DISCUSSION PAPER PI-1109
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