Sharing the longevity risk - Confex



Sharing the longevity risk between annuitants and annuity provider

Annamaria Olivieri - University of Parma (Italy) - annamaria.olivieri@unipr.it

Ermanno Pitacco - University of Trieste (Italy) - ermanno.pitacco@deams.units.it

Abstract

The benefits provided by (conventional) life annuity and pension products imply “guarantees” to annuitants and hence risks borne by the annuity provider, that is, the insurance company or the pension fund. Risks inherent in guarantees have clearly emerged in recent and current scenarios, in particular because of volatility in financial markets and trends in mortality / longevity, provided that the amount of benefits is guaranteed whatever the investment yield and the experienced mortality may be.

Appropriate modelling tools are then needed for pricing and reserving. In particular, a shift from deterministic models, only based on expected present values, to more complex stochastic models, allowing for various risk causes and components and the relevant impact on portfolio results, should update the actuarial toolkit. However the implementation of complex mathematical methods often constitutes, on the one hand, an obstacle on the way towards sound pricing and reserving principles. On the other hand, facing the risks by charging high premiums can make life annuities even less attractive than currently perceived by potential customers (see, for example, Pitacco (2012)).

Appropriate solutions should be suggested, aiming at providing retirees with effective alternatives to the income drawdown (or “self-annuitization”). An intermediate solution, that can be placed between life annuities managed by annuity providers and income drawdown, is represented by “group self-annuitization” (GSA), as suggested by Wadsworth et al. (2001) (where this structure is named “annuitized fund”). The concept of GSA has been analyzed in depth by Piggott et al. (2005). Testing the effectiveness of GSA schemes allowing for uncertain longevity trends is the main aim of Sherris and Qiao (2011).

In the framework of life annuities managed by annuity providers, innovative product designs can be conceived. If the life annuity is conventional, i.e. the benefit is not linked to mortality / longevity experience, the annuity provider bears the risk of unanticipated mortality improvements, that is the non-diversifiable aggregate longevity risk (besides the individual longevity risk). However, non-conventional life annuities can be defined, aiming at linking, to some extent, the annuity benefit to the mortality experienced in the group of annuitants, and / or in the market of life annuities (or pensions) and / or in the population. This link implies sharing the risks arising from experienced mortality between annuitants and annuity provider.

Various approaches can be adopted in order to link annuity benefits to mortality experience, or to updated forecasts of future mortality trends. Some basic ideas, involving both the accumulation and the decumulation (or payout) phase, are presented by Pitacco et al. (2009) (in particular, see Sect. 7.5). Several specific models have been proposed, which provide interesting contributions to the technical literature. The “adaptive algorithmic annuities”, which rely on a progressive updating of mortality forecasts and the consequent adjustment of annuity benefits have been designed by Lüty et al. (2001). In Richter and Weber (2011) life annuity products providing benefits linked to actual mortality experience are analyzed. The contribution by van de Ven andWeale (2008) allows for uncertainty in future mortality trends, and proposes mortality-adjusted annuities in which the aggregate mortality risk is transferred to annuitants; the adjustment is determined also accounting for risk aversion of the annuitants. In Denuit et al. (2011) an appropriate longevity index is designed in order to adapt the annuity benefit, accounting for unexpected longevity improvements experienced by a given reference population and aiming at transferring to the annuitants only the aggregate component of the longevity risk.

The above models usually link the adjustment of the annuity benefit either to the mortality experienced by a pool of annuitants (in particular an annuity portfolio or a pension fund), or to the availability of new projected life tables (either market or population tables).

We propose a rather general model that aims at providing a unifying point of view from which several practicable schemes, sharing the common purpose of transferring part of the longevity risk to the annuitants, can be analyzed and compared. We only focus on the decumulation phase, assuming that an individual holds a given amount at a given time (e.g. at retirement), and that the amount itself is converted into an immediate life annuity.

We assume that the life annuity is not a unit-linked one, that is, the assets backing the liabilities mainly consist of fixed interest securities, so that a minimum interest rate can be guaranteed. Moreover, if the investment yield is higher than the guaranteed interest rate, the annuity benefit can be increased via some investment profit participation mechanism. As regards the longevity risk, we consider the possibility of changing the annuity benefit by relating the benefit itself to the experienced mortality, or to updated mortality forecasts, or both. Moreover, the relation between the change in the benefit and the mortality referred to may be either “direct”, or “adjusted” according to an inference mechanism (as the one proposed by Olivieri and Pitacco (2009)). Finally, distribution of investment profits among the annuitants is considered; in the case of unanticipated mortality improvements leading to a reduction in the annuity benefit, investment profit participation can mitigate the reduction itself. Some numerical examples are provided in order to test and compare the effect of various linking arrangements.

Keywords

Life annuities, Longevity risk, Guaranteed benefit.

References

Denuit, M., Haberman, S., and Renshaw, A. (2011). Longevity-indexed life annuities. North American Actuarial Journal, 15(1):97–111.

Lüty, H., Keller, P. L., Binswangen, K., and Gmür, B. (2001). Adaptive algorithmic annuities. Mitteilungen der Schweizerischen Aktuarvereinigung, 2:123–138.

Olivieri, A. and Pitacco, E. (2009). Stochastic mortality: the impact on target capital. ASTIN Bulletin, 39(2):541–563.

Piggott, J., Valdez, E. A., and Detzel, B. (2005). The simple analytics of a pooled annuity fund. Journal of Risk and Insurance, 72(3):49–520.

Pitacco E. (2012), From “benefits” to “guarantees”: looking at life insurance products in a new framework, Working paper

Pitacco, E., Denuit, M., Haberman, S., and Olivieri, A. (2009). Modelling Longevity Dynamics for Pensions and Annuity Business. Oxford University Press.

Richter, A. and Weber, F. (2011). Mortality-indexed annuities: Managing longevity risk via product design. North American Actuarial Journal, 15(2):212–236.

Sherris, M. and Qiao, C. (2011). Managing systematic mortality risk with group self pooling and annuitisation schemes. ARC Centre of Excellence in Population Ageing Research. Working Paper No. 2011/4. Available at SSRN: . van de Ven, J. and Weale, M. (2008). Risk and mortality-adjusted annuities. National Institute of Economic and Social Research. London. Discussion Paper No. 322. Available online: 110826.pdf .

Wadsworth, M., Findlater, A., and Boardman, T. (2001). Reinventing annuities. Presented to the Staple Inn Actuarial Society. Available online:

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