Natural Hedging of Life and Annuity Mortality Risks

Abstract

ABSTRACT. The values of life insurance and annuity liabilities move in opposite directions in response to a change in the underlying mortality. Natural hedging utilizes this to stabilize aggregate liability cash flows. We find empirical evidence that suggests that annuity writing insurers who use natural hedging also charge lower premiums than otherwise similar insurers. This indicates that insurers who are able to utilize natural hedging have a competitive advantage. In addition, we show how a mortality swap might be used to provide the benefits of natural hedging.

Stochastic Mortality, Macroeconomic Risks, and Life Insurer Solvency

“…4. Including annuities, i.e., contracts written on the opposite site of mortality risk, would give rise to natural hedging opportunities, as analyzed in Gründl, Post, and Schulze (2006) and Cox and Lin (2007). Additionally, dependencies between lapse and surrender rates and macroeconomic conditions (Browne, Carson and Hoyt, 2001;Kim, 2005) could be accounted for.…”

“…Gründl, Post, and Schulze (2006) and Cox and Lin (2007) examine natural hedging opportunities in the annuity and life insurance business; Dowd, Cairns, and Blake (2006), Hári et al (2008b), and Bauer and Weber (2008) assess the impact of stochastic mortality on an insurer's risk exposure.…”

Longevity Risk

“…Whereas old-age pension liabilities are sensitive to long-life risk (the risk that individuals live longer than anticipated), the opposite holds for death benefit insurance, which is adversely affected by short-life risk. This implies that portfolios of death benefit contracts can provide a natural hedge for the mortality risk in old-age pension liabilities (see, for example, Promislow 2001, Cox andLin 2007). In addition, there may be hedge potential from combining old-age pension annuities and partner pension annuities.…”

“…Sometimes, natural hedges exist, see, for example, Milevsky and Promislow (2001) or Cox and Lin (2007). We illustrate the diversification possibilities through product mix in Section 5.3.…”

“…11 As a consequence of this market incompleteness, arbitrage arguments are insufficient to obtain unique market prices of annuities and related products. This seriously complicates the fair valuation of liabilities depending on future survival 11 Sometimes, there are natural hedge possibilities, see, for example, Milevsky and Promislow (2001) or Cox and Lin (2007). See also Section 5.3. outcomes due to the presence of a (longevity) risk premium.…”