Produktgarantien und Aktienkrise — Implikationen für die Kapitalanlagepolitik von Lebensversicherungsunternehmen

The present contribution analyzes the implications of two central factors influencing the asset allocation decision of (German) life insurance companies, the development of the equity market on one hand and the interest rate guarantees included in traditional life insurance products on the other. The adverse development of share prices in 2000–2002 implies the necessity to consider not only ?normal“ volatility but also worst case-developments for the purpose of risk control. Formally this is done by using the risk measures value-at-risk and conditional value-at-risk. The specific ?myopic“ nature of interest rate guarantees in German life insurance products, which are granted on a yearly basis implies — beyond the general control of the shortfall risk with respect to the guaranteed interest rates — the necessity to per-form the asset allocation on a yearly basis to be in conformity with the time horizon of the liabilities.On the basis of a quantitative approach corresponding model calculations are performed. Thereby not only a pure market valuation is considered but also institutional peculiarities (hidden reserves, accounting norms) of German life insurance companies. The possibility of a riskless one-year investment, either based on market values or on balance sheet values, is revealed to be crucial for giving interest rate guarantees on a yearly basis.     

Creating Customer Value in Participating Life Insurance

The 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.     

Risk assessment of surplus appropriation schemes in participating life insurance

The aim of this paper is to analyze a life insurance company’s risk exposure with respect to different surplus appropriation schemes in participating life insurance. In this regard, three surplus appropriation schemes are considered, including the bonus system, the interest-bearing accumulation, and the system of shortening the contract term. We further examine an insurance company that offers all three schemes, i.e. each system is used for one third of the policyholders. Focus is laid on the effect of different asset portfolios and shocks to mortality on the insurer’s risk situation with respect to the policyholder’s age level at contract inception.     

An Investment Management Methodology for Publicly Held Property/Casualty Insurers

Investment officers of publicly held property/casualty companies wrestle with the question of how best to contribute to shareholder value. Should they view themselves as managers of a closed‐end investment company that happens to be funded by insurance underwriting? Or should they instead be investing funds primarily to defease the firm's liabilities and thus support the operations of a company whose principal value derives from its insurance activities? The authors of this article suggest that the investment policy of most insurance companies should have two primary objectives: (1) immunizing insurance reserves with a fixed‐income portfolio and (2) earning “abnormal returns” on surplus in “a responsible and disciplined” way. The latter means adhering to an asset allocation approach that takes account of the risk‐reward tradeoffs presented by a broad variety of investment types as well as the accounting treatment of investment income. Both accounting and economic considerations lead the authors to suggest that after‐tax net investment income (“NII”), as defined by U.S. GAAP, is the best benchmark of performance. While focusing mainly on the fixed income part of the portfolio, the authors suggest active management and portfolio approaches that aim to produce a growing, but relatively stable NII. Consistent with GAAP's treatment of NII (which includes interest income but excludes most capital gains) as “recurring income,” the authors argue that the market appears to assign significantly higher multiples to NII than to other sources of reported income.     

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.     

On the Interaction between Transfer Restrictions and Crediting Strategies in Guaranteed Funds

Guaranteed funds with crediting rates for fixed periods determined by a pension provider or insurance company are common features of accumulation annuity contracts. Policyholders can transfer money back and forth between these accounts and money market accounts that give them features similar to demand deposits, and yet they frequently credit a higher rate than the money market. Transfer restrictions are commonly employed to prevent arbitrage. In this article, we model the interaction between company and policyholder as a multiperiod game in which the company maximizes risk-neutral expected present value of profits and the policyholder maximizes his expected discounted utility. We find that the optimal strategy on the part of the company is to credit a rate higher than the money market rate in the first period to entice the policyholder to invest in the guaranteed fund. The company then credits the floor in the remaining periods as the policyholder transfers out the maximum amount. This does better for the policyholder in low interest rate environments and worse in high interest rate environments and acts as a type of “interest rate insurance” for the policyholder.     

