Analysis of Systemic Risk in the Insurance Industry

In this paper, we discuss the systemic relevance of the insurance sector. Systemic risk is defined as the propensity of a financial institution to be undercapitalised when the financial system as a whole is undercapitalised. By the law of large numbers, traditional lines of insurance with idiosyncratic non-catastrophic risks cannot be systemic. On the contrary, undiversified insurers specialised in activities whose insured risks are highly correlated with GDP are systemic. In the life insurance sector, some contractual clauses such as unhedged minimum guarantees and free options to surrender raise the chance of systemic relevance. On the contrary, life insurers satisfying the classic solvency capital requirements contribute to the liquidity of financial markets thanks to the long-termist approach of their portfolio management. Finally, using historical data in the U.S. on the contribution of different sectors to the aggregate volatility of the economy, we show that investment banking is almost twice as volatile as aggregate GDP, while insurance is one fifth as volatile as aggregate GDP. The insurance sector thus appears to be a stabilising force of the economy.     

Application of Relational Models in Mortality Immunization

The prediction of future mortality rates by any existing mortality models is hardly exact, which causes an exposure to mortality (longevity) risk for life insurers (annuity providers). Since a change in mortality rates has opposite impacts on the surpluses of life insurance and annuity, hedging strategies of mortality and longevity risks can be implemented by creating an insurance portfolio of both life insurance and annuity products. In this article, we apply relational models to capture the mortality movements by assuming that the realized mortality sequence is a proportional change and/or a constant shift of the expected one, and the size of the changes varies in the length of the sequences. Then we create a variety of non-size-free matching strategies to determine the weights of life insurance and annuity products in an insurance portfolio for mortality immunization, where the weights depend on the sizes of the proportional and/or constant changes. Comparing the hedging performances of four non-size-free matching strategies with corresponding size-free ones proposed by Lin and Tsai, we demonstrate with simulation illustrations that the non-size-free matching strategies can hedge against mortality and longevity risks more effectively than the size-free ones.     

A Review of Catastrophic Risks for Life Insurers

Catastrophic mortality events are characterized by a sudden and concentrated increase in mortality and as such present a major risk to life insurers. Such events include pandemics, war, natural disasters, terrorist attacks, and industrial, transport, and other accidents. Of these, pandemics arising from influenza are considered the most significant threat to the life insurance industry due to their capacity to cause a major increase in claims. We review the features and mortality implications of an influenza pandemic for life insurers, and describe a range of other risks that are likely to emerge as well.     

Uniqueness of the fair premium for equity-linked life insurance contracts

An equity-linked life insurance contract combines an endowment life insurance and an investment strategy with a minimum guarantee. The benefit of this contract is determined by the guaranteed amount plus a bonus equal to a call on the portfolio. This bonus is similar to an Asian option. This article analyzes the relationship between the periodic insurance premium and its proportional share invested into the portfolio. For a general model of the financial risks we show the existence and uniqueness of an insurance premium. Furthermore the premium is strictly increasing and convex as a function of the share invested.     

Exploring the market risk profiles of US and European stock insurers

Market risks account for an integral part of insurers' risk profiles. We explore market risk sensitivities of insurers in the United States and Europe. Based on panel regression models and daily market data from 2012 to 2018, we find that sensitivities are particularly driven by insurers' product portfolio. The influence of interest rate movements on stock returns is 60% larger for US than for European life insurers. For the former, interest rate risk is a dominant market risk with an effect that is five times larger than through corporate credit risk. For European life insurers, the sensitivity to interest rate changes is only 44% larger than toward credit default swap of government bonds, underlining the relevance of sovereign credit risk.     

基于产品组合视角我国寿险公司综合免疫策略研究

针对我国人寿保险公司的经营面临着日益加大的市场风险与死亡率风险．提出了一种同时规避死亡率风险与利率风险的综合免疫策略。假设寿险公司采取资产主导的资产负债管理模式，通过对寿险公司两类主要产品（死亡给付产品和生存给付产品）的组合比例调整，实现对死亡率风险和利率风险的双重免疫。为此首先建立寿险公司死亡率自然对冲模型，在此基础上将利率风险引入模型，进而构建起同时规避死亡率和利率风险的寿险公司综合免疫产品组合策略。     

Asset and liability management for insurance products with minimum guarantees: The UK case

Modern insurance products are becoming increasingly complex, offering various guarantees, surrender options and bonus provisions. A case in point are the with-profits insurance policies offered by UK insurers. While these policies have been offered in some form for centuries, in recent years their structure and management have become substantially more involved. The products are particularly complicated due to the wide discretion they afford insurers in determining the bonuses policyholders receive. In this paper, we study the problem of an insurance firm attempting to structure the portfolio underlying its with-profits fund. The resulting optimization problem, a non-linear program with stochastic variables, is presented in detail. Numerical results show how the model can be used to analyze the alternatives available to the insurer, such as different bonus policies and reserving methods.     

