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Evolution of coupled lives' dependency across generations and pricing impact

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  • Elisa Luciano
  • Jaap Spreeuw
  • Elena Vigna

Abstract

This paper studies the dependence between coupled lives - both within and across generations - and its effects on prices of reversionary annuities in the presence of longevity risk. Longevity risk is represented via a stochastic mortality intensity. Dependence is modelled through copula functions. We consider Archimedean single and multi-parameter copulas. We find that dependence decreases when passing from older generations to younger generations. Not only the level of dependence but also its features - as measured by the copula - change across generations: the best-fit Archimedean copula is not the same across generations. Moreover, for all the generations under exam the single-parameter copula is dominated by the two-parameter one. The independence assumption produces quantifiable mispricing of reversionary annuities. The misspecification of the copula produces different mispricing effects on different generations. The research is conducted using a well-known dataset of double life contracts.

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Bibliographic Info

Paper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 258.

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Length: 24 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:cca:wpaper:258

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Related research

Keywords: copula; goodness-of-fit; significance test; stochastic mortality; generation effect; reversionary annuity.;

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  1. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2007. "Modelling stochastic mortality for dependent lives," Carlo Alberto Notebooks 43, Collegio Carlo Alberto.
  2. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
  3. Schrager, David F., 2006. "Affine stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 81-97, February.
  4. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer, vol. 64(4), pages 811-834, August.
  5. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
  6. Elisa Luciano & Elena Vigna, 2006. "Non mean reverting affne processes for stochastic mortality," Carlo Alberto Notebooks 30, Collegio Carlo Alberto.
  7. Ivan Kojadinovic & Jun Yan, . "Modeling Multivariate Distributions with Continuous Margins Using the copula R Package," Journal of Statistical Software, American Statistical Association, vol. 34(i09).
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