Asset/Liability Management: From Immunization to Option-Pricing Theory

  • Elias S. W. Shiu
Part of the Huebner International Series on Risk, Insurance, and Economic Security book series (HSRI, volume 17)


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.


Interest Rate Financial Management Life Insurance Company Interest Rate Risk Bond Portfolio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bierwag, G.O. (1987). Duration Analysis: Managing Interest Rate Risk. Ballinger, Cambridge, Mass.Google Scholar
  2. 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.CrossRefGoogle Scholar
  3. 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.Google Scholar
  4. Black, F., and P. Karasinski (1991). “Bond and Option Pricing When Short Rates Are Lognormal,” Financial Analysts Journal (July-August), 52–59.Google Scholar
  5. Black, F., and M. Scholes (1973). “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy 81, 637–659.CrossRefGoogle Scholar
  6. Borch, K. (1960). “The Safety Loading of Reinsurance Premiums,” Skandinavisk Aktuarietiaskrift, 163–184. Reprinted in Borch (1990), 61–81.Google Scholar
  7. Borch, K. (1990). Economics of Insurance. Elsevier, Amsterdam.Google Scholar
  8. Bühlmann, H. (1980). “An Economic Premium Principle,” ASTIN Bulletin 11, 52–60.Google Scholar
  9. Bühlmann, H. (1984). “The General Economic Premium Principle,” ASTIN Bulletin 14, 13–21.Google Scholar
  10. 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.Google Scholar
  11. 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.CrossRefGoogle Scholar
  12. Dothan, M.U. (1990). Prices in Financial Markets. Oxford University Press, New York.Google Scholar
  13. Duffie, D. (1992). Dynamic Asset Pricing Theory. Princeton University Press, Princeton.Google Scholar
  14. 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.Google Scholar
  15. Fisher, L. (1980). “Evolution of the Immunization Concept.” In Leibowitz (1980), 21–26.Google Scholar
  16. Fong, H. G., and O. Vasicek (1983). “Return Maximization for Immunized Portfolio.” In Kaufman, Bierwag and Toevs (1983), 227–238.Google Scholar
  17. Fong, H. G., and O. Vasicek (1984). “A Risk Minimizing Strategy for Portfolio Immunization,” Journal of Finance 39, 1541–1546.CrossRefGoogle Scholar
  18. Granito, M.R. (1984). Bond Portfolio Immunization. Lexington Books, Lexington, Mass.Google Scholar
  19. Griffin, M.W. (1990). “An Excess Spread Approach to Nonparticipating Insurance Products,” Transactions of the Society of Actuaries 42,231–248; Discussion 249–258.Google Scholar
  20. Harrison, J.M., and D. Kreps (1979). “Martingales and Arbitrage in Multiperiod Securities Markets,” Journal of Economic Theory 20, 381–408.CrossRefGoogle Scholar
  21. Hawawini, G.A. (ed.) (1982). Bond Duration and Immunization: Early Developments and Recent Contributions. Garland Publishing, New York.Google Scholar
  22. Hickman, J.C. (1971). “Investment Implications of the Actuarial Design of Life Insurance Products,” Journal of Risk and Insurance 38, 571–583.CrossRefGoogle Scholar
  23. Hicks, J.R. (1939). Value and Capital. Clarendon Press, Oxford.Google Scholar
  24. Hiller, R.S., and C. Schaack (1990). “A Classification of Structured Bond Portfolio Modeling Techniques,” Journal of Portfolio Management (Fall), 37–48.Google Scholar
  25. Ho, T.S.Y. (1992a). “Managing Illiquid Bonds and the Linear Path Space,” Journal of Fixed Income 2 no. 1, 80–94.CrossRefGoogle Scholar
  26. Ho, T.S.Y. (1992b). “Key Rate Durations: Measures of Interest Rate Risks,” Journal of Fixed Income 2 no. 2, 29–44.CrossRefGoogle Scholar
  27. Ho, T.S.Y., and S.-B. Lee (1986). “Term Structure Movements and Pricing Interest Rate Contingent Claims,” Journal of Finance 41, 1011–1029.CrossRefGoogle Scholar
  28. Huang, C.-F., and R.H. Litzenberger (1988). Foundations for Financial Economics. Elsevier, New York.Google Scholar
  29. 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.CrossRefGoogle Scholar
  30. Jamshidian, F. (1991). “Forward Induction and Construction of Yield Curve Diffusion Models,” Journal of Fixed Income 1, 62–74.CrossRefGoogle Scholar
  31. 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.Google Scholar
  32. 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.Google Scholar
  33. 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.Google Scholar
  34. Koopmans, K.C. (1942). The Risk of Interest Fluctuations in Life Insurance Companies. Perm Mutual Life Insurance Company, Philadelphia.Google Scholar
  35. 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.Google Scholar
  36. 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.Google Scholar
  37. 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).Google Scholar
  38. Mitchell, R.B. (1974). From Actuarius to Actuary. Society of Actuaries, Chicago.Google Scholar
  39. Montrucchio, L., and L. Peccati (1991). “A Note on Shiu-Fisher-Weil Immunization Theorem,” Insurance: Mathematics and Economics 10, 125–131.CrossRefGoogle Scholar
  40. 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.Google Scholar
  41. 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.Google Scholar
  42. 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).Google Scholar
  43. 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.CrossRefGoogle Scholar
  44. 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.Google Scholar
  45. Reitano, R.R. (1991a). “Multivariate Duration Analysis,” Transactions of the Society of Actuaries 43, 335–376; Discussion 377–391.Google Scholar
  46. Reitano, R.R. (1991b). “Multivariate Immunization Theory,” Transactions of the Society of Actuaries 43, 393–428; Discussion 429–441.Google Scholar
  47. 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.Google Scholar
  48. Samuelson, P.A. (1945). “The Effect of Interest Rate Increases on the Banking System,” American Economic Review 35, 16–27.Google Scholar
  49. Shiu, E.S.W. (1988). “Immunization of Multiple Liabilities,” Insurance: Mathematics and Economics 7, 219–224.CrossRefGoogle Scholar
  50. Shiu, E.S.W. (1990). “On Redington’s Theory of Immunization,” Insurance: Mathematics and Economics 9, 171–175.CrossRefGoogle Scholar
  51. Society of Actuaries Committee on Life Insurance Company Valuation Principles (1987). The Valuation Actuary Handbook. Society of Actuaries, Itasca, Illinois.Google Scholar
  52. Sonderman, D. (1991). “Reinsurance in Arbitrage-Free Markets,” Insurance: Mathematics and Economics 10, 191–202.CrossRefGoogle Scholar
  53. 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.Google Scholar
  54. Tilley, J.A. (1992). “An Actuarial Layman’s Guide to Building Stochastic Interest Rate Generators,” Transactions of the Society of Actuaries 44, to appear.Google Scholar
  55. 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.Google Scholar
  56. 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.Google Scholar
  57. Weil, R.L. (1973). “Macaulay’s Duration: An Appreciation,” Journal of Business 46, 589–592.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Elias S. W. Shiu
    • 1
  1. 1.University of IowaUSA

Personalised recommendations