Participating Life Insurance Contracts Research Articles

Return smoothing in life insurance from a client perspective

Participating (or with-profit) life insurance contracts play an important role in private old-age provision in many countries. Life insurers pool the assets and liabilities of a heterogeneous portfolio of such contracts and typically perform some return smoothing in the collective investment. Participating contracts were historically equipped with a cliquet-style (year-to-year) guarantee. The current low interest rate environment and regulatory requirements have forced life insurers to develop new product designs with lower and/or different types of guarantees. However, observed demand as well as the findings of several studies show that (year-to-year) guarantees are (subjectively) highly attractive for long-term investors. In this paper, we show that return smoothing alone (that is, without guarantees) can significantly increase the attractiveness for such investors. Most importantly, we show that many (loss averse) long-term investors will even prefer products without guarantee but with smoothed returns over other products with guarantee features. The results hold for long-term investors who not only consider the terminal value but at least partially also evaluate potential annual changes in the account value (even if such changes only have a rather low impact on the decision). Additionally, we show that the descriptive model used in this paper is able to explain the popularity of traditional participating life insurance products in Germany providing further evidence that long-term investors consider potential annual value chances already when making the investment decision.

Nonconcave Optimal Investment with Value-at-Risk Constraint: An Application to Life Insurance Contracts

This paper studies a value-at-risk (VaR)-regulated optimal portfolio problem of the equity holders of a participating life insurance contract. In a setting with unhedgeable mortality risk and compl...

How to derive optimal guarantee levels in participating life insurance contracts

PurposeThe purpose of this paper is to show how an insurance company can maximize the policyholder’s utility by setting the level of the interest rate guarantee in line with his preferences.Design/methodology/approachThe authors develop a general model of life insurance, taking stochastic interest rates, early default and regular premium payments into account. Furthermore, the authors assume that equity holders must receive risk-adequate returns on their initial equity contribution and that the insurance company has to maintain a solvency restriction.FindingsThe findings show that the optimal level for the interest rate guarantee is in general far below the maximum value typically set by the supervisory authorities and insurance companies.Originality/valueThe authors conclude that the approach of deviating from the maximum interest rate guarantee level given by the regulatory requirements can create additional value for the rational policyholder. In contrast to Schmeiser and Wagner (2014), the second finding shows that the interest rate guarantee embedded in a life insurance product becomes less attractive compared to a pure investment in the underlying asset portfolio to the policyholder when the guarantee level is lowered too far or the contract duration is short. They also refute Schmeiser and Wagner (2014) by showing that the equity capital required by the insurance company increases with the level of the guarantee, even if the insurer is flexible with respect to its asset allocation. The last finding is that a policyholder with higher risk aversion does not generally prefer a higher guarantee level.

Valuation of Guaranteed Unitized Participating Life Insurance under MEGB2 Distribution

Crisis events have significantly changed the view that extreme events in financial markets have negligible probability. Especially in the life insurance market, the price of guaranteed participating life insurance contract will be affected by a change in asset volatility which leads to the fluctuations in embedded option value. Considering the correlation of different asset prices, MEGB2 (multivariate exponential generalized beta of the second kind) distribution is proposed to price guaranteed participating life insurance contract which can effectively describe the dependence structure of assets under some extreme risks. Assuming the returns of two different assets follow the MEGB2 distribution, a multifactor fair valuation pricing model of insurance contract is split into four components: the basic contract, the annual dividend option, the terminal dividend option, and the surrender option. This paper studies the effect of death rate, minimum guaranteed yield rate, annual dividend ratio, terminal dividend ratio, and surrender on the embedded option values and calculates the single premium of the insurance contract under different influence factors. The Least-Squares Monte Carlo simulation method is used to simulate the pricing model. This article makes a comparison in the sensitivity of the pricing parameters under the MEGB2 distribution and Multivariate Normal distribution asset returns. Finally, an optimal hedging strategy is designed to cover the possible risks of the underlying assets, which can effectively hedge the risks of portfolio.

Dynamic hybrid products with guarantees—An optimal portfolio framework

Dynamic hybrid products are pension products that consist of a dynamic combination of classical with profits participating life insurance contracts (or a bank account) and fund savings plans. To put such products in an optimal utility framework, we derive an optimal combination of a money market account, a CPPI-style fund and a free fund in continuous trading via transforming the original investment problem into a conventional portfolio problem in the presence of a guarantee condition. By this, we obtain (semi-) explicit forms of the dynamic weights for the different ingredients of a dynamic hybrid product.

Policy characteristics and stakeholder returns in participating life insurance: which contracts can lead to a win-win?

