Natural Hedging Strategies for Life Insurers: Impact of Product Design and Risk Measure

Abstract

Natural hedging allows life insurers to manage long-term longevity and investment risks of life annuity products through offsetting risks in life insurance products. Benefits include a reduction in risk-based capital. We use stochastic mortality and interest rate models to assess life insurance and annuity capital requirements and to quantify the benefits of natural hedging for a range of different types of life insurance product designs and risk measures based on probability of insurer solvency. We show that level-premium life insurance products with a medium duration (around 20-30 years) can better hedge annuity products than whole life products. Renewable term life insurance products have less hedge effectiveness than level-premium term insurance. Results vary with the risk measure used, with the 1-year horizon Solvency II risk measure showing lower natural hedging benefits of life insurance compared to multiple-period risk measures. IntroductionLife annuities are recognized as an important product that protects individuals against longevity risk and investment risk in retirement. The recent global financial crisis, which resulted in significant falls and high volatility in equity markets, highlighted the benefits of such products in a retired individual's portfolio. With increasing life expectancies in most developed countries, many retirees face the risk of outliving their retirement funds and savings. Blake, Cairns, and Dowd (2008) highlight how life annuities provide retirees with a stable income that protects against longevity and also protects retirees from investment risk. Despite this, life annuity markets

Immunization and Hedging of Post Retirement Income Annuity Products

“…2 (t) = 0 and we assume the two mortality factors are independent, consistent with the assumption made in Biffis [10], Blackburn and Sherris [11] and Wong et al [12].…”

“…We used the estimation methods in Koopman and Durbin [14] and Wong et al [12] based on the Kalman filter. The calibrated parameters for the mortality model are shown in Table 1.…”

Systematic longevity risk: to bear or to insure?

“…A limitation of our work is the exclusion of channels that may reduce the insurer's effective longevity exposure, such as synergies in product offering (e.g., natural hedging of systematic longevity risk via the sale of annuities and life insurance contracts; Gatzert and Wesker, 2012; Wong et al ., 2017), access to reinsurance (Baione et al ., 2017), and shadow insurance (Koijen and Yogo, 2016). In such a scenario, the annuity contract could be sold at a lower price.…”

Natural Hedges With Immunization Strategies of Mortality and Interest Rates

“…Tsai (2013, 2014) further define and derive mortality durations and convexities with respect to an instantaneously proportional change and an instantaneously constant movement, respectively, in q (the one-year death probability), p (the one-year survival probability), ln(μ), (q/p), and ln(q/p); they also propose mortality duration and convexity matching strategies to determine the weights of two or three life insurance and annuity products and achieve quite satisfactory hedge effectiveness (HE). Wong et al (2017) quantify the benefits of natural hedges for a range of different types of life insurance product designs and risk measures based on the probability of insurer's solvency. Luciano et al (2017) provide natural hedging strategies with delta and gamma hedges for life insurance and annuity businesses on a single generation or on different generations in the presence of both longevity and interest rate risks.…”