Surrender risk in the context of the quantitative assessment of participating life insurance contracts under Solvency II

Participating life insurance contracts entitle the policyholder to participate in the company's annual surplus. Typically, they are also equipped with a surrender option that allows the policyholder to terminate the contract prior to maturity, receiving a predetermined surrender value. The option interacts with (often cliquet-style) interest guarantees that are a key feature of traditional participating contracts. Surrender options can considerably affect an insurer's liabilities and bear material risks. This paper addresses the recognition of those risks in the quantitative assessment of a heterogeneous insurance portfolio under Solvency II, taking into account the complex interrelation between minimum interest guarantees, reserving requirements, and profit sharing. The lapse risk module of the Solvency II standard formula requires the identification of portfolio segments that are exposed to a specific change of surrender rates (long-term increase/decrease, one-off increase). We provide a heuristic that identifies homogeneous risk groups in the sense that the respective stress would increase the insurer's liabilities. Our approach can be used to derive an appropriate segmentation in practical applications. We further analyze implications of the segmentation on the Risk Margin (as part of the Technical Provisions under Solvency II) and discuss consequences of policyholder options on the calculation of Going Concern Reserve and Surplus Funds. To illustrate our findings, we set up a stochastic balance sheet and cash flow projection model for a stylized life insurance company. We conclude that current methods used for practical applications underestimate surrender risk under Solvency II and that the proposed modeling refinements may improve the appropriateness of solvency ratios for participating business.