An Empirical Study of Insurance Performance Measure

This author applies Insurance Performance Measure (IPM) to a set of Indian insurance companies over the period 2005–2016. This is the first article published that applies the IPM model on real industry data and studies its implications. The IPM was introduced in a Winter 2002 JACF article by Joseph Calandro, Jr., then at General Star management, a subsidiary of Berkshire Hathaway and by Scott Lane, then an accounting professor at the University of New Haven. Those authors explained why financial reporting for insurance companies was so challenging and presented the IPM metric as a better way to assess industry and company performance. Evaluating P&C companies is difficult because the unique format of insurance company financials does not lend itself to traditional financial accounting analysis and because the industry's preeminent performance measure, the Underwriting Ratio, captures underwriting and claims activity but says nothing about investment and risk distribution (reinsurance). By contrast, the IPM represents the interrelation of underwriting, investment and reinsurance along with a hurdle rate and is quite consistent with Warren Buffett's expressed desire for a balanced overview of industry performance. IPM uses financial data without modification thereby simplifying and fastening computation. Operationally, it could help in negotiations for reinsurance renewals and identify “Maximum Profitable capacity”—the threshold limit for overall profitability.     

A new basis of calculation for collective pensions insurance in Norway

The writing of collective pensions insurance in Norway was first taken up in 1917 by the “Norske Folk”, a life insurance company, founded by the seven oldest Norwegian life insurance companies, and a short time afterwards this kind of insurance was also taken up by the “Norske Forenede”. Finally, in 1931, the “Samvirke” which had been established a short time before by the Norwegian Cooperative Association, began to write collective pensions insurance.     

Life insurance in a contingent claim framework: Pricing and regulatory implications

In this paper we develop a contingent claim model to evaluate the equity and liabilities of a life insurance company. The limited liability of shareholders is explicitly modelled. We focus on a specific type of life insurance policy—namely, the profit-sharing policy. In this policy, the policyholder is entitled to a guaranteed interest rate and a percentage of the company's yearly financial revenues. The implicit equilibrium interest rate and profit-sharing ratio are derived and analyzed. We finally discuss regulatory measures frequently encountered in the life insurance business such as rate ceilings, capital ratios, and asset restrictions.     

Life Insurance Liabilities at Market Value: An Analysis of Insolvency Risk, Bonus Policy, and Regulatory Intervention Rules in a Barrier Option Framework

This article takes a contingent claim approach to the market valuation of equity and liabilities in life insurance companies. A model is presented that explicitly takes into account the following: (i) the holders of life insurance contracts (LICs) have the first claim on the company's assets, whereas equity holders have limited liability; (ii) interest rate guarantees are common elements of LICs; and (iii) LICs according to the so‐called contribution principle are entitled to receive a fair share of any investment surplus. Furthermore, a regulatory mechanism in the form of an intervention rule is built into the model. This mechanism is shown to significantly reduce the insolvency risk of the issued contracts, and it implies that the various claims on the company's assets become more exotic and obtain barrier option properties. Closed valuation formulas are nevertheless derived. Finally, some representative numerical examples illustrate how the model can be used to establish the set of initially fair contracts and to determine the market values of contracts after their inception.     

Explaining variation in risk across insurance companies

The purpose of this study is to determine what firm-specific factors affect the risk of insurance companies. Traditional methods used to identify potential failures have been severely criticized. Thus, alternative approaches to risk assessment should be of interest to investors and managers of these companies. Models for measuring the impact of factors on risk are developed and empirically tested. The models employed explain a high proportion of variation in risk levels across companies. The sensitivity of insurance company risk to financial characteristics vary with the variable used as a proxy for risk and the type of insurance company assessed. Given the strong relationships between firm-specific characteristics and company risk, it appears that the risk of insurance companies can be effectively controlled with proper management.     

Cash-Flow Valuation and Value at Risk

The cash-flow valuation method (CFVM) has been developed in Canada for the valuation of insurance company annuity products. Its range of application is expected to be extended shortly to the valuation of most other life insurance company products. The CFVM is based on the use of “best-guess” assumptions, supplemented by specific provisions for adverse deviations. In this paper, special attention is paid to the calculation of the provision for adverse deviations with respect to the interest rate risk. We show that the determination of this provision is the analog for life insurance and annuity policy liabilities of the calculation by banks of Value at Risk (VaR) with respect to portfolios of securities held for trading.     

