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Immunization Using a Parametric Model of the Term Structure

Author

Listed:
  • Jorge Miguel Ventura Bravo

    (Department of Economics, University of Évora)

  • Carlos Manuel Pereira da Silva

    (ISEG - School of Economics and Management, Technical University of Lisbon)

Abstract

In this paper, we develop a new immunization model based on a parametric specification of the term structure of interest rates. The model extends traditional duration analysis to account for both parallel and non-parallel term structure shifts that have an economic meaning. Contrary to most interest rate risk models, we analyse both first-order and second-order conditions for bond portfolio immunization and conclude that the key to successful protection will be to build up a bond portfolio such that the gradient of its future value is zero, and such that its Hessian matrix is positive semidefinite. In addition, we provide explicit formulae for new parametric interest rate risk measures and present alternative approaches to implement the immunization strategy. Furthermore, we provide useful expressions for the sensitivity of interest rate risk measures to changes in term structure shape parameters.

Suggested Citation

  • Jorge Miguel Ventura Bravo & Carlos Manuel Pereira da Silva, 2005. "Immunization Using a Parametric Model of the Term Structure," Economics Working Papers 19_2005, University of Évora, Department of Economics (Portugal).
    • Handle: RePEc:evo:wpecon:19_2005
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    File URL: http://hdl.handle.net/10174/8422
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    References listed on IDEAS

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    1. Cooper, I. A., 1977. "Asset Values, Interest-Rate Changes, and Duration," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(5), pages 701-723, December.
    2. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    3. Ventura Bravo, Jorge Miguel & Pereira da Silva, Carlos Manuel, 2006. "Immunization using a stochastic-process independent multi-factor model: The Portuguese experience," Journal of Banking & Finance, Elsevier, vol. 30(1), pages 133-156, January.
    4. Ingersoll, Jonathan E. & Skelton, Jeffrey & Weil, Roman L., 1978. "Duration Forty Years Later," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(4), pages 627-650, November.
    5. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348, October.
    6. Fong, H Gifford & Vasicek, Oldrich A, 1984. "A Risk Minimizing Strategy for Portfolio Immunization," Journal of Finance, American Finance Association, vol. 39(5), pages 1541-1546, December.
    7. Khang, Chulsoon, 1979. "Bond Immunization When Short-Term Interest Rates Fluctuate More Than Long-Term Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 14(5), pages 1085-1090, December.
    8. Bierwag, G. O., 1977. "Immunization, Duration, and the Term Structure of Interest Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(5), pages 725-742, December.
    9. Lars E.O. Svensson, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992 - 1994," NBER Working Papers 4871, National Bureau of Economic Research, Inc.
    10. Elton, Edwin J & Gruber, Martin J & Michaely, Roni, 1990. "The Structure of Spot Rates and Immunization," Journal of Finance, American Finance Association, vol. 45(2), pages 629-642, June.
    11. Fisher, Lawrence & Weil, Roman L, 1971. "Coping with the Risk of Interest-Rate Fluctuations: Returns to Bondholders from Naive and Optimal Strategies," The Journal of Business, University of Chicago Press, vol. 44(4), pages 408-431, October.
    12. Xueping Wu, 2000. "A New Stochastic Duration Based on the Vasicek and CIR Term Structure Theories," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 27(7‐8), pages 911-932, September.
    13. Knez, Peter J & Litterman, Robert & Scheinkman, Jose Alexandre, 1994. "Explorations into Factors Explaining Money Market Returns," Journal of Finance, American Finance Association, vol. 49(5), pages 1861-1882, December.
    14. Michael W. Brandt & Amir Yaron, 2003. "Time-Consistent No-Arbitrage Models of the Term Structure," NBER Working Papers 9458, National Bureau of Economic Research, Inc.
    15. Chambers, Donald R. & Carleton, Willard T. & McEnally, Richard W., 1988. "Immunizing Default-Free Bond Portfolios with a Duration Vector," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(1), pages 89-104, March.
    16. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1979. "Duration and the Measurement of Basis Risk," The Journal of Business, University of Chicago Press, vol. 52(1), pages 51-61, January.
    17. Svensson, Lars E O, 1994. "Estimating and Interpreting Forward Interest Rates: Sweden 1992-4," CEPR Discussion Papers 1051, C.E.P.R. Discussion Papers.
    18. Gultekin, N Bulent & Rogalski, Richard J, 1984. "Alternative Duration Specifications and the Measurement of Basis Risk: Empirical Tests," The Journal of Business, University of Chicago Press, vol. 57(2), pages 241-264, April.
    19. Xueping Wu, 2000. "A New Stochastic Duration Based on the Vasicek and CIR Term Structure Theories," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 27(7‐8), pages 911-932, September.
    20. Prisman, Eliezer Z. & Shores, Marilyn R., 1988. "Duration measures for specific term structure estimations and applications to bond portfolio immunization," Journal of Banking & Finance, Elsevier, vol. 12(3), pages 493-504, September.
    21. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    22. Dai, Qiang & Singleton, Kenneth J., 2002. "Expectation puzzles, time-varying risk premia, and affine models of the term structure," Journal of Financial Economics, Elsevier, vol. 63(3), pages 415-441, March.
    23. David Bolder & David Stréliski, 1999. "Yield Curve Modelling at the Bank of Canada," Technical Reports 84, Bank of Canada.
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    Cited by:

    1. Almeida, Caio & Lund, Bruno, 2014. "Immunization of Fixed-Income Portfolios Using an Exponential Parametric Model," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 34(2), November.

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    More about this item

    Keywords

    Immunization; duration; parametric model; interest rate risk;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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