Participating life insurance contracts and pension plans often include a return guarantee and participation in the surplus of the institution’s result. The final account value in such contracts depends on the investment policy driven by solvency requirements, as well as on the level of market returns, the guarantee and the participation rates. Using a contingent claim model for such contracts, we assume a competitive market with minimum solvency requirements similar to Solvency II. We consider solvency requirements on maturity and 1-year time horizons, as well as contracts with single and periodic premium payments. Through numerical analyses, we link the expected returns for equity holders and policyholders in various situations. Using the return on equity and policyholder internal rate of return along with utility measures, we assess which contract settings optimize the return compromise for both stakeholders in a low-interest-rate environment. Our results extend the academic literature by building on the work by Schmeiser and Wagner (J Risk Insur 82(3):659–686, 2015) and are relevant for practitioners, given the current financial market environment and difficulties in insurance-linked savings plans with guarantees.

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.

Valuation and risk assessment of participating life insurance in the presence of credit risk

In participating life insurance, management decisions regarding the asset composition can substantially impact the value of a policy from the policyholders’ perspective as well as the insurer’s risk situation. Due to the long-term guarantees often embedded in these contracts, life insurers typically invest a considerable portion of their capital in long-term assets such as corporate and government bonds. Besides interest rate risk, the value of these bond investments is thus particularly influenced by credit risk. Thus, the aim of this paper is to examine the impact of market risk associated with the asset composition on fair valuation and risk assessment with focus on credit risk and its interaction with equity risk and interest rate risk. Our analysis emphasizes that the consideration of credit risk associated with bonds has a strong impact on the fair valuation and risk measurement in the context of participating life insurance contracts, even in case of higher grade bond exposures.

Fair Valuation of Cliquet-Style Return Guarantees in a Heterogeneous Life Insurance Portfolio

In Europe, participating life insurance contracts are often equipped with a return guarantee. The current low interest rate environment has again refreshed the discussion on risk management and fair valuation of such embedded options. Typcially, this problem is discussed from the viewpoint of a single contract or a homogeneous insurance portfolio. In practice, however, insurance portfolios are heterogeneous. Rapidly changing conditions on interest rate markets have, for example, led to big differences in guarantee levels within an insurance portfolio. Contracts in an insurance portfolios can - unlike the case of asset portfolios - not be priced independently: Their premiums are invested in the same reference portfolio; the contracts interact by joint reserves and joint default risk of the policy sponsor. In this exposition, we discuss the fair valuation of individual insurance contracts with an annual (cliquet-style) return guarantee in a heterogeneous life insurance portfolio.

Gompertz–Makeham parameter estimations and valuation approaches: Turkish life insurance sector

For participating life insurance, the objective of insurance companies is to control the investments of policyholders by considering changing market conditions within the scope of risk management and increase their returns. Given that insurance companies compete in the market with participating life insurance, insurers and academicians attempt to develop this product. This paper compares net premium valuation and paid-up valuation methods used in the valuation of participating life insurance contracts in Turkey. The development of a single endowment policy with a level premium payment has been modeled as a time-continuous Markov chain model. Mortality in Turkey has been determined by calculating the parameter values of the Gompertz–Makeham function. It has been observed that insurance companies would not face valuation losses using the paid-up valuation method, even though policyholders stopped premium payments before the policy term. Moreover, compared with other valuation methods, the paid-up valuation method has been found to offer freedom of investment.

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.

Dynamic hybrid products in life insurance: Assessing the policyholders’ viewpoint

Dynamic hybrid life insurance products are intended to meet new consumer needs regarding stability in terms of guarantees as well as sufficient upside potential. In contrast to traditional participating or classical unit-linked life insurance products, the guarantee offered to the policyholders is achieved by a periodical rebalancing process between three funds: the policy reserves (i.e. the premium reserve stock, thus causing interaction effects with traditional participating life insurance contracts), a guarantee fund, and an equity fund. In this paper, we consider an insurer offering both, dynamic hybrid and traditional participating life insurance contracts and focus on the policyholders’ perspective. The results show that higher guarantees do not necessarily imply a higher willingness-to-pay, but that in case of dynamic hybrid contracts, a minimum guarantee level should be offered in order to ensure that the willingness-to-pay exceeds the minimum premium the insurer has to charge when selling the contract. In addition, strong interaction effects can be found between the two products, which particularly impact the willingness-to-pay of the dynamic hybrids.

Dynamic Hybrid Products in Life Insurance: Assessing the Policyholderss Viewpoint

Dynamic hybrid life insurance products are intended to meet new consumer needs regarding stability in terms of guarantees as well as sufficient upside potential. In contrast to traditional participating or classical unit-linked life insurance products, the guarantee offered to the policyholders is achieved by a periodical rebalancing process between three funds: the policy reserves (i.e. the premium reserve stock, thus causing interaction effects with traditional participating life insurance contracts), a guarantee fund, and an equity fund. In this paper, we consider an insurer offering both, dynamic hybrid and traditional participating life insurance contracts and focus on the policyholders’ perspective. The results show that higher guarantees do not necessarily imply a higher willingness-to-pay, but that in case of dynamic hybrid contracts, a minimum guarantee level should be offered in order to ensure that the willingness-to-pay exceeds the minimum premium the insurer has to charge when selling the contract. In addition, strong interaction effects can be found between the two products, which particularly impact the willingness-to-pay of the dynamic hybrids.

