Different Shades of Risk: Mortality Trends Implied by Term Insurance Prices

Abstract

To infer forward-looking, market-based mortality trends, we estimate a flexible affine stochastic mortality model based on a set of U.S. term life insurance prices using a generalized method of moments approach. We find that neither mortality shocks nor stochasticity in the aggregate trend seem to affect the prices. In contrast, allowing for heterogeneity in the mortality rates across carriers is crucial. We conclude that for life insurance, rather than aggregate mortality risk, the key risks emanate from the composition of the portfolio of policyholders. These findings have consequences for mortality risk management and emphasize important directions for mortality-related actuarial research.

ACKNOWLEDGMENTS

A previous version of this article was presented at the Twelfth International Longevity Risk and Capital Markets Solutions Conference (Longevity 12) under the title “Mortality Trends Implied by Term Insurance Prices,” and parts are taken from the earlier working paper, “The Risk in Catastrophe Mortality Securitization Transactions” by the second author. The authors are grateful for helpful comments from an anonymous referee, Johnny Li, Jin-Chuan Duan, Yue Kuen Kwok, and other participants of the Insurance Risk and Finance Research Centre (IRFRC) 2017 Annual Conference, the Longevity 12 conference, and Perspectives on Actuarial Risks in Talks of Young Researchers.

FUNDING

The authors are grateful for financial support under the Society of Actuaries CAE grant “New Trends in Longevity.”

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Notes

1 In insurance practice, actuaries rely on so-called select-and-ultimate tables to account for this type of selection, where the “select” tables used in early policy years display lower mortality due to underwriting examinations.

2 This assumption, again, is motivated by competitive pressures in the market. Large differences in costs should be competed away unless they are linked to aspects relating to underlying heterogeneity.

3 Including them in the estimation procedure leads to problems when including a complex mortality model, because the impact on insurance prices is similar to those originating from certain components. We obtain reasonable magnitudes not too different from the set values in the context of simple mortality models.

4 The A.M. Best data is extracted from the insurance database in Georgia State University.