Asset Liability Management of Longevity and Interest Rate Risks: Using Survival–Mortality Bonds

Abstract

In this article, we propose to attach a mortality index to a conventional bond, called a survival–mortality (SM) bond. Its cash flow pattern is like a conventional bond but it can be separated into a survival (S) part and a mortality (M) part; the cash flow pattern in the former is like an annuity or a longevity bond and that in the latter is like a mortality–catastrophe bond. We further propose to split it into S, M, and SM zero-coupon STRIPS (Separate Trading Registered Interest and Principal Securities). We apply these S, M, and SM issues to hedging longevity risk and interest rate risk of 1-year and multiple-year annuity exposures for the asset liability management of an annuity provider by adopting mortality, interest, mortality–interest duration, and convexity matching strategies. Numerical illustrations show that using SM STRIPS rather than S STRIPS can be sufficient to hedge the risks embedded in 1-year annuity exposures, whereas for multiple-year annuity exposures using S issues is more effective to reduce longevity risk and interest rate risk than using SM issues. We can infer that mortality-linked bonds play an essential role in asset liability management; the proposed survival–mortality bonds will be a feasible way to develop an efficient market for longevity risk.

Acknowledgements

The authors thank the referees for their valuable comments and suggestions. Support from the NSERC (Natural Sciences and Engineering Research Council) of Canada and the MOST (Minister of Science and Technology) of Taiwan is gratefully acknowledged.

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Notes

1 Typical mortality catastrophe bonds act more like a put option with a trigger point and an exhaustion point––for example, the Vita bonds issued by Swiss Re (see, for example, Y. Lin, Liu, and Yu [2013] and Chen, MacMinn, and Sun [2015, 2017]), whereas the coupon payment and principle in the M bond increase proportionally with the mortality rate.

2 Many studies have advised government intervention to improve annuity markets (Blake and Burrows 2001; Brown and Orszag 2006; Blake, Boardman, and Cairns 2014) because a low level of voluntary annuitization creates social problems for government policymakers.

3 Before 1985, a number of brokerage firms created their own zero-coupon securities by stripping the coupons from Treasury bills and bonds, meaning the coupons became separate investments that were sold separately. Treasury STRIPS have been issued by the U.S. Treasury and backed by the U.S. government since the STRIPS system was introduced in 1985.

4 Interest rate immunization whereby the value of a portfolio will be little affected in response to a change in interest rates has been adopted widely in the asset liability management of life insurers; see, for example, Fooladi and Roberts (2004) and Courtois and Denuit (2007). Mortality rate immunization, which creates natural hedge opportunities for life insurers and annuity providers through a proper allocation of life insurance and annuity products, has also aroused some attention; see, for example, Li and Hardy (2011), Li and Luo (2012), and T. Lin and Tsai (2013, 2014). T. Lin and Tsai (2020b) further developed mortality interest rate immunization by deriving mortality interest durations and convexities of the prices of life insurance and annuity products and then applied it to natural hedges.

Additional information

Funding

Ministry of Science and Technology, Taiwan; Natural Sciences and Engineering Research Council of Canada.