A Proposal on How the Regulator Should Set Minimum Interest Rate Guarantees in Participating Life Insurance Contracts

AbstractWe consider a contingent claim model framework for participating life insurance contracts and assume a competitive market with minimum solvency requirements as provided by Solvency II. In a first step, the implications of the regulator's imposing a particular interest rate guarantee on the insurer's asset allocation are analyzed in a reference situation. We study the sensitivity of the interaction between the interest rate guarantee and the asset allocation when the risk‐free interest rate changes. Particular attention is paid to the current market situation where the guaranteed interest rate is often close to the risk‐free interest rate. In a second step, we assess at what level the interest rate guarantee should be set by the regulator in order to maximize policyholders' utility. We show that the results yielded by the proposed concept to derive an optimal value for the interest rate guarantee are very stable for various model parameters.

Fair Valuation and Risk Assessment of Dynamic Hybrid Products in Life Insurance: A Portfolio Consideration

Dynamic hybrid products are innovative life insurance products particularly offered in the German market and intended to meet new consumer needs regarding stability and upside potential. These products are characterised by a periodical rebalancing process between the policy reserves (i.e. the premium reserve stock), a guarantee fund and an equity fund. The policy reserve thereby corresponds to the one also valid for traditional participating life insurance products. Hence, funds of dynamic hybrids that are allocated to the policy reserves in times of adverse capital market environments earn the same policy interest rate determined for the participating life insurance policyholders and, hence, at least a guaranteed interest rate. In this paper, we study the fair valuation and risk situation of an insurer offering both dynamic hybrid and traditional participating life insurance contracts. The results reveal considerable interaction effects between the two contract types within the portfolio that strongly depend on the portfolio composition, thereby emphasising merits as well as risks associated with offering dynamic hybrids.

Fair Valuation of Life Insurance Contracts Under a Two-Sided Jump Diffusion Model

In this article, we study the fair valuation of participating life insurance contract, which is one of the most common life insurance products, under the two-sided jump diffusion model with the consideration of default risk. The participating life insurance contracts considered here can be expressed as portfolios of options as shown by Grosen and Jøgrgensen (1997). We can give the Laplace transforms for these options under the two-sided jump diffusion model, and then price these options by inverting Laplace transforms.

A performance analysis of participating life insurance contracts

Participating life insurance contracts are one of the most important products in the European life insurance market. Even though these contract forms are very common, only very little research has been conducted in respect to their performance. Hence, we conduct a performance analysis to provide a decision support for policyholders. We decompose a participating life insurance contract in a term life insurance and a savings part and simulate the cash flow distribution of the latter. Simulation results are compared with cash flows resulting from two benchmarks investing in the same portfolio of assets but without investment guarantees and bonus distribution schemes, in order to measure the impact of these two product features. To provide a realistic picture within the two alternatives, we take transaction costs and wealth transfers between different groups of policyholders into account. We show that the payoff distribution strongly depends on the initial reserve situation and managerial discretion. Results indicate that policyholders will in general profit from a better payoff distribution of the participating life insurance compared to a mutual fund benchmark but not compared to an exchange-traded fund benchmark portfolio.

A performance analysis of participating life insurance contracts

Traditional life insurance products, in particular participating life insurance contracts, are often criticized. Their performance is often said to be poor compared to other investment alternatives. Interestingly, this perception appears to persist although very little research has been conducted into the performance of participating life insurance contracts. But are participating life insurance contracts actually bad for policyholders? We conduct a performance analysis based on contracts offered in the German market, in order to provide evidence to support decision making by policyholders.

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.

On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View

AbstractIn recent years, market-consistent valuation approaches have gained an increasing importance for insurance companies. This has triggered an increasing interest among practitioners and academics, and a number of specific studies on such valuation approaches have been published.In this paper, we present a generic model for the valuation of life insurance contracts and embedded options. Furthermore, we describe various numerical valuation approaches within our generic setup. We particularly focus on contracts containing early exercise features since these present (numerically) challenging valuation problems.Based on an example of participating life insurance contracts, we illustrate the different approaches and compare their efficiency in a simple and a generalized Black-Scholes setup, respectively. Moreover, we study the impact of the considered early exercise feature on our example contract and analyze the influence of model risk by additionally introducing an exponential Lévy model.