Working Papers

Ermanno Pitacco

Heterogeneity of a population in respect of mortality is due to differences among the individuals, which are caused by various risk factors. Some risk factors are observable while others are unobservable. The set of observable risk factors clearly depends on the type of population addressed. The impact of observable risk factors on individual mortality, in particular when they also constitute “rating factors” in the calculation of premiums and other actuarial values, is usually expressed approximately, according to some pragmatic approach. For example, additive or multiplicative adjustments to the average age-specific mortality are frequently adopted. Heterogeneity due to unobservable risk factors can conversely be quantified by adopting the concept of individual “frailty”. However, individual frailty can be interpreted and consequently modeled in several ways, according to the causes which are considered as originating the frailty itself: congenital characteristics, environmental features, lifestyle aspects, etc. It follows that the individual frailty can, in particular, be assumed either constant or variable throughout the lifetime.

Keywords: Heterogeneity, Frailty, Risk factors, Force of mortality, Mortality laws, Parametric models, Special-rate annuities.

Fedor Iskhakov and Michael Keane

We structurally estimate a life-cycle model of consumption, labor supply and retirement, using data from the Australian HILDA panel. We use the model to evaluate effects of Australia’s Age Pension system and income tax policy on labor supply, consumption and retirement. Our model accounts for human capital, savings, uninsurable wage risk and credit constraints. We account for “bunching" of hours by assuming a discrete set of hours levels, and we investigate labor supply on both the intensive and extensive margins. Our model allows us to quantify the effects of anticipated and unanticipated tax and pension policy changes at different points of the life-cycle. Our results imply that Australia’s Age Pension system as currently designed is poorly targeted. Our simulations suggest that a doubling of taper rates, combined with a 5.9% reduction of income tax rates, would be budget neutral and Pareto improving.

Yajing Xu, Michael Sherris and Jonathan Ziveyi

The pricing of longevity-linked securities depends not only on the stochastic uncertainty of the underlying risk factors, but also the attitude of investors towards those factors. In this research, we investigate how to estimate the market risk premium of longevity risk using investable retirement indexes, incorporating uncertain real interest rates using an affine dynamic Nelson-Siegel model. 

Michael Sherris, Yajing Xu and Jonathan Ziveyi.

Multi-country risk management of longevity risk provides new opportunities to hedge mortality and interest rate risks in guaranteed lifetime income streams. This requires consideration of both interest rate and mortality risks in multiple countries. For this purpose, we develop value-based longevity indexes for multiple cohorts in two different countries that take into account the major sources of risks impacting life insurance portfolios, mortality and interest rates. To construct the indexes we propose a cohort-based affine model for multi-country mortality and use an arbitrage-free multi-country Nelson-Siegel model for the dynamics of interest rates. Index based longevity hedging strategies have the advantages of efficiency, liquidity and lower cost but introduce basis risk. Graphical risk metrics are a way to effectively capture the relationship between an insurer’s portfolio and hedging strategies. We illustrate the effectiveness of using a value–based index for longevity risk management between two countries using graphical basis risk metrics. To show the impact of both interest rate and mortality risk we use Australia and UK as domestic and foreign countries, and, to show the impact of mortality only, we use the male populations of the Netherlands and France with common interest rates and basis risk arising only from differences in mortality risks.