Biometric Solvency Risk for Portfolios of General Life Contracts. I. The Single-Life Multiple Decrement Case

Abstract

Solvency II splits life insurance risk into seven risk classes consisting of three biometric risks (mortality risk, longevity risk, and disability/morbidity risk) and four nonbiometric risks (lapse risk, expense risk, revision risk, and catastrophe risk). The best estimate liabilities for the biometric risks are valued with biometric life tables (mortality and disability tables), while those of the nonbiometric risks require alternative valuation methods. The present study is restricted to biometric risks encountered in traditional single-life insurance contracts with multiple causes of decrement. Based on the results of quantitative impact studies, process risk was deemed to be not significant enough to warrant an explicit calculation. It was therefore assumed to be implicitly included in the systematic/parameter risk, resulting in a less complex standard formula. For the purpose of internal models and improved risk management, it appears important to capture separately or simultaneously all risk components of biometric risks. Besides its being of interest for its own sake, this leads to a better understanding of the standard approach and its application extent. Based on a total balance sheet approach we express the liability risk solvency capital of an insurance portfolio as value-at-risk and conditional value-at-risk of the prospective liability risk understood as random present value of future cash flows at a given time. The proposed approach is then applied to determine the biometric solvency capital for a portfolio of general life contracts. Using the conditional mean and variance of a portfolio’s prospective liability risk and a gamma distribution approximation we obtain simple solvency capital formulas as well as corresponding solvency capital ratios. To account for the possibility of systematic/parameter risk, we propose either to shift the biometric life tables or to apply a stochastic biometric model, which allows for random biometric rates. A numerical illustration for a cohort of immediate life annuities in arrears reveals the importance of process risk in the assessment of longevity risk solvency capital.     

Multivariate Tweedie lifetimes: the impact of dependence

Systematic longevity risk is increasingly relevant for public pension schemes and insurance companies that provide life benefits. In view of this, mortality models should incorporate dependence between lives. However, the independent lifetime assumption is still heavily relied upon in the risk management of life insurance and annuity portfolios. This paper applies a multivariate Tweedie distribution to incorporate dependence, which it induces through a common shock component. Model parameter estimation is developed based on the method of moments and generalized to allow for truncated observations. The estimation procedure is explicitly developed for various important distributions belonging to the Tweedie family, and finally assessed using simulation.     

An Optimal Product Mix for Hedging Longevity Risk in Life Insurance Companies: The Immunization Theory Approach

This article investigates the natural hedging strategy to deal with longevity risks for life insurance companies. We propose an immunization model that incorporates a stochastic mortality dynamic to calculate the optimal life insurance–annuity product mix ratio to hedge against longevity risks. We model the dynamic of the changes in future mortality using the well‐known Lee–Carter model and discuss the model risk issue by comparing the results between the Lee–Carter and Cairns–Blake–Dowd models. On the basis of the mortality experience and insurance products in the United States, we demonstrate that the proposed model can lead to an optimal product mix and effectively reduce longevity risks for life insurance companies.     

Deposit Insurance, Capital Adequacy Requirements and Interest Rate Dynamics

This paper examines the long run interaction among deposit insurance, bank deposit rates and capital adequacy requirements. Using analysis similar to the price discrimination model of Lott and Roberts (1991) we find that a competitive environment among banks would link the spread between insured and uninsured deposit rates to the size of the insurance premium. We also find that banks that choose to operate at the regulatory minimum capital level, would increase asset risk with increased capital requirements if (1) the implicit interest paid to insured and uninsured depositors is equally sensitive to changes in risk and capital adequacy and (2) the insurance premium is independent of the level of risk and capital adequacy. Under the present risk-based premium structure, asset risk has the potential to decline when the regulatory agency raises capital requirements. Finally, we examine the time series behavior of insured and uninsured interest rates to see if it is consistent with our theoretical model. We find that insured and uninsured rates, along with deposit insurance premiums, are cointegrated series as suggested by our model.     

Use of a Markov Model to Estimate Long-Term Insured Lives’ Mortality Risk Associated With BRCA1 and BRCA2 Gene Mutations

Abstract

There is uncertainty regarding the degree of insurance risk associated with BRCA1/2, the gene mutations associated with breast cancer. Most reports to date have been based on high-risk populations selected from families with multiple and/or early-onset cancers; more favorable data have been reported in studies without this selection bias.

This paper discusses use of a Markov model to estimate mortality risk associated with BRCA1/2 gene mutations in female life insurance applicants. The goal is to derive a range of risk estimates based on different assumptions of breast and ovarian cancer incidence. A particular strength of the model is that transition probabilities after cancer diagnosis vary with age and cancer stage, as do excess hazard rates.

Data calculated by the model indicate that no single mortality curve characterizes risk for all life insurance applicants with a BRCA1/2 mutation. Rather, mortality risk depends on breast and ovarian cancer incidence rates and subsequent mortality rates, and on the method used to deal with competing breast and ovarian cancer incidence and mortality rates. Further refinement of risk estimates will depend on better incidence data and on resolution of complex statistical problems, such as informative censoring.

