The Interaction of Guarantees, Surplus Distribution, and Asset Allocation in With Profit Life Insurance Policies

Traditional life insurance policies in many markets are sold with minimum interest rate guarantees. In the case of a so-called cliquet style guarantee, the guaranteed return must be credited to the policyholder’s account each year. Usually, life insurers try to provide this guaranteed rate of interest plus some stable surplus on the policyholder’s account every year by applying the so-called average interest principle: Building up reserves in years of good returns on assets and using these reserves to keep surplus stable in years of low returns. The primary focus of most existing literature in this area is on the fair (i.e. risk-neutral) valuation of life insurance contracts. Since most insurers do not apply risk-neutral (or riskminimizing) hedging strategies, an analysis of the resulting risks seems very important. Therefore, the present paper will concentrate on the risk a contract imposes on the insurer, measured by shortfall probabilities under the so-called “real-world probability measure P”. We develop a rather general model and analyze the impact interest rate guarantees have on the risk exposure of the insurance company and how default risks depend on characteristics of the contract, on the insurer’s reserve situation and asset allocation, on management decisions, as well as on regulatory parameters. In particular, the interaction of the parameters is analyzed yielding results that should be of interest for insurers as well as regulators.