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Immunization Using a Parametric Model of the Term Structure

Author

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  • 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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    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.
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    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.
    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(05), pages 1085-1090, December.
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    More about this item

    Keywords

    Immunization; duration; parametric model; interest rate risk;

    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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