Essays on Minimum Return Guarantee Schemes in the Framework of Life Insurance Contracts

The insurance industry is currently experiencing a transformation. Challenges, such as the long and persistent phase of low interest rates, increasing regulation, sustainability requirements, growing competition, demographic developments and the current COVID-19 pandemic are exerting increasing pressure on insurance companies, leading to a constant evolution of their product range.

The capital requirements under Solvency II force insurance companies to cover high risks with a correspondingly high level of equity. Traditional (German) life insurance contracts are designed to allow the policyholder to participate with her savings fraction in returns from a chosen investment portfolio, while  in practice any losses are excluded by a minimum return guarantee. For the provision of this minimum return guarantee, the policyholder has to pay a premium such that the contribution payments of traditional life insurance contracts with guarantee commitments can be divided into two components: The guarantee costs and the participation fraction in the investment portfolio. Although the guaranteed interest rate has fallen in recent years, these contracts are too risky and therefore too expensive for insurance companies in view of the low interest rate environment and high market fluctuations. In addition, insurance companies still hold old life insurance contracts in their portfolio with high guarantee promises that can not be realized due to the current low level of interest rates.

As a result, traditional life insurance contracts are increasingly becoming less important, while new, so-called innovative life insurance products are moving to the center of the product range offered by insurance companies. These products include, for example,  select products where the policyholder has the right to choose each year between a capped index participation or a guaranteed interest rate. Additionally, other models propose a guaranteed interest rate that is continuously adjusted to a reference interest rate and is thus only fixed in principle but not in amount when the contract is concluded. 

However, the ongoing low interest rate phase and the associated continuous reduction in the guaranteed interest rate to 0.25% in 2022 means that insurance companies may no longer be able to guarantee 100% of the policyholder's contributions (German Federal Ministry of Finance (2021)). The regulatory requirements of Solvency II result in the fact that the 100% contribution guarantee complicates the generation of appropriate returns for the policyholders by reducing the flexibility of investments. Accordingly, minimum return guarantee schemes included in traditional and innovative life insurance contracts should be reconsidered.

The first consequences in practice can be seen in the fact that the leading insurance company in Germany, Allianz Lebensversicherungs-AG, has abandoned the 100% contribution guarantee at the beginning of 2021. Now their policyholders only have the option of choosing between minimum return guarantees of 90, 80 and 60% at the end of the maturity when they conclude new insurance contracts as e.g. KomfortDynamik, InvestFlex and IndexSelect. Other insurance companies followed the decision of Allianz: At the beginning of 2021, R+V Lebensversicherung AG also abandoned the 100% contribution guarantee and instead offers products, such as PrivatRente Performance which guarantees a maximum of 90% of the contribution payments at the start of the pension. HDI Lebensversicherung AG also offers a range of selectable minimum return guarantees with its product TwoTrust Vario. Policyholders can choose between a guaranteed contribution of 0-80%, an increasing guarantee rate and an individual guarantee increase in the form of lock-in features.

With the reduced guarantees, the strictly regulated insurance companies are allowed to invest the policyholder's contributions in a riskier but also in a potentially more profitable way, i.e. the lower the guarantee rate, the higher the potential return. Moreover, the policyholder's benefit must also be taken into account when designing insurance contracts with minimum return guarantees. Some policyholders may still prefer the full contribution guarantee, while others may have a growing interest in the increasing return opportunities offered by contracts with lower guarantee rates. In principle, the general demand for life insurance contracts with minimum return guarantees remains high: 32\% of new business contracts concluded in Germany are determined by life insurance contracts with minimum return guarantees (GDV (2021a)).

It is now the challenge of the insurance companies to develop an appropriate minimum return guarantee scheme which is of low risk and accordingly requires low equity capital backing but also shows consideration for the utility of the policyholder. This optimal design of different guarantee schemes is subject of the present thesis. In the context of the above problem, the thesis analyzes the cost drivers, risk management and utility aspects of different guarantee schemes in life insurance contracts with a single contribution and periodic contributions. Thus, life insurance contracts where the minimum return guarantee depends on the development of the insurance company's asset return (e.g. terminal, lookback and cliquet guarantee schemes) will be discussed as well as piecewise defined versions where the minimum return guarantee depends on the development of the future term structure. Additionally, different dynamic investment and hedging strategies of the insurance company are considered and compared to a general benchmark portfolio that maximizes the expected utility of the policyholder in the case where no guarantee is prescribed (Merton (1971)).

For this purpose, methods from option pricing theory as well as numerical methods for the approximation of expected values are needed. The analysis of different guarantee schemes with regard to their valuation provides important insights for the insurance industry as well as for academics in the research field of life insurance and risk management.  



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