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On the efficient utilisation of duration

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  • Dierkes, Thomas
  • Ortmann, Karl Michael

Abstract

In this article we present a new approach to estimate the change of the present value of a given cashflow pattern caused by an interest rate shift. Our approximation is based on analysing the evolution of the present value function through a linear differential equation. The outcome is far more accurate than the standard approach achieved by a Taylor expansion. Furthermore, we derive an approximation formula of second order that produces nearly accurate results. In particular, we prove that our method is superior to any known alternative approximation formula based on duration. In order to demonstrate the power of this improved approximation we apply it to coupon bonds, level annuities, and level perpetuities. We finally generalise the approach to a non-flat term structure. As for applications in insurance, we estimate the change of the discounted value of future liabilities due to a proportional shift in the set of capital accumulation factors. These findings are of particular importance to capital adequacy calculations with respect to interest rate stress scenarios that are part of regulatory solvency requirements.

Suggested Citation

  • Dierkes, Thomas & Ortmann, Karl Michael, 2015. "On the efficient utilisation of duration," Insurance: Mathematics and Economics, Elsevier, vol. 60(C), pages 29-37.
    • Handle: RePEc:eee:insuma:v:60:y:2015:i:c:p:29-37
    DOI: 10.1016/j.insmatheco.2014.11.002
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    References listed on IDEAS

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    1. Leonard Tchuindjo, 2008. "An accurate formula for bond-portfolio stress testing," Journal of Risk Finance, Emerald Group Publishing, vol. 9(3), pages 262-277, May.
    2. Miles Livingston & Lei Zhou, 2005. "Exponential Duration: A More Accurate Estimation Of Interest Rate Risk," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 28(3), pages 343-361, September.
    3. Osborne, Michael J., 2005. "On the computation of a formula for the duration of a bond that yields precise results," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(1), pages 161-183, February.
    4. Emanuele Bajo & Massimiliano Barbi & David Hillier, 2013. "Interest rate risk estimation: a new duration-based approach," Applied Economics, Taylor & Francis Journals, vol. 45(19), pages 2697-2704, July.
    5. Michael Osborne, 2014. "Multiple Interest Rate Analysis: Theory and Applications," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-137-37277-2, December.
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    Cited by:

    1. Vahidreza Yousefi & Siamak Haji Yakhchali & Jolanta Tamošaitienė, 2019. "Application of Duration Measure in Quantifying the Sensitivity of Project Returns to Changes in Discount Rates," Administrative Sciences, MDPI, vol. 9(1), pages 1-14, February.
    2. Luciano Quattrocchio & Luisa Tibiletti & Mariacristina Uberti, 2021. "Pricing a Lease Contract in Presence of Late Payment Extra-Charges," International Journal of Business and Management, Canadian Center of Science and Education, vol. 14(11), pages 179-179, July.

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    More about this item

    Keywords

    Duration; Bond price elasticity; Interest rate shock; Stress test; Solvency;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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