Minimum return rate guarantees under default risk: optimal design of quantile guarantees

Abstract

The paper analyzes the design of participating life insurance contracts with minimum return rate guarantees. Without default risk, the insured receives the maximum of a guaranteed rate and a participation in the investment returns. With default risk, the payoff is modified by a default put implying a compound option. We represent the yearly returns of the liabilities by a portfolio of plain vanilla options. In a Black and Scholes model, the optimal payoff constrained by a maximal shortfall probability can be stated in closed form. Due to the completeness of the market, it can be implemented for any equity to debt ratio. Keywords Guarantee scheme • Derivatives • Life insurance • Return rate guarantees • Default risk • Regulatory requirements • Utility to the insured JEL Classification G 31 • G 22 The authors gratefully acknowledge financial support by the German Insurance Science Association (DVfVW). In addition the authors would like to thank the two anonymous referees for their valuable and helpful suggestions and comments.