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Natural delta gamma hedging of longevity and interest rate risk

Author

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  • Elisa Luciano

    ()

  • Luca Regis

    ()

  • Elena Vigna

    ()

Abstract

The paper presents closed-form Delta and Gamma hedges for an- nuities and death assurances, in the presence of both longevity and interest-rate risk. Longevity risk is modelled through an extension of the classical Gompertz law, while interest rate risk is modelled via an Hull-and-White process. We theoretically provide natural hedg- ing strategies, considering also contracts written on di erent genera- tions. We provide a UK-population and bond-market calibrated exam- ple. We compute longevity exposures and explicitly calculate Delta- Gamma hedges. Re-insurance is needed in order to set-up portfolios which are Delta-Gamma neutral to both longevity and interest-rate risk.

Suggested Citation

  • Elisa Luciano & Luca Regis & Elena Vigna, 2012. "Natural delta gamma hedging of longevity and interest rate risk," ICER Working Papers - Applied Mathematics Series 21-2011, ICER - International Centre for Economic Research.
  • Handle: RePEc:icr:wpmath:21-2011
    as

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    File URL: http://www.biblioecon.unito.it/biblioservizi/RePEc/icr/wp2011/ICERwp21-11.pdf
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    References listed on IDEAS

    as
    1. David Blake & Andrew Cairns & Kevin Dowd & Richard MacMinn, 2006. "Longevity Bonds: Financial Engineering, Valuation, and Hedging," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 647-672.
    2. Elisa Luciano & Luca Regis & Elena Vigna, 2011. "Delta and Gamma hedging of mortality and interest rate risk," ICER Working Papers - Applied Mathematics Series 01-2011, ICER - International Centre for Economic Research.
    3. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    4. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
    5. Jennifer L. Wang & H.C. Huang & Sharon S. Yang & Jeffrey T. Tsai, 2010. "An Optimal Product Mix for Hedging Longevity Risk in Life Insurance Companies: The Immunization Theory Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 473-497.
    6. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    7. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    8. Hári, Norbert & De Waegenaere, Anja & Melenberg, Bertrand & Nijman, Theo E., 2008. "Longevity risk in portfolios of pension annuities," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 505-519, April.
    9. Robert Jarrow & Stuart Turnbull, 1994. "Delta, gamma and bucket hedging of interest rate derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(1), pages 21-48.
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