Key q-duration: a framework for hedging longevity risk. (English) Zbl 1277.91089

Summary: When hedging longevity 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 small number of q-forward contracts. We further propose an extension for hedging the longevity risk associated with multiple birth cohorts, and another extension for accommodating population basis risk.


91B30 Risk theory, insurance (MSC2010)
91D20 Mathematical geography and demography
91G20 Derivative securities (option pricing, hedging, etc.)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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