摘要：Using the widely-cited Lee-Carter mortality model, we quantify aggregate mortality risk as the risk
that the average annuitant lives longer than is predicted by the model, and we conclude that annuity
business exposes insurance companies to substantial mortality risk. We calculate that a markup of
3.7% on an annuity premium (or else shareholders’ capital equal to 3.7% of the expected present
value of annuity payments) would reduce the probability of insolvency resulting from uncertain
aggregate mortality trends to 5% and a markup of 5.4% would reduce the probability of insolvency
to 1%. Using the same model, we find that a projection scale commonly referred to by the insurance
industry underestimates aggregate mortality improvements. Annuities that are priced on that
projection scale without any conservative margin appear to be substantially underpriced. Insurance
companies could deal with aggregate mortality risk by transferring it to financial markets through
mortality-contingent bonds, one of which has recently been offered. We calculate the returns that
investors would have obtained on such bonds had they been available over a long period. Using both
the Capital and the Consumption Capital Asset Pricing Models, we determine the risk premium that
investors would have required on such bonds. At plausible coefficients of risk aversion, annuity
providers should be able to hedge aggregate mortality risk via such bonds at a very low cost.
