How to derive optimal guarantee levels in participating life insurance contracts

Abstract

PurposeThe purpose of this paper is to show how an insurance company can maximize the policyholder’s utility by setting the level of the interest rate guarantee in line with his preferences.Design/methodology/approachThe authors develop a general model of life insurance, taking stochastic interest rates, early default and regular premium payments into account. Furthermore, the authors assume that equity holders must receive risk-adequate returns on their initial equity contribution and that the insurance company has to maintain a solvency restriction.FindingsThe findings show that the optimal level for the interest rate guarantee is in general far below the maximum value typically set by the supervisory authorities and insurance companies.Originality/valueThe authors conclude that the approach of deviating from the maximum interest rate guarantee level given by the regulatory requirements can create additional value for the rational policyholder. In contrast to Schmeiser and Wagner (2014), the second finding shows that the interest rate guarantee embedded in a life insurance product becomes less attractive compared to a pure investment in the underlying asset portfolio to the policyholder when the guarantee level is lowered too far or the contract duration is short. They also refute Schmeiser and Wagner (2014) by showing that the equity capital required by the insurance company increases with the level of the guarantee, even if the insurer is flexible with respect to its asset allocation. The last finding is that a policyholder with higher risk aversion does not generally prefer a higher guarantee level.