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European Actuarial Journal

Erschienen in:

01.07.2015 | Original Research Paper

Analyzing the effect of low interest rates on the surplus participation of life insurance policies with different annual interest rate guarantees

verfasst von: Peter Hieber, Ralf Korn, Matthias Scherer

Erschienen in: European Actuarial Journal | Ausgabe 1/2015

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Abstract

We analyze the effects of a prevailing low interest rates regime on investment decisions of insurance companies and on the risk/return profile of participating life insurance policies with different contractually guaranteed minimum annual return. Our analysis is based on German legislation and a stylized insurance company with two cohorts of insured persons having different minimal return guarantees. Our findings shed some light on the non-trivial interrelation between profit distribution, minimum guarantees, and resulting profitability for the different cohorts. Moreover, we investigate the complex role of the risk reserve that allows insurance companies to redistribute profits in time and, less obviously, also between the cohorts.

Vorheriger Artikel The impact of covariates on a bonus–malus system: an application of Taylor’s model

Nächster Artikel Optimal supervisory rules for pension funds under diverse pension security mechanisms

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A lot of attention has been drawn to the pricing of (individual) life insurance contracts with this cliquet-type options, see for example, [1‐5, 7, 9, 10, 12].

In Germany this is regulated via the minimum funding ordinance (Mindestzuführungsverordnung), see http://www.gesetze-im-internet.de/mindzv/index.html.

Grosen and Jørgensen [10] state that “many insurers now face claims from distinct groups of liability holders distinguished by different guaranteed interest rates in their policies. This raises the problem of how to avoid inequitable treatment of different classes of policyholders within the same fund. Some companies [...] have tremendous concerns over the definition of a correct and fair distribution policy [...]”.

In practice, insurance companies earn additional money by the difference between true and best-estimate actuarial assumptions, i.e., in their assumptions on administrative costs or mortality. This income is, however, rather stable over time and is thus—for simplicity—neglected in this analysis. Instead, we concentrate on the financial risks.

In Germany, at least \(90\,\%\) of returns have to be distributed to the policyholders (compare the minimum funding ordinance “Mindestzuführungsverordnung”).

In Germany, the regulator tries to (at least) mitigate the unequal treatment by rules (3) and (4): If a high guarantee contract benefits by rules (3) or (4), it might not benefit fully from a high surplus in later years as part of a compensation for the other cotracts.

Historic daily data was obtained from Reuters (ticker names: DE10YT=RR, GREXP, and GDAXI).

Mortality tables are, for example, available from the German government agency Statistisches Bundesamt, see https://www.destatis.de.

Note that these also include hidden risk reserves that can be accumulated, for example, by exploiting accounting rules.

Bacinello A (2003) Fair pricing of a guarantee life insurance participating contract embedding surrender option. J Risk Insur 70(3):461–487MathSciNetCrossRef

Barbarin J, Devolder P (2005) Risk measure and fair valuation of an investment guarantee in life insurance. Insur Math Econ 37:297–323MATHMathSciNetCrossRef

Bauer D, Kiesel R, Kling A, Ruß J (2005) Risk neutral valuation of participating life insurance contracts. Insur Math Econ 39(2):171–183CrossRef

Bohnert A, Gatzert N (2012) Analyzing surplus appropriation schemes in participating life insurance from the insurer’s and the policyholder’s perspective. Insur Math Econ 50(2):64–78MATHMathSciNetCrossRef

Bryis E, de Varenne F (1997) On the risk of life insurance liabilities: debunking some common pitfalls. J Risk Insur 64(4):673–694CrossRef

Døskeland T, Nordahl H (2008) Intergenerational effects of guaranteed pension contracts. In: The Geneva risk and insurance review, vol. 33

Goecke O (2013) Pension saving schemes with return smoothing mechanism. Insur Math Econ 53:678–689MATHMathSciNetCrossRef

Graf S, Kling A, Ruß J (2011) Risk analysis and valuation of life insurance contracts: combining actuarial and financial approaches. Insur Math Econ 49(10):115–125MATHCrossRef

Grosen J, Jørgensen P (2000) Fair valuation of life insurance liabilities: the impact of interest rate guarantees, surrender options and bonus policies. Insur Math Econ 26(1):37–57MATHCrossRef

10.

Grosen J, Jørgensen P (2002) Life insurance liabilities at market value: an analysis of insolvency risk, bonus policy, and regulatory intervention rules in a barrier option framework. J Risk Insur 69(1):63–91CrossRef

11.

Jaquemod R (ed) (2005) Stochastisches Unternehmensmodell für deutsche Lebensversicherungen. VVW, Karlsruhe

12.

Kling A, Ruß J (2004) Differenzierung der Überschüsse konventioneller Lebensversicherungsverträge mit unterschiedlichem Garantiezins: Betrug treuer Kunden oder finanzmathematische Notwendigkeit? Institut für Finanz-und Aktuarwissenschaften Ulm

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Patel J, Read C (1996) Handbook of the normal distribution. In: Statistics: a series of textbooks and monographs, 2nd edn

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Vasicek O (1977) An equilibrium characterization of the term structure. J Financ Econ 5(2):177–188CrossRef

Titel: Analyzing the effect of low interest rates on the surplus participation of life insurance policies with different annual interest rate guarantees
verfasst von: Peter Hieber
Ralf Korn
Matthias Scherer
Publikationsdatum: 01.07.2015
Verlag: Springer Berlin Heidelberg
Erschienen in: European Actuarial Journal / Ausgabe 1/2015
Print ISSN: 2190-9733
Elektronische ISSN: 2190-9741
DOI: https://doi.org/10.1007/s13385-014-0102-3

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The impact of covariates on a bonus–malus system: an application of Taylor’s model

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