A Cautionary Note on Natural Hedging of Longevity Risk

In this article, we examine the so-called natural hedging approach for life insurers to internally manage their longevity risk exposure by adjusting their insurance portfolio. In particular, unlike the existing literature, we also consider a nonparametric mortality forecasting model that avoids the assumption that all mortality rates are driven by the same factor(s).

Our primary finding is that higher order variations in mortality rates may considerably affect the performance of natural hedging. More precisely, although results based on a parametric single factor model—in line with the existing literature—imply that almost all longevity risk can be hedged, results are far less encouraging for the nonparametric mortality model. Our finding is supported by robustness tests based on alternative mortality models.     

The Economics of Insurance Intermediaries

This article analyzes the economic functions of independent insurance intermediaries (brokers and independent agents), focusing on the commercial property–casualty insurance market. The article investigates the functions performed by intermediaries, the competitiveness of the market, the compensation arrangements for intermediaries, and the process by which policies are placed with insurers. Insurance intermediaries are essentially market makers who match the insurance needs of policyholders with insurers who have the capability of meeting those needs. Intermediary compensation comprises premium‐based commissions, expressed as a percentage of the premium paid, and contingent commissions based on the profitability, persistency, and/or volume of the business placed with the insurer. Empirical evidence is provided that premium‐based and contingent commissions are passed on to policyholders in the premium. However, contingent commissions can enhance competitive bidding by aligning the insurer's and the intermediary's interests. This alignment of interests gives insurers more confidence in the selection of risks and thus helps to break the “winner's curse” and encourages insurers to bid more aggressively. Independent intermediaries also help markets operate more efficiently by reducing the information asymmetries between insurers and buyers that can cause adverse selection.     

The Impact of Disability Insurance on a Portfolio of Life Insurances

The aim of this article is to study the impact of disability insurance on an insurer's risk situation for a portfolio that also consists of annuity and term life contracts. We provide a model framework using discrete time nonhomogeneous bivariate Markov renewal processes and in a simulation study focus on diversification benefits as well as potential natural hedging effects (risk-minimizing or risk-immunizing portfolio compositions) that may arise within the portfolio because of the different types of biometric risks. Our analyses emphasize that disability insurances are a less efficient tool to hedge shocks to mortality and that their high sensitivity toward shocks to disability risks cannot be easily counterbalanced by other life insurance products. However, the addition of disability insurance can still considerably lower the overall company risk.     

An Actuarial Premium Pricing Model for Nonnormal Insurance and Financial Risks in Incomplete Markets

Abstract

A model for pricing insurance and financial risks, based on recent developments in actuarial premium principles with elliptical distributions, is developed for application to incomplete markets and heavy-tailed distributions. The pricing model involves an application of a generalized variance premium principle from insurance pricing to the pricing of a portfolio of nontraded risks relative to a portfolio of traded risks. This pricing model for a portfolio of insurance or financial risks reflects preferences for features of the distributions other than mean and variance, including kurtosis. The model reduces to the Capital Asset Pricing Model for multinormal portfolios and to a form of the CAPM in the case where the traded and nontraded risks have the same elliptical distribution.     

A Model of an Oligopoly in an Insurance Market

This article analyzes the behavior of an oligopoly of risk-averse insurers that insure many consumers facing identical independent risks; however, the probability of a loss is ex ante not known with certainty. It is shown that there is a continuum of equilibria in the Bertrand game. The most plausible equilibrium can be obtained by requiring that all insurers are content with the number of policies they sell given the equilibrium premium.     

Optimal rate classification for enhanced annuities

For a given premium, enhanced annuities pay higher pensions to policyholders with impaired health. Even though risk classification is a common concept in the insurance sector and should allow insurers to increase their profitability, enhanced annuities are rarely offered outside of the United Kingdom. The paper provides a general method of determining an optimal risk classification system for enhanced annuities that will maximize an insurance company’s profits. The cost of risk classification, as well as that incurred when insureds are assigned to inappropriate risk classes (a chief component of underwriting risk), are explicitly considered.     

Infant mortality: an insured population perspective

Many insurers offer life coverage to individuals during the first year of life. The policies tend to have small face values, but frequently contain premium waiver or additional purchase options. General population mortality is significantly higher at this age relative to older children and even middle-aged adults. This article presents the mortality experience of an insured cohort in which death occurred under 1 year of age. In summary, the insured population's mortality rate was significantly lower and the leading causes of death were different than the general population.     

Time Varying Market Leverage, the Market Risk Premium and the Cost of Capital

This paper shows that, when as usual the market portfolio is proxied by a share portfolio, then the conventional Ibbotson (1999) estimator of the market risk premium violates Miller–Modigliani (1958 and 1963) propositions II and III. A new estimator of the market risk premium is proposed which is free of these defects. In addition, across the range of market leverages experienced in the US in the period 1952–1997, it generates estimates of the market risk premium that differ from those generated by the Ibbotson methodology by up to 2.5 percentage points, and weighted average costs of capital for firms that differ by up to 2.6 percentage points.     

