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Key q-duration: A Framework for Hedging Longevity Risk

Johnny Siu-Hang Li, and Ancheng Luo

When hedging lobgevity risk with standardized contracts, the hedger needs to calibrate the hedge carefully so that it can effectively reduce the risk. In this article, we present a calibration method that is based on matching mortality rate sensitivities. Specifically, we introduce a measure called key q-duration, which allows us to estimate the price sensitivity of a life-contingent liability to each portion of the underlying mortality curve. Given this measure, one can easily construct a longevity hedge with a handful of mortality forwards. Our empirical results indicate that using key q-durations, a hedge effectiveness of more than 97% can be attained with only five mortality forwards. We also investigate other important issues that are related to standardized longevity hedges, including the adaptation needed for hedging multiple birth cohorts, and the quantification of sampling risk and basis risk.

Keywords: Cairns-Blake-Dowd model; Mortality forwards; Securitization