Fair valuation of cliquet-style return guarantees in (homogeneous and) heterogeneous life insurance portfolios

Peter Hieber, Jan Natolski, Ralf Werner

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Participating life insurance contracts allow the policyholder to participate in the annual return of a reference portfolio. Additionally, they are often equipped with an annual (cliquet-style) return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. While this problem is typically discussed from the viewpoint of a single contract or a homogeneous* insurance portfolio, contracts are, in practice, managed within a heterogeneous insurance portfolio. Their valuation must then–unlike the case of asset portfolios–take account of portfolio effects: Their premiums are invested in the same reference portfolio; the contracts interact by a joint reserve, individual surrender options and joint default risk of the policy sponsor. Here, we discuss the impact of portfolio effects on the fair valuation of insurance contracts jointly managed in (homogeneous and) heterogeneous life insurance portfolios. First, in a rather general setting, including stochastic interest rates, we consider the case that otherwise homogeneous contracts interact due to the default risk of the policy sponsor. Second, and more importantly, we then also consider the case when policies are allowed to differ in further aspects like the guaranteed rate or time to maturity. We also provide an extensive numerical example for further analysis.

Original languageEnglish
Pages (from-to)478-507
Number of pages30
JournalScandinavian Actuarial Journal
Volume2019
Issue number6
DOIs
StatePublished - 3 Jul 2019

Keywords

  • G13
  • G22
  • Life insurance
  • embedded options
  • fair valuation
  • heterogeneous portfolios
  • participating contracts
  • return guarantee

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