二叉树利率期限结构模型应用初探——以寿险公司资产负债管理为例

近年来我国寿险公司经营风险加剧，寿险公司资产负债管理正逐渐成为实务界和学术界关注的焦点。本文在深入研究随机规划、利率期限结构、投资组合等相关理论的基础上，对比分析均衡模型和无套利模型的差异，指出无套利模型更适于构楚随机规划问题中利率情景树的构建。在无套利模型中，二叉树Black-Derman-Toy模型简单易操作，可以避免三叉树模型计算量大，效率不高等缺点。因此本文采用二叉树方法以Black-Derman-Toy模型构造利率情景树，与随机规划模型相结合的资产负偾管理方法，协调、管理寿险公司资产负偾现金流，减少了随机规划模型处理随机利率分布的技术性难度。     

Mitigating Interest Rate Risk in Variable Annuities: An Analysis of Hedging Effectiveness under Model Risk

Variable annuities are investment vehicles offered by insurance companies that combine a life insurance policy with long-term financial guarantees. These guarantees expose the insurer to market risks, such as volatility and interest rate risks, which can be managed only with a hedging strategy. The objective of this article is to study the effectiveness of dynamic delta-rho hedging strategies for mitigating interest rate risk in variable annuities with either a guaranteed minimum death benefit or guaranteed minimum withdrawal benefit rider. Our analysis centers on three important practical issues: (1) the robustness of delta-rho hedging strategies to model uncertainty, (2) the impact of guarantee features (maturity versus withdrawal benefits) on the performance of the hedging strategy, and (3) the importance of hedging interest rate risk in either a low and stable or rising interest rate environment. Overall, we find that the impact of interest rate risk is equally felt for the two types of products considered, and that interest rate hedges do lead to a significant risk reduction for the insurer, even when the ongoing low interest rate environment is factored in.     

The Financial Modeling of Property-Casualty Insurance Companies

This paper describes a financial model currently being used by a major U.S. multiline property-casualty insurer. The model, which was first developed for solvency monitoring purposes, is now being employed for a variety of internal management purposes as well, including (1) the allocation of equity to corporate units, thereby allowing measurements of profitability by business segment and policy year, as well as analysis of the progression of “free surplus,” (2) the analysis of major risks–such as inflation risks, interest rate risks, and reserving risks–that have heretofore been difficult to quantify, and (3) consideration of varying scenarios on the company’s financial performance, both of macroeconomic conditions as well as of the insurance environment.

Many aspects of financial modeling do not differ significantly between life and property-casualty insurers, and these are not discussed in the paper. Rather, the paper focuses on the following topics:

1. Surplus allocation and profitability: how economic surplus and the returns on this surplus are determined by line of business, separately for new business and for the runoff of existing business, and how the progression of free surplus is viewed.

2. Multifaceted risks: how to model risks that affect multiple components of the insurer’s operations, such as economic risks and financial risks. The multiple effects of macroeconomic conditions and changing inflation rates on workers’ compensation claim frequencies and severities complicate the basic interest rate path modeling of life insurance products and annuity contracts.

3. Scenario building: how to construct scenarios of macroeconomic conditions or industry cyclical movements to test the resilience of the company to changing external conditions.     

Fair Valuation of Participating Life Insurance Contracts with Jump Risk

The purpose of this article is to value participating life insurance contracts when the linked portfolio is modeled by a jump-diffusion. More precisely, this process has a Brownian component and a compound Poisson one, where the jump size is driven by a double exponential distribution. Specifically here, the bankruptcy risk of the insurance company is considered. Thus, market and credit risks are taken into account. A quasi-closed-form formula is obtained in fair value for the price of the considered life insurance contract. This allows us to investigate the impact of strategic parameters as well as structural ones, as is shown in the numerical section of this paper. In particular, we study the impact on the contract of the volatility, jump intensity, jump asymmetry, company leverage, guaranteed rate, participation rate and level of the default barrier, and comment on how they are likely to increase the probability of early default of the issuer.     

