Surplus Participation Research Articles

Life reinsurance under perfect and asymmetric information

This paper studies life reinsurance as a solution to default risk in equity-linked life insurance products with surplus participation. The problem is considered under both perfect and asymmetric information about the insurer's risk profile between the reinsurer and the insurer. In both cases, we analyze the existence of proportional reinsurance and the impact of the insurer's investment strategies on optimal reinsurance. We find that the more risky the insurer's investment portfolio is, the more risk the insurer tends to transfer to the reinsurer. Further, information asymmetry leads to additional information costs and consequently to a larger reinsurance premium and a lower reinsurance share.

Interaction effects between dynamic hybrid products and traditional deferred annuities in the German life insurance market

Dynamic hybrid products emerged in 2007 and are now well established in the German life insurance market. In this article, we study interaction effects between dynamic hybrid products and traditional deferred annuity contracts, that are sold by the same insurance company. The key question we investigate is whether the presence of dynamic hybrid products has a negative effect on the payout of traditional insurance products. We do so by using data drawn from a Monte Carlo simulation that is based on a model presented in this article. These data reveal that dynamic hybrid products reduce the payment to policyholders of traditional deferred annuities via the channel of surplus participation.

Current developments in German pension schemes: What are the benefits of the new target pension?

We analyze the newly introduced German occupational pension scheme called target pension (“Zielrente”), which links the beneficiaries’ benefits during the retirement phase to the mortality experienced among the pension beneficiaries and the performance of the financial market, from a pension beneficiary’s perspective. We model the contract payoffs related to the target pension according to the new enhancement law on German occupational law. Specifically, we include two parameters in the plan design, one to control the surplus participation and one to control the loss participation. These parameters are chosen in such a way that the initial wealth of the retiree equals the initial value of the target pension. With the help of expected lifetime utility and wealth equivalent, we find that the target pension provides a meaningful supplement to the first and third pillar. Further, we find some comparative advantages of the target pension over the traditional pure defined benefit and some defined contribution plans from a policyholder’s point of view. Our analysis with reasonable parameter choices shows that target pension plans can be outperformed by defined contribution plans with variable annuities, while the latter are accompanied by a considerably higher ruin probability.

Current Developments in German Pension Schemes: What Are the Benefits of the New Target Pension?

We analyze the newly introduced German occupational pension scheme called target pension (Zielrente), which links the beneficiaries' benefits during the retirement phase to the mortality experienced among the pension beneficiaries and the performance of the financial market, from a pension beneficiary's perspective. We model the contract payoffs related to the target pension according to the new enhancement law on German occupational law. Specifically, we include two parameters in the plan design, one to control the surplus participation and one to control the loss participation. These parameters are chosen in such a way that the initial wealth of the retiree equals the initial value of the target pension. With the help of expected lifetime utility and wealth equivalent, we find that the target pension provides a meaningful supplement to the first and third pillar. Further, we find some comparative advantages of the target pension over the traditional pure defined benefit and some defined contribution plans from a policyholder's point of view. Our analysis shows that target pension plans can be outperformed by defined contribution plans with variable annuities, while the latter are accompanied by a considerably higher ruin probability.

An analysis of transaction costs in participating life insurance under mean–variance preferences

Transaction costs with respect to distribution and administration play a crucial role for the performance of participating life insurance products. The aim of this paper is to investigate the impact of such initial and annual transaction costs on policyholder mean–variance preferences depending on the contract features, comparing a point-to-point guarantee, a cliquet-style guarantee, and a money-back guarantee with annual surplus component. We extend previous work by deriving analytical solutions for the maximum allowed initial transaction costs as well as the risk aversion parameter that ensure a given customer preference level for different contract types. We further conduct simulation analyses to identify key factors in regard to transaction costs. One main finding is that in the present setting, insurers can indeed charge higher costs for more complex products with cliquet-style features, and that the difference in costs between the various product types increases considerably in a low interest-rate environment. However, these results are heavily impacted and even reversed depending on the risk–return asset characteristics, as insurers with a riskier asset management strategy may no longer be able to charge higher transaction costs for complex products with a strong annual cliquet-style surplus participation component without reducing their attractiveness to customers.

Unisex pricing of German participating life annuities—Boon or bane for customer and insurance company?