Widespread use of genetic information by insurance consumers could have important economic implications. For companies that sell individually underwritten products, profitability might decrease. Consumers might find higher prices and reduced availability, with a corresponding decrease in quantity of insurance purchased. Insurance and consumer ramifications would vary by cover, with living-benefit products, such as critical-illness insurance, most adversely affected. Societal choices are limited. Given assumptions in the cited scenario, it is likely premiums would rise and quantity of insurance purchased would decrease even with no change in existing social policy; attempted legal or regulatory remedies would further accentuate price increases and reductions in quantity purchased.     

The pernicious effects of contaminated data in risk management

Banks hold capital to guard against unexpected surges in losses and long freezes in financial markets. The minimum level of capital is set by banking regulators as a function of the banks’ own estimates of their risk exposures. As a result, a great challenge for both banks and regulators is to validate internal risk models. We show that a large fraction of US and international banks uses contaminated data when testing their models. In particular, most banks validate their market risk model using profit-and-loss (P/L) data that include fees and commissions and intraday trading revenues. This practice is inconsistent with the definition of the employed market risk measure. Using both bank data and simulations, we find that data contamination has dramatic implications for model validation and can lead to the acceptance of misspecified risk models. Moreover, our estimates suggest that the use of contaminated data can significantly reduce (market-risk induced) regulatory capital.     

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.     

Bank Capital Requirements, Capital Structure and Regulation

This paper studies the impact of capital requirements, deposit insurance and franchise value on a bank’s capital structure. We find that properly regulated banks voluntarily choose to maintain capital in excess of the minimum required. Central to this decision is both firm franchise value and the ability of regulators to place banks in receivership stripping equity holders of firm value. These features of our model help explain both the capital structure of the large mortgage Government Sponsored Enterprises and the recent increase in risk taking through leverage by financial institutions. The insights gained from the model are useful in guiding the discussion of financial regulatory reforms.     

Modeling the Impact of Genetics on Insurance

The role of probabilistic models in the debate over genetics and insurance is discussed. A Markov model is used to show that, under quite extreme assumptions, adverse selection in life insurance ought to be controllable. The statistical problems of estimating small differences in mortality are discussed; these might limit the use of many genetic disorders as rating factors. The influence of the insurance industry on policy-making, especially through its support of research, is discussed. It is suggested that participating contracts are suitable and simple vehicles to carry the genetic risks in life insurance.     

Social security, life insurance and annuities for families

In this paper we ask whether an aspect of social security, namely its role as a provider of insurance against uncertain life spans, is welfare enhancing. To this end we use an OLG model where agents have a bequest motive and differ in sex and marital status and where families are formed and destroyed and their characteristics evolve (exogenously) according to U.S. demographic patterns of marriage, divorce, fertility and mortality. We compare the implications of social security under a variety of market structures that differ in the extent to which life insurance and annuities are available. We find that social security is a bad idea. In economies where the private sector provides annuities and life insurance, it is a bad idea for the standard reason that it distorts the intertemporal margin by lowering the capital stock. In the absence of such securities social security is still a very bad idea, only marginally less so compared with economies with annuities and life insurance. We also explore these issues in a world where people live longer and we find no differences in our answers. As a by-product of our analysis we find that the existence of life insurance opportunities for people is important in welfare terms while that of annuities is not.     

Konventionelle und moderne Einschätzungsmethoden in der Lebensversicherungsmedizin

The concepts of tariffs in the life insurance are built up with several layers of models. The foundation of the risk assessment of an applicant is the mortality rate in the actuarial model, based on the selection factors of gender and age. In the conventional medical risk assessment the anomalies of the applicant will be transformed into extra mortality rates. With modern methods of evaluation, the risk factors of the applicant will be assessed with statistical practices, in relation to the average values of the insurance portfolio. The deviations built up the insurance medical adjustment factor of the actuarial mortality rate and the basis of the insurance economical classification of the applicant to a risk class or a tariff portfolio.     

Portfolio Choice and Life Insurance: The CRRA Case

We solve a portfolio choice problem that includes life insurance and labor income under constant relative risk aversion (CRRA) preferences. We focus on the correlation between the dynamics of human capital and financial capital and model the utility of the family as opposed to separating consumption and bequest. We simplify the underlying Hamilton–Jacobi–Bellman equation using a similarity reduction technique that leads to an efficient numerical solution. Households for whom shocks to human capital are negatively correlated with shocks to financial capital should own more life insurance with greater equity/stock exposure. Life insurance hedges human capital and is insensitive to the family's risk aversion, consistent with practitioner guidance.     

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.     

