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Surplus participation schemes for life annuities under Solvency II

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Abstract

Under the new European Solvency II capital requirements life insurance companies have to implement a market-consistent valuation framework. A special challenge is the estimation of the market value of liabilities for products containing future discretionary surplus payments such as with-profit or participating life annuities (PLAs). We develop a realistic stochastic asset and liability company model with longevity and capital market risk for participating life annuities. Based on this model we project future cash flows to policyholders and calculate the solvency capital requirement (SCR) over the cohort’s lifetime. Besides the insurer’s point of view, we also analyse the utility implications for different types of annuitants. Our model and analysis are not only interesting for those acting under Solvency II regulation, but also in further economic valuation frameworks of the pension business of insurance companies.

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Notes

  1. See GDV [22]. PLA are also widely used in Austria [34] and Switzerland [33]. In the USA, such companies as TIAA use annuities with surplus participation in company pensions plans.

  2. Although we consistently implement Solvency II regulations as well as the specifics of German PLAs in our model, the techniques can be transferred, and the results can be related to further economic valuation frameworks of the annuity business of a life insurance company. Similar frameworks are the Swiss Solvency Test or the market consistent embedded value (MCEV).

  3. Other (sub-)modules of the standard formula are not considered in our simplified model; nevertheless, the model can simply be extended for further research.

  4. In our base case, we estimate the parameters of the interest rate model with data up to 2009, since afterwards significant interest rate reductions were introduced by the ECB as part of its quantitative easing policy. We assume, however, that the extremely low interest rate environment is not permanent in the long term. Thus, in order to provide a generalised model, we refrain from using market data since 2010 to calibrate the CIR model. In sensitivity analysis, we separately illustrate the impact of higher and lower long-term mean interest rates (see Table 4 in Sect. 4.4). The impact of lower guaranteed interest rates on the annuitants utility are discussed in Bruszas et al. [7].

  5. See Albrecht and Maurer [1], p. 206.

  6. Note the calculation of asset-surpluses is based on income payments (dividends and coupons), realized gains and losses relative to historical costs, but not on non-realized capital gains and losses. This allows smoothing of surplus payments to policyholders (see Maurer et al. [28] for a discussion).

  7. This model ensures a good fit for higher ages by exploiting the near log-linearity of the mortality curve. Specifically, we use the German Life Tables (period 1 × 1) for males and females; last modified: March 29, 2017, version MPv5 for the period 1990–2015. See http://www.mortality.org.

  8. As management rule for the surplus allocation, we use the Solvency I requirements complemented by the already committed surplus reserve.

  9. The above-mentioned regulatory requirements are valid since introduction of the Life Insurance Reform Act (LVRG) in 2014, which also governs the minimum surplus distribution. Before that, inter alia, policyholders were eligible for 75% of mortality surplus, and offsetting negative returns with positive returns from other risk categories was prohibited.

  10. In practice, a deterministic term structure is given in terms of the risk-free interest rate by the European Commission. In our model, we use the simulated and projected interest rates according to the CIR model.

  11. The standard formula assumes that the individual SCRs are Gaussian and linearly dependent. Nevertheless, these assumptions might cause problems. For example, if returns are non-Gaussian, which is observed for the most important classes of risk, the use of the value-at-risk might lead to a mismatch of the SCR and the underlying riskiness (Boonen [6]).

  12. In contrast to the SCR ratio, for the calculation of the SCR according to the standard formula, we do not account for the risk margin, as within in the standard formula the risk margin is assumed to stay unchanged from stress scenarios to avoid circularity (see for example Burkhart et al. [8]). This is why we set up the simplified economic balance sheet without a risk margin.

  13. In practice, a going concern insurer would use uncommitted surplus reserve from already existing insurance portfolios for the committed surplus reserve of a new cohort, which in turn would repay the interest-free loan in terms of its contribution to the collective uncommitted surplus reserve.

  14. Notice that in our model we abstain from a risk-based re-pricing of the UE FLA compared to the PLA with the same surplus distribution. Thus, we confine to contrast PLAs with different surplus participations as well as PLAs to their corresponding UE FLA with the assumption of the same feasible price.

  15. Current and historical quotes for immediate PLAs without tax incentives and with two classes of surplus participation options—surplus annuitisation and direct payment. For current data provided by Morgen & Morgen, a comparison platform, we retrieve quotes for an immediate participating life annuity with a one-off contribution of €100,000 for males and females aged 67 in 2016. Our quote history starts 2006, retrieved for males and females aged 60, 65 and 70 in the respective year. The database embraces the vast majority (over 90%) of the tariffs offered by annuity providers in the German insurance market. According to BaFin [9], the top five companies comprise together about 40% of market as measured by the gross premium earned.

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Acknowledgements

Research support was provided by the Frankfurter Verein für Versicherungswissenschaft, the German Investment and Asset Management Association (BVI), and the Research Center SAFE, funded by the State of Hessen initiative for research excellence, LOEWE. We thank the initiative High Performance Computing in Hessen for granting us computing time at the LOEWE-CSC and Lichtenberg Cluster.

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  1. Department of Finance, Goethe University Frankfurt, House of Finance, Theodor-W.-Adorno-Platz 3, 60323, Frankfurt, Germany

    Sandy Both, Vanya Horneff, Barbara Kaschützke & Raimond Maurer

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  1. Sandy Both
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  2. Vanya Horneff
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Correspondence to Raimond Maurer.

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Both, S., Horneff, V., Kaschützke, B. et al. Surplus participation schemes for life annuities under Solvency II. Eur. Actuar. J. 9, 391–421 (2019). https://doi.org/10.1007/s13385-019-00203-3

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