Financial Intermediary Versus Production Approach to Efficiency of Marketing Distribution Systems and Organizational Structure of Insurance Companies

An examination of the efficiency of the marketing distribution channel and organizational structure for insurance companies is presented from a framework that views the insurer as a financial intermediary rather than as a “production entity” which produces “value added” through loss payments. Within this financial intermediary approach, solvency can be a primary concern for regulators of insurance companies, claims‐paying ability can be a primary concern for policyholders, and return on investment can be a primary concern for investors. These three variables (solvency, financial return, and claims‐paying ability) are considered as outputs of the insurance firm. The financial intermediary approach acknowledges that interests potentially conflict, and the strategic decision makers for the firm must balance one concern versus another when managing the insurance company. Accordingly, we investigate the efficiency of insurance companies using data envelopment analysis (DEA) having as insurer output an appropriately selected (for the firm under investigation) combination of solvency, claims‐paying ability, and return on investment as outputs. These efficiency evaluations are further examined to study stock versus mutual form of organizational structure and agency versus direct marketing arrangements, which are examined separately and in combination. Comparisons with the “value‐added” or “production” approach to insurer efficiency are presented. A new DEA approach and interpretation is also presented.     

The Poisson Log-Bilinear Lee-Carter Model

Abstract

Life insurance companies deal with two fundamental types of risks when issuing annuity contracts: financial risk and demographic risk. Recent work on the latter has focused on modeling the trend in mortality as a stochastic process. A popular method for modeling death rates is the Lee-Carter model. This methodology has become widely used, and various extensions and modifications have been proposed to obtain a broader interpretation and to capture the main features of the dynamics of mortality rates. In order to improve the measurement of uncertainty in survival probability estimates, in particular for older ages, the paper proposes an extension based on simulation procedures and on the bootstrap methodology. It aims to obtain more reliable and accurate mortality projections, based on the idea of obtaining an acceptable accuracy of the estimate by means of variance reducing techniques. In this way the forecasting procedure becomes more efficient. The longevity question constitutes a critical element in the solvency appraisal of pension annuities. The demographic models used for the cash flow distributions in a portfolio impact on the mathematical reserve and surplus calculations and affect the risk management choices for a pension plan. The paper extends the investigation of the impact of survival uncertainty for life annuity portfolios and for a guaranteed annuity option in the case where interest rates are stochastic. In a framework in which insurance companies need to use internal models for risk management purposes and for determining their solvency capital requirement, the authors consider the surplus value, calculated as the ratio between the market value of the projected assets to that of the liabilities, as a meaningful measure of the company’s financial position, expressing the degree to which the liabilities are covered by the assets.     

Betriebsunterbrechungsversicherung bei kleinen und mittleren Unternehmen

The business interruption caused by a property claim is an existential risk both for large industrial companies and for small to medium enterprises (SME). It is especially relevant for companies working on a more complex sales and production infrastructure. Statistics show that in case of a large property claim the cost of the accompanying business interruption claim frequently exceeds the property claim. In Germany, however, the share of companies opting for business interruption insurance is much smaller than those opting for property insurance. This is especially true for SME that can hardly cover the risk themselves. The goal of this paper is to analyze the insurance decision for a business interruption policy with a special focus on SME. As a database we use the results of a representative survey among 1802 German SME with up to 100 employees. Our results show that the decision for a business interruption policy is not only dependent on hard factors such as company size and industry, but also driven by the so-called “insurance mentality”, which includes risk aversion, insurance know-how and price-sensitivity.     

Joint Insolvency Analysis of a Shared MAP Risk Process: A Capital Allocation Application

In recent years, multivariate insurance risk processes have received increasing attention in risk theory. First-passage-time problems in the context of these insurance risk processes are of primary interest for risk management purposes. In this article we study joint-ruin problems of two risk undertakers in a proportionally shared Markovian claim arrival process. Building on the existing work in the literature, joint-ruin–related quantities are thoroughly analyzed by capitalizing on existing results in certain univariate insurance surplus processes. Finally, an application is considered where the finite-time and infinite-time joint-ruin probabilities are used as risk measures to allocate risk capital among different business lines. The proposed joint-ruin allocation principle enables us to not only capture the risk dynamics over a given time horizon, but also overcome the “cross-subsidizing” effect of many existing allocation principles.