Dynamic Portfolio Choice with Stochastic Wage and Life Insurance

We study optimal insurance, consumption, and portfolio choice in a framework where a family purchases life insurance to protect the loss of the wage earner's human capital. Explicit solutions are obtained by employing constant absolute risk aversion utility functions. We show that the optimal life insurance purchase is not a monotonic function of the correlation between the wage and the financial market. Meanwhile, the life insurance decision is explicitly affected by the family's risk preferences in general. The model also predicts that a family uses life insurance and investment portfolio choice to hedge stochastic wage risk.     

Value-at-risk vs. building block regulation in banking

Existing regulatory capital requirements are often criticized for only being loosely linked to the economic risk of the banks' assets. In view of the attempts of international regulators to introduce more risk sensitive capital requirements, we theoretically examine the effect of specific regulatory capital requirements on the risk-taking behavior of banks. More precisely, we develop a continuous time framework where the banks' choice of asset risk is endogenously determined. We compare regulation based on the Basel I building block approach to value-at-risk or ‘internal model’-based capital requirements with respect to risk taking behavior, deposit insurance liability, and shareholder value. The main findings are: (i) value-at-risk-based capital regulation creates a stronger incentive to reduce asset risk when banks are solvent, (ii) solvent banks that reduce their asset risk reduce the current value of the deposit insurance liability significantly, (iii) under value-at-risk regulation the risk reduction behavior of banks is less sensitive to changes in their investment opportunity set, and (iv) banks' equityholders can benefit from risk-based capital requirements.     

The Determinants of Financial Derivatives Use in the United Kingdom Life Insurance Industry

This paper examines the determinants of financial derivatives use in the United Kingdom life insurance industry. We estimate a probit regression model and a Heckman two-stage sample selection regression model using a sample of eighty-eight U.K. life insurers in 1995. Our results indicate that the propensity to use derivative instruments is positively related to a firm's size, leverage and international links, and negatively related to the extent of reinsurance. We also find that mutual life insurance firms have a greater propensity than stock firms to use derivatives. The positive relation with leverage and the negative relation with reinsurance support the hypothesis that U.K. life insurers use derivatives to offset risk, rather than as a speculative means of income generation. Firm size and organizational form are the main influences on the extent of financial derivatives use.     

中国寿险市场存在逆向选择吗?——来自CHARLS数据的经验证据

我国寿险市场是否存在逆向选择问题,在理论和实证两个方面缺乏细致的讨论。本文利用CHARLS数据和正相关理论检验了我国定期寿险和终身寿险市场中的逆向选择问题。我们选取了死亡率这一远期指标和健康状况这一近期指标来衡量消费者的死亡风险,从广延边际和集约边际两个方面利用正相关理论进行了深入的研究。实证结论表明,以死亡率和健康状况衡量的死亡风险与寿险消费负相关或者不相关,即我国寿险市场并不存在逆向选择问题。然后,我们讨论了模型的内生性问题,并根据年龄变量检验了结论的稳健性,实证结果表明我们的结论是稳健的。最后,本文利用双变量Probit模型设计了一个机制,并利用该机制验证了利他动机是我国寿险市场不存在逆向选择的原因之一。     

中国寿险市场存在逆向选择吗?——来自CHARLS数据的经验证据

我国寿险市场是否存在逆向选择问题,在理论和实证两个方面缺乏细致的讨论。本文利用CHARLS数据和正相关理论检验了我国定期寿险和终身寿险市场中的逆向选择问题。我们选取了死亡率这一远期指标和健康状况这一近期指标来衡量消费者的死亡风险,从广延边际和集约边际两个方面利用正相关理论进行了深入的研究。实证结论表明,以死亡率和健康状况衡量的死亡风险与寿险消费负相关或者不相关,即我国寿险市场并不存在逆向选择问题。然后,我们讨论了模型的内生性问题,并根据年龄变量检验了结论的稳健性,实证结果表明我们的结论是稳健的。最后,本文利用双变量Probit模型设计了一个机制,并利用该机制验证了利他动机是我国寿险市场不存在逆向选择的原因之一。     

Risk,Capital, and Operating Efficiency: Evidence from Taiwan’s Life Insurance Market

ABSTRACT

In this article, we investigate the relationships among risk, capital, and operating efficiency for Taiwanese life insurance companies from 2004 to 2009 by using the two-stage least-square approach. We find a positive relation between inefficiency and product risk. At the same time, efficient insurers are seen as taking higher asset risk than inefficient insurers. A contrasting finding also shows that the relationship between capital and product risk is positive, while the relationship between capital and asset risk is negative. Moreover, we present a negative relationship between inefficiency and capital level, indicating that well-capitalized insurers operate more efficiently than poorly capitalized insurers.     

Application of Coherent Risk Measures to Capital Requirements in Insurance

Risk measurements go hand in hand with setting of capital minima by companies as well as by regulators. We review the properties of coherent risk measures and examine their implications for capital requirement in insurance. We also comment on the specific risk-based capital computations.