhoof, I.T. (1972). “The Interest Rate Assumption and the Maturity Structure of the Assets of a Life Insurance Company,” Transactions of the Society of Actuaries 24, 157–192; Discussion, 193–205.
Weil, R.L. (1973). “Macaulay’s Duration: An Appreciation,” Journal of Business 46, 589–592.
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Shiu, E.S.W. (1993). Asset/Liability Management: From Immunization to Option-Pricing Theory. In: Cummins, J.D., Lamm-Tennant, J. (eds) Financial Management of Life Insurance Companies. Huebner International Series on Risk, Insurance, and Economic Security, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2208-5_8
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DOI: https://doi.org/10.1007/978-94-011-2208-5_8
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