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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.

MSC:

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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