Academic journal article Journal of Risk and Insurance

An Optimal Product Mix for Hedging Longevity Risk in Life Insurance Companies: The Immunization Theory Approach

Academic journal article Journal of Risk and Insurance

An Optimal Product Mix for Hedging Longevity Risk in Life Insurance Companies: The Immunization Theory Approach

Article excerpt


This article investigates the natural hedging strategy to deal with longevity risks for life insurance companies. We propose an immunization model that incorporates a stochastic mortality dynamic to calculate the optimal life insurance-annuity product mix ratio to hedge against longevity risks. We model the dynamic of the changes in future mortality using the well-known Lee-Carter model and discuss the model risk issue by comparing the results between the Lee-Carter and Cairns-Blake-Dowd models. On the basis of the mortality experience and insurance products in the United States, we demonstrate that the proposed model can lead to an optimal product mix and effectively reduce longevity risks for life insurance companies.


In the past decade, annuity premiums in the United States have accounted for more than 50 percent of life insurers' premium income, with an average growth rate of 10.2 percent from 1988 to 2005 (American Council of Life Insurers, 2005). However, longevity risk (1)--or uncertainty about long-term trends in mortality rates and the impact on the long-term probability of survival of an individual--represents a critical threat to private insurers because it increases the payout period and the liability costs of providing annuities. In particular, human mortality has declined globally over the course of the twentieth century. (2) As Willets (2004) points out, mortality) improvements do not occur in a smooth upward fashion but rather exhibit a "cohort effect." (3) Recent medical discoveries may increase human life spans even beyond the currently projected mortality table used by insurance companies. These issues have made it far more difficult for insurance actuaries to price annuity products correctly, and the resulting inaccurate mortality assumptions lead to major risks. Therefore, hedging longevity risks has taken on an increasingly important role for life insurance companies.

When considering how to hedge longevity risks, most prior research investigates mortality risk and pricing issues for annuity products (Friedman and Warshawsky, 1990; Frees, Carriere, and Valdez, 1996; Brown, Mitchell, and Poterba, 2000; Mitchell et al., 2001). More recent studies focus on the impact of stochastic mortality changes on life insurance and annuities (Marceau and Gaillardetz, 1999; Wilkie, Waters, and Yang, 2003; Cairns, Blake, and Dowd, 2006a). In addition, many financial vehicles, such as mortality derivatives and survivor bonds, have been proposed to reduce or hedge the longevity risks of annuity. Blake and Burrows (2001) first proposed that issuing survivor bonds (4) could help a pension fund insure against the longevity risk, and more recent studies also extend the issue of securitization of longevity risk (e.g., Dowd, 2003; Blake, Cairns, and Dowd, 2006; Blake, Cairns, Dowd, and MacMinn, 2006; Lin and Cox, 2005; Cox, Lin, and Wang, 2006; Denuit, Devolder, and Goderniaux, 2007). Dowd et al. (2006) suggest that a survivor swap can serve as a more advantageous survivor derivative than a survivor bond, because it can be arranged at a lower transaction cost and does not require a liquid market. (5)

Similar to the concept of survivor swap, insurers can hedge longevity risks internally between their own business products (life insurance and annuity), which are sensitive in opposing ways to the changes in mortality rates. This approach provides a so-called natural hedging strategy. If the future mortality of a cohort improves relative to current expectations, life insurers gain a profit because they can pay the death benefit later than initially expected, whereas annuity insurers suffer losses because they must pay annuity benefits for longer than they initially expected. Therefore, life insurance can serve as a dynamic hedge vehicle against unexpected mortality risk. Yet relatively few academic papers have investigated the issue of natural hedging. Cox and Lin (2007) suggest that natural hedging is appealing but may be too expensive to be effective in the context of internal life insurance and annuity products. …

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