Advertisement

European Actuarial Journal

, Volume 9, Issue 2, pp 391–421 | Cite as

Surplus participation schemes for life annuities under Solvency II

  • Sandy Both
  • Vanya Horneff
  • Barbara Kaschützke
  • Raimond MaurerEmail author
Original Research Paper
  • 56 Downloads

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.

Keywords

Participating life annuity Market-consistent valuation Longevity risk Lifetime utility Stochastic modelling Solvency II 

JEL Classification

G11 G22 H55 J26 J32 

Notes

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.

References

  1. 1.
    Albrecht P, Maurer R (2015) Investment und Risikomanagement. StuttgartGoogle Scholar
  2. 2.
    Al-Darwish A, Hafeman M, Impavido G, Kemp M, O’Malley P (2014) Possible unintended consequences of basel III and solvency II. Br Actuar J 19:273–325CrossRefGoogle Scholar
  3. 3.
    Bauer D, Kiesel R, Kling A, Ruß J (2006) Risk-neutral valuation of participating life insurance contracts. Insur Math Econ 39:171–183MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bibby BM, Sørensen M (1995) Martingale estimating functions for discretely observed diffusion processes. Bernoulli 1:17–39MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bohnert A, Gatzert N, Jørgensen PL (2015) On the management of life insurance company risk by strategic choice of product mix, investment strategy and surplus appropriation schemes. Insur Math Econ 60:83–97MathSciNetCrossRefGoogle Scholar
  6. 6.
    Boonen TJ (2017) Solvency II solvency capital requirement for life insurance companies based on expected shortfall. Eur Actuar J 7:1–20MathSciNetCrossRefGoogle Scholar
  7. 7.
    Bruszas S, Kaschützke B, Maurer R, Siegelin I (2018) Unisex pricing of German participating life annuities—boon or bane for customer and insurance company? Insur Math Econ 78:230–245MathSciNetCrossRefGoogle Scholar
  8. 8.
    Burkhart T, Reuß A, Zwiesler HJ (2015) Participating life insurance contracts under Solvency II: inheritance effects and allowance for a Going Concern Reserve. Eur Actuar J 5:203–244MathSciNetCrossRefGoogle Scholar
  9. 9.
    Bundesanstalt für Finanzdienstleistungsaufsicht (BaFin) (2016a) Lebensversicherung 2015 (Tabelle 30, 141, 160), Statistik der Erstversicherungsunternehmen—2015, Bonn und Frankfurt am Main 2016Google Scholar
  10. 10.
    Bundesanstalt für Finanzdienstleistungsaufsicht (BaFin) (2016b) Erste Erkenntnisse aus den Sparten unter Solvency II. Attachment to a press release, Frankfurt am MainGoogle Scholar
  11. 11.
    Bundesanstalt für Finanzdienstleistungsaufsicht (BaFin) (2018) Jahresbericht 2017, Frankfurt am MainGoogle Scholar
  12. 12.
    Cairns A, Blake D, Dowd K (2006) A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. J Risk Insur 73:687–718CrossRefGoogle Scholar
  13. 13.
    Charupat N, Kamstra M, Mileysky M (2015) The sluggish and asymmetric reaction of life annuity prices to changes in interest rates. J Risk Insur 83:519–555CrossRefGoogle Scholar
  14. 14.
    Cox J, Ingersoll J, Ross S (1985) An intertemporal general equilibrium model of asset prices. Econometrica 53:363–384MathSciNetCrossRefGoogle Scholar
  15. 15.
    Eling M, Holder S (2013) The value of interest rate guarantees in participating life insurance contracts: status quo and alternative product design. Insur Math Econ 53:491–503MathSciNetCrossRefGoogle Scholar
  16. 16.
    EIOPA (2011) Report on the fifth quantitative impact study (QIS5) for solvency II, EIOPA-BoS-15/035. https://eiopa.europa.eu/Publications/Reports/QIS5_Report_Final.pdf. Accessed 12 Dec 2018
  17. 17.
    EIOPA (2017) Technical documentation of the methodology to derive EIPOA’s risk-free interest rate term structures, EIOPA-BoS-15/035. https://eiopa.europa.eu/Publications/Standards/Technical%20Documentation%20%2827%20June%202017%29.pdf. Accessed 12 Dec 2018