This paper explores how the requirement of gender-neutral premium calculation and the new rules of surplus participation for participating life annuities (PLA) affect insurance company’s profitability and policyholder’s wellbeing. We analyse real data observed for annuity prices in the German market followed by the examination of the impact of unisex calculation, allowing for different assumed and realised gender compositions. To this end, we develop a realistically calibrated asset and liability model for a PLA with stochastic mortality, interest rates, and equity returns. We show that for males, the disadvantages of PLA’s unisex pricing as compared to the gender-specific calculation are substantially lower, if we measure them by considering a lifetime utility that accounts for both distributed surpluses and stochastic mortality. For the insurance company, the gender mix composition turns out to be less important than the capital market influence. Moreover, participating life annuities turn out to be an efficient means to share actual mortality experience between insurance company and the annuitant, and can be, at least to a certain extent, considered a substitute for indemnity longevity hedge.

Allowance for surplus funds under Solvency II: adequate reflection of risk sharing between policyholders and shareholders in a risk-based solvency framework?

In several member states of the European Union, collective bonus reserves are set up as part of the statutory reserves backing traditional participating life insurance business. Although primarily reserved for policyholders’ future surplus participation, national law (for example in Germany and Austria) allows the insurance companies to use these funds to (partly) cover future losses. Under the risk-based solvency framework Solvency II, the loss absorbency of these buffer reserves is explicitly recognized by so-called surplus funds which are classified as Basic Own Funds. This paper performs a profound analysis of the approach currently used in Germany to reflect this type of risk sharing between policyholders and shareholders in the Solvency II framework. The comprehensive methodology developed in this paper can be used to determine the economic value of surplus funds and ensures that no double-counting of future cash flows occurs. It can easily be adapted to other countries, in particular Austria. Based on a stochastic balance sheet and cash flow projection model, we present numerical results that illustrate how the allowance for Surplus Funds affects Basic Own Funds, Solvency Capital Requirement, Risk Margin and Deferred Taxes under Solvency II. We conclude that the current valuation approach appears to be internally consistent, but some of the underlying assumptions are questionable. In particular, the valuation approach should be refined in order to better reflect local statutory requirements, including both, accounting rules and other regulatory constraints for participating business.

Participating life insurance contracts under Solvency II: inheritance effects and allowance for a Going Concern Reserve

Some details of the Solvency II framework are still under discussion. A crucial aspect in the debate is the appropriate reflection of surplus participation mechanisms that apply to traditional participating life insurance contracts. In particular, the inheritance of profits between existing business and new business resulting from the surplus participation process has to be incorporated in the Solvency II valuation framework which requires a run off valuation of the existing portfolio under going concern assumptions. This paper analyzes the inheritance effects caused by the pre-financing of acquisition cost of new business via cost surplus of existing business which is inherent in traditional German life insurance. We show that in the context of Solvency II an allowance for the inherited funds—denoted as Going Concern Reserve (GCR)—is justified and in line with the Solvency II valuation principles. Based on a stochastic balance sheet and cash flow projection model, we present a methodology to quantify the GCR and provide a profound analysis of the GCR and its components. Our results show that the GCR has significant impact on the overall solvency situation of life insurance companies offering participating contracts.

Analyzing the effect of low interest rates on the surplus participation of life insurance policies with different annual interest rate guarantees

We analyze the effects of a prevailing low interest rates regime on investment decisions of insurance companies and on the risk/return profile of participating life insurance policies with different contractually guaranteed minimum annual return. Our analysis is based on German legislation and a stylized insurance company with two cohorts of insured persons having different minimal return guarantees. Our findings shed some light on the non-trivial interrelation between profit distribution, minimum guarantees, and resulting profitability for the different cohorts. Moreover, we investigate the complex role of the risk reserve that allows insurance companies to redistribute profits in time and, less obviously, also between the cohorts.

Creating Customer Value in Participating Life Insurance

AbstractThe value of a life insurance contract may differ depending on whether it is looked at from the customer's point of view or that of the insurance company. We assume that the insurer is able to replicate the life insurance contract's cash flows via assets traded on the capital market and can hence apply risk‐neutral valuation techniques. The policyholder, on the other hand, will take risk preferences and diversification opportunities into account when placing a value on that same contract. Customer value is represented by policyholder willingness to pay and depends on the contract parameters, that is, the guaranteed interest rate and the annual and terminal surplus participation rate. The aim of this article is to analyze and compare these two perspectives. In particular, we identify contract parameter combinations that—while keeping the contract value fixed for the insurer—maximize customer value. In addition, we derive explicit expressions for a selection of specific cases. Our results suggest that a customer segmentation in this sense, that is, based on the different ways customers evaluate life insurance contracts and embedded investment guarantees while ensuring fair values, is worthwhile for insurance companies as doing so can result in substantial increases in policyholder willingness to pay.