Feintuning im Recht der Lebensversicherung zu § 169 Abs. 5 VVG – Neues zum Stornoabzug bei Einmalbeitr?gen sowie zu separaten Abschlusskostenvereinbarungen

The first part of this article deals with surrender charges. Due to the incredible increase of single premium life assurances this already written off instrument came back to discussion. The increase is based on the high income within the range of life assurances compared to interest income for safe investments. Speculations against to the collective of insured become possible as the right of the policyholder to notice a life assurance at any time, §?168 VVG, is inalienable, even concerning single premium assurances. Alerted by that, the Federal Financial Supervisory Authority (??BaFin??) demands appropriate surrender charges within the single premium matters. However, literature prefers a surrender charge caused by capital market which is consolidated into a lump sum to the amount of 0,2 per cent regarding the total payment of interest, for each year by which the single premium contract is going to be terminated before expiring after 10 years. This point of view can basically be followed. For reasons of principle consideration, the surrender charge must certainly be determined significantly lower than proposed, namely with 0,1 per cent each year. De lege ferenda, the alternative to make restrictions to the right to give notice for single premium assurances may be taken into consideration. The second part of this article deals with acquisition costs. The regional court of Rostock considers a separate agreement relating to cost averaging??whereby the policyholder must continue to pay the instalments for the acquisition costs even after the termination of the life assurance??to be a ??Umgehungsgesch?ft?? (evasive transaction) to §?169 V 2 VVG and is for that reason void. This cannot be followed. A?thoroughly interpretation of the provision shows that it does not prohibit the result, namely the deduction of the surrender value below the value which is determined by §?169 III VVG. The result is rather then prohibited when it is achieved by the non-transparent way of a set off of the costs with the paid assurance premium. That point of view of the regional court of Rostock is therefore contra legem. As the right to modify law is reserved to the legislative authority, it is well advised to observe the actual development for a certain period of time. In regard to that result the policyholder is not made vulnerable. Oftentimes, the liability for consulting activities of the insurer and his intermediaries will interfere in his favour.     

The Impacts of Surrender Options on Reserve Durations

Estimating the interest rate risk of life insurance reserves is essential for insurers, and surrender options are critical to the estimation. This article advances our understanding of how surrender options affect the durations of reserves. We identify a pattern of the reserve duration with respect to the interest rate that is important in explaining how surrender rate levels and the interest-rate sensitivity of surrenders affect reserve durations. We further found that the surrender behavior that is more positively related to the interest rate produces larger/smaller effective dollar durations when the interest rate is low/high.     

Expensive Mistakes: Operational Risk in Life Insurance

Although insurers have developed sophisticated techniques for measuring and managing mortality risks, asset–liability mismatch, and interest rate risks, they may underestimate the potential cost of operational risks. This is a case study of an Australian life insurer, which made a series of very expensive mistakes.     

Optimal hedging of demographic risk in life insurance

A Markov chain model is taken to describe the development of a multi-state life insurance policy or portfolio in a stochastic economic?Cdemographic environment. It is assumed that there exists an arbitrage-free market with tradeable securities derived from demographic indices. Adopting a mean-variance criterion, two problems are formulated and solved. First, how can an insurer optimally hedge environmental risk by trading in a given set of derivatives? Second, assuming that insurers perform optimal hedging strategies in a given derivatives market, how can the very derivatives be designed in order to minimize the average hedging error across a given population of insurers? The paper comes with the caveat emptor that the theory will find its prime applications, not in securitization of longevity risk, but rather in securitization of catastrophic mortality risk.     

Health insurers' operations in the face of health care reform: An analysis of the Supplemental Health Care Exhibit

The Patient Protection and Affordable Care Act (ACA) introduced significant changes to the health insurance marketplace in the United States. The act also imposed reporting requirements on insurers. The law has required insurers since 2010 to file yearly the Supplemental Health Care Exhibit (SHCE). The SHCE provides unique information on how health insurers operate. We analyze data in the SCHE to understand how insurers have complied with one of the major new regulations affecting health insurers' operations arising from the ACA—the Medical Loss Ratio (MLR) Provision. This requires that insurers spend a minimum percentage of their premium revenue on medical claims, quality improvement expenses, and deductible fraud and abuse detection and recovery expenses. Our analysis of the 2010–2017 SHCE indicates that insurers' underwriting performance worsened in the early years of the ACA as they worked to increase MLRs to become ACA‐compliant. Analysis of the SHCE further reveals that insurers' profits from managing uninsured plans grew as the profitability of underwriting insured plans decreased. Future research on health insurer operations is warranted. The currently underutilized and data‐rich SHCE provides unique information that makes future research possible.