  18. 18.
    European Union (2002) Official Journal of the European Communities, Directive 2002/83/EC of the European Parliament and of the Council of 5 November 2002. OJ L 345/1. https://eur-lex.europa.eu/eli/dir/2002/83/oj. Accessed 12 Dec 2018
  19. 19.
    European Union (2015) Commission delegated regulation (EU) 2015/35 of 10 October 2014 supplementing directive 2009/138/EC. OJ L 12/1. https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:32015R0035&from=EN. Accessed 12 Dec 2018
  20. 20.
    Gatzert N, Holzmüller I, Schmeisser H (2012) Creating customer value in participating life insurance. J Risk Insur 60:645–670CrossRefGoogle Scholar
  21. 21.
    Gatzert N, Kling A (2007) Analysis of participating life insurance contracts: a unification approach. J Risk Insur 74:547–570CrossRefGoogle Scholar
  22. 22.
    GDV (2018) Lebensversicherung in Zahlen 2018. https://www.gdv.de/de/zahlen-und-fakten/publikationen/lebensversicherung-in-zahlen. Accessed 22 May 2019
  23. 23.
    Horneff W, Maurer R, Rogalla R (2010) Dynamic portfolio choice with deferred annuities. J Bank Finance 34:2652–2664CrossRefGoogle Scholar
  24. 24.
    Kling A, Richter A, Ruß J (2007) The impact of surplus distribution on the risk exposure of with-profit life insurance policies including interest rate guarantees. J Risk Insur 74:571–589CrossRefGoogle Scholar
  25. 25.
    Kling A, Richter A, Ruß J (2007) The interaction of guarantees, surplus distribution, and asset allocation in with-profit life insurance policies. Insur Math Econ 40:164–1782MathSciNetCrossRefGoogle Scholar
  26. 26.
    Maurer R, Mitchell OS, Rogalla R, Kartashov V (2013) Lifecycle portfolio choice with systematic longevity risk and variable investment-linked deferred annuities. J Risk Insur 80:649–676CrossRefGoogle Scholar
  27. 27.
    Maurer R, Rogalla R, Siegelin I (2013) Participating payout life annuities: lessons from Germany. ASTIN Bull 43:159–187MathSciNetCrossRefGoogle Scholar
  28. 28.
    Maurer R, Mitchell OS, Rogalla R, Siegelin I (2016) Accounting and actuarial smoothing of retirement payouts in participating life annuities. Insur Math Econ 71:268–283MathSciNetCrossRefGoogle Scholar
  29. 29.
    Milevsky M, Young V (2007) Annuitization and asset allocation. J Econ Dyn Control 31:3138–3177MathSciNetCrossRefGoogle Scholar
  30. 30.
    Reuß A, Ruß J, Wieland J (2016) Participating life insurance products with alternative guarantees: reconciling policyholders’ and insurers’ interests. Risks 4:11CrossRefGoogle Scholar
  31. 31.
    Richter A, Weber F (2011) Mortality-indexed annuities: avoiding unwanted risk. N Am Actuar J 15:212–236MathSciNetCrossRefGoogle Scholar
  32. 32.
    Schmeisser H, Wagner J (2013) The impact of introducing guaranty schemes on pricing and capital structure. J Risk Insur 80:273–308CrossRefGoogle Scholar
  33. 33.
    Schweizerischer Versicherungsverband (SVV) (2017) Zahlen und Fakten der privaten Versicherungswirtschaft. https://issuu.com/swissinsurers/docs/svv_zahlen_fakten_2017_de. Accessed 19 Dec 2018
  34. 34.
    Versicherungsverband Österreich (VVÖ 2018) Jahresbericht 2017 https://www.vvo.at/vvo/vvo.nsf/sysPages/jahresbericht.html. Accessed 19 Dec 2018
  35. 35.
    Zaglauer Z, Bauer D (2008) Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment. Insur Math Econ 43:29–40MathSciNetCrossRefGoogle Scholar

Copyright information

© EAJ Association 2019

Authors and Affiliations

  • Sandy Both
    • 1
  • Vanya Horneff
    • 1
  • Barbara Kaschützke
    • 1
  • Raimond Maurer
    • 1
    Email author
  1. 1.Department of FinanceGoethe University FrankfurtFrankfurtGermany

Personalised recommendations