Surrender Risk in the Context of the Quantitative Assessment of Participating Life Insurance Contracts under Solvency II

Abstract

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.

Neural calibration of hidden inhomogeneous Markov chains -- Information decompression in life insurance

“…Therefore, we employ the common (α, β, γ 1 , γ 2 ) expense structure, see e.g. [10,23]. These factors are related to the acquisition of the contract (α), the collection of premiums (β) and administrative charges during the time of premium payments (γ 1 ) and thereafter (γ 2 ).…”

“…by consulting applied research in [10]. Since the maximum admissible actuarial interest rate in Germany for the years 2015 and 2016 is 1.25%, see [16], we set the discount factor v to v := 1.0125 −1 .…”

On the Market-Consistent Valuation of Participating Life Insurance Heterogeneous Contracts under Longevity Risk

“…Here, the heterogeneity between groups of policyholders stems from their offered minimum interest rate guarantees and contract maturities. In this respect, this paper is related to Hansen and Miltersen (2002) and Burkhart (2018). Hansen and Miltersen (2002) deal with the case of participating life insurance contracts sold to heterogeneous customers, but do not take into account biometric and default risk.…”

“…Hansen and Miltersen (2002) deal with the case of participating life insurance contracts sold to heterogeneous customers, but do not take into account biometric and default risk. 1 Burkhart (2018) particularly addresses surrender risk in the assessment of a heterogeneous insurance portfolio under Solvency II, and considers the interaction between minimum interest rate guarantee, surplus participation and reserving requirement.…”

Modeling surrender risk in life insurance: theoretical and experimental insight

“…On the other hand, there exists extensive empirical research, which aims to identify the main risk drivers for lapse events and to test for modeling hypotheses, as well as the quality of modeling approaches to capture the underlying risk, see e.g. [2,7,15,29,41,52]. The most common modeling classes include logistic regressions and tree based methods as CART and random forests, where the evaluation is typically performed with metrics on the respective confusion matrix or the related receiver operating curve (ROC) for assessment and model choice.…”