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Consistent Dynamic Affine Mortality Model for Longevity Risk Applications

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Author Info

  • Craig Blackburn

    ()
    (School of Risk and Actuarial Studies and ARC Centre of Excellence in Population Ageing Research, Australian School of Business, University of New South Wales)

  • Michael Sherris

    ()
    (School of Risk and Actuarial Studies and ARC Centre of Excellence in Population Ageing Research, Australian School of Business, University of New South Wales)

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    Abstract

    This paper proposes and assesses consistent multi-factor dynamic affine mortality models for longevity risk applications. The dynamics of the model produce closed-form expressions for survival curves. The framework includes an arbitrage-free model specification. There are multiple risk factors allowing applications to hedging and pricing mortality and longevity bonds, mortality derivatives and more general risk management problems. A state-space representation is used to estimate parameters for the model with the Kalman filter. A 3-factor model specification is shown to provide a good fit to the observed survival curves especially for older ages, and performs better than the 2-factor models. Consistent models are shown to improve model performance and stability.

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    File URL: http://cepar.edu.au/media/48733/Longevity%20Risk%20Applications.pdf
    File Function: First version, 2011
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    Bibliographic Info

    Paper provided by ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales in its series Working Papers with number 201107.

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    Length: 33 pages
    Date of creation: May 2011
    Date of revision:
    Handle: RePEc:asb:wpaper:201107

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    Related research

    Keywords: Mortality model; longevity risk; multi-factor; affine; arbitrage-free; consistent; Kalman filter; Swedish mortality;

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    References

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    1. Elisa Luciano & Elena Vigna, 2006. "Non mean reverting affne processes for stochastic mortality," Carlo Alberto Notebooks 30, Collegio Carlo Alberto.
    2. Jens H.E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2008. "An Arbitrage-Free Generalized Nelson-Siegel Term Structure Model," NBER Working Papers 14463, National Bureau of Economic Research, Inc.
    3. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
    4. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(01), pages 115-130, March.
    5. repec:aah:aarmng:1999-4 is not listed on IDEAS
    6. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
    7. De Rossi, Giuliano, 2004. "Kalman filtering of consistent forward rate curves: a tool to estimate and model dynamically the term structure," Journal of Empirical Finance, Elsevier, vol. 11(2), pages 277-308, March.
    8. Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
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