Equity-linked pension schemes with guarantees

This paper analyses the relationship between the level of a return guarantee in an equity-linked pension scheme and the proportion of an investor’s contribution needed to finance this guarantee. Three types of schemes are considered: investment guarantee, contribution guarantee and surplus participation. The evaluation of each scheme involves pricing an Asian option, for which relatively tight upper and lower bounds can be calculated in a numerically efficient manner. We find a negative (and for two contract specifications also concave) relationship between the participation in the surplus return of the investment strategy and the guarantee level in terms of a minimum rate of return. Furthermore, the introduction of the possibility of early termination of the contract (e.g. due to the death of the investor) has no qualitative and very little quantitative impact on this relationship.

A joint valuation of premium payment and surrender options in participating life insurance contracts

In addition to an interest rate guarantee and annual surplus participation, life insurance contracts typically embed the right to stop premium payments during the term of the contract (paid-up option), to resume payments later (resumption option), or to terminate the contract early (surrender option). Terminal guarantees are on benefits payable upon death, survival and surrender. The latter are adapted after exercising the options. A model framework including these features and an algorithm to jointly value the premium payment and surrender options is presented. In a first step, the standard principles of risk-neutral evaluation are applied and the policyholder is assumed to use an economically rational exercise strategy. In a second step, option value sensitivity on different contract parameters, benefit adaptation mechanisms, and exercise behavior is analyzed numerically. The two latter are the main drivers for the option value.

Does Surplus Participation Reflect Market Discipline? An Analysis of the German Life Insurance Market

The aim of this paper is to analyze whether the level of surplus participation affects customer demand. We use multivariate linear regression models and data on surplus participation, new business, and lapse for the German life insurance market from 1998 to 2008. We find a significant positive dependence between surplus participation and new business growth as well as a significant negative dependence between surplus participation and growth of lapse volume. Overall, these findings indicate that customers do react to changes in product characteristics, which might be seen as indicative of market discipline. Our results are important for insurance company managers, regulators, and boards of insurance associations.

Risk analysis and valuation of life insurance contracts: Combining actuarial and financial approaches

In this paper, we analyze traditional (i.e. not unit-linked) participating life insurance contracts with a guaranteed interest rate and surplus participation. We consider three different surplus distribution models and an asset allocation that consists of money market, bonds with different maturities, and stocks. In this setting, we combine actuarial and financial approaches by selecting a risk minimizing asset allocation (under the real world measure P ) and distributing terminal surplus such that the contract value (under the pricing measure Q ) is fair. We prove that this strategy is always possible unless the insurance contracts introduce arbitrage opportunities in the market. We then analyze differences between the different surplus distribution models and investigate the impact of the selected risk measure on the risk minimizing portfolio.

Assessing the Risk Potential of Premium Payment Options in Participating Life Insurance Contracts

AbstractMost life insurance contracts embed the right to stop premium payments during the term of the contract (paid‐up option). Thereby, the contract is not terminated but continues with reduced benefits and often provides the right to resume premium payments later, thus increasing the previously reduced benefits (resumption option). In our analysis, we start with a basic contract with two standard options, namely, an interest rate guarantee and annual surplus participation. Next, in addition to the features of the basic contract, a paid‐up and resumption option is included in the framework. The valuation process is not based on assumptions about a particular policyholders' exercise strategy but instead assesses the risk potential from the insurer's viewpoint by providing an upper bound for any possible exercise behavior. This approach provides important information to the insurer about the potential hazard of offering the paid‐up and resumption option. Further, the approach allows an analysis of the impact of guaranteed interest rate, annual surplus participation, and investment volatility on the values of the premium payment options.

Implicit Options in Life Insurance: Valuation and Risk Management

Participating life insurance contracts typically contain various types of implicit options. These implicit options can be very valuable and can thus represent a significant risk to insurance companies if they practice insufficient risk management. Options become especially risky through interaction with other options included in the contracts, which makes their evaluation even more complex. This article provides a comprehensive overview and classification of implicit options in participating life insurance contracts and discusses the relevant literature. It points out the potential problems particularly associated with the valuation of rights to early exercise due to policyholder exercise behavior. The risk potential of the interaction of implicit options is illustrated with numerical examples by means of a life insurance contract that includes common implicit options, i.e., a guaranteed interest rate, stochastic annual surplus participation, and paid-up and resumption options. Valuation is conducted using risk-neutral valuation, a concept that implicitly assumes the implementation of risk management measures such as hedging strategies.