Modelling and management of longevity risk: Approximations to survivor functions and dynamic hedging

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This paper looks at the development of dynamic hedging strategies for typical pension plan liabilities using longevity-linked hedging instruments. Progress in this area has been hindered by the lack of closed-form formulae for the valuation of mortality-linked liabilities and assets, and the consequent requirement for simulations within simulations. We propose the use of the probit function along with a Taylor expansion to approximate longevity-contingent values. This makes it possible to develop and implement computationally efficient, discrete-time delta hedging strategies using q-forwards as hedging instruments.

The methods are tested using the model proposed by Cairns et al. (2006a) (CBD). We find that the probit approximations are generally very accurate, and that the discrete-time hedging strategy is very effective at reducing risk. (C) 2011 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)438-453
Number of pages16
JournalInsurance: Mathematics and Economics
Issue number3
Publication statusPublished - Nov 2011


  • Longevity risk
  • Dynamic hedging
  • Delta hedging
  • Probit-Taylor approximation
  • CBD model
  • q-forward
  • Solvency II

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