Spatial natural hedging: a general framework with application to the mortality of U.S. states

Abstract

It is well known that coupling life and death benefits within an insurance portfolio may be a beneficial longevity risk reduction technique, especially when policies are underwritten in the same geographical region. However, though desirable, the lack of available capacity of life insurance instruments in terms of underlying cohorts or duration of products underwritten within a given region can substantially constrain the use of natural hedging strategies for life insurance companies. That is why the primary objective of this paper is to investigate the implementation and effectiveness of natural hedging strategies when considering the geographical or spatial dimension. Starting from a well-known multi-population mortality model, we evaluate the relevance of natural hedging strategies and their susceptibility to basis risk resulting from age, period, and spatial effects. Our novel theoretical findings provide direct insights into specific and often complex positions necessary for optimal real-world hedging. In a practical numerical application predicated on U.S. mortality data, we demonstrate the situation of a U.S.-based insurance company capable of selling policies across different states. Though often unable to curtail product sales, an insurance company using our analytical tool can effectively, through marketing strategies, stimulate or destimulate sales to approach an optimal hedging position of an overall portfolio.

Keywords:

• Spatial natural hedging
• longevity risk
• U.S. mortality rates
• mortality uncertainty

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 A similar reasoning applies to states within the European Union, for instance.

2 See: https://content.naic.org/industry-ucaa-definitions.

3 See: https://content.naic.org/sites/default/files/publication-sta-bb-volume-one.pdf.

4 When it comes to the European Economic Area (EEA), the European Insurance and Occupational Pensions Authority (EIOPA) reports similar cross-border activity of life insurers in Europe. See: https://www.eiopa.europa.eu/tools-and-data/insurance-statistics_en#cross-border-premiums.

5 Notice that throughout the paper, we abstract from the presence of interest-rate risk in liability valuation. The interested reader may find this issue tackled in Wong et al. (2017) and Luciano et al. (2017), for instance.

6 Due to data limitation regarding differential mortality rates of annuitants and term insurance policy holders, we consider the same mortality dynamics for annuitants and life insurance policyholders in the same state. Considering these two groups as sub-populations would introduce an additional source of basis risk between the hedging portfolio and the portfolio to be hedged. Empirical evidence however, points to little relevance of this basis risk source, see Kwon and Jones (2006). Notice, however, that this basis risk source is additional to the basis risk arising from the different ages at which the two types of contracts payout cash-flows, for which we account for with our mortality model.

7 We exclude the states of Alaska and Hawaii as they do not share a land-border with another state, as well as Washington, D.C..

8 The CDC provides two sets of mortality data: the ‘Detailed Mortality’ and the ‘Compressed Mortality.’ The ‘Detailed Mortality’ dataset is available for the period of 1999–2018 only, but contains single-year-of-age population and death counts from age 0 to 99 for all 50 states. The ‘Compressed Mortality’ dataset is separated into three periods: 1968–1978, 1979–1998, 1999–2016. The difference between them lies in the ICD (cause of death) code used, which is irrelevant to this paper. More importantly, the ‘Compressed Mortality’ dataset contains the population and death counts of all states for age groups only (5-year age groups for ages 1–24; 10-year age groups for ages 25–84; open interval for age 85+).

9 Notice that we could have used several alternative methods. First, we could have splitted forecasted age-group rates instead of observed ones, as in Renshaw and Haberman (2003) and Villegas and Haberman (2014). Second, we could have used other disaggregation methods, such as interpolation through splines as the Human Mortality Database does.

10 The use of term insurance rather than whole-life insurance policies is indeed prudential in terms of the performance evaluation of the natural hedging strategy. Such performance would be improved if whole-life insurance was available and used.

11 Also, if the reinsurance is fairly priced, optimal strategies are also more cost-effective that the constrained ones. In practice, usually, reinsurance, when available, is costly. This would lead to a decrease in the strategy cost-effectiveness.