Analyzing the e ect of low interest rates on the surplus participation of life insurance policies with di erent annual interest rate guarantees

We analyze the e ects of a prevailing low interest rates regime on investment decisions of insurance companies and on the risk/return pro le of participating life insurance policies with di erent contractually guaranteed minimum annual return. Our analysis is based on German legislation and a stylized insurance company with two cohorts of insured persons having di erent minimal return guarantees. Our ndings shed some light on the non-trivial interrelation between pro t distribution, minimum guarantees, and resulting pro tability for the di erent cohorts. Moreover, we investigate the complex role of the risk reserve that allows insurance companies to redistribute pro ts in time and, less obviously, also between the cohorts. Owning a participating (or with-pro t) life insurance contract provides one with a contractually guaranteed minimum annual rate of return. This minimal rate of return is regulated by law and settled when the contract is signed; it is furthermore xed until the contract expires. Heuristically speaking, this corresponds to a Cliquet-type option on the return of the managed funds of the insured Peter Hieber acknowledges funding by the German Association of Insurance Science (DVFVW). A lot of attention has been drawn to the pricing of (individual) life insurance contracts with this cliquet-type options, see, for example, Bryis and de Varenne [1997], Grosen and Jørgensen [2000], Grosen and Jørgensen [2002], Bacinello [2003], Kling and Ruÿ [2004], Bauer et al. [2005], Barbarin and Devolder [2005], Bohnert and Gatzert [2012], and Goecke [2013].