Valuation of cliquet-style guarantees with death benefits

Yaodi Yong*, Hailiang Yang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, we consider the problem of valuing an equity-linked insurance product with a cliquet-style payoff. The premium is invested in a reference asset whose dynamic is modeled by a geometric Brownian motion. The policy delivers a payment to the beneficiary at either a fixed maturity or the time upon the insured's death, whichever comes first. The residual lifetime of a policyholder is described by a random variable, assumed to be independent of the asset price process, and its distribution is approximated by a linear sum of exponential distributions. Under such characterization, closed-form valuation formulae are derived for the contract considered. Moreover, a discrete-time setting is briefly discussed. Finally, numerical examples are provided to illustrate our proposed approach.
Original languageEnglish
Article number17
Pages (from-to)359-375
Number of pages17
JournalJournal of Industrial and Management Optimization
Issue number1
Publication statusPublished - 15 Jan 2023
Externally publishedYes


  • Equity-indexed annuity;
  • Cliquet-style guarantee;
  • Life insurance;
  • Death bene- ts.


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