Structured settlement annuities, part 1: overview and the underwriting process

Structured settlement underwriting is the underwriting of medically impaired lives for the purchase of an annuity to fund the settlement. Other than risk assessment, structured settlement (SS) underwriting has little in common with traditional life insurance underwriting. Most noteworthy of these differences is the relative lack of actuarial data on which to base decisions about mortality and the necessity for prospective thinking about risk assessment. The purpose of this paper is to provide a foundation for understanding the structured settlement business and to contrast the underwriting of structured settlements with that of traditional life insurance. This is the first part of a two-part article on SS annuities. Part 2 deals with the mortality experience in SS annuitants and the life-table methodology used to calculate life expectancy for annuitants at increased mortality risk.     

Auswirkungen von Enhanced Annuities auf den Bestand eines Versicherers

The value for money of a standard annuity is the higher, the longer the life expectancy of an insured, and therefore it is only acceptable for persons with an above average life expectancy. The discrepancy is intensified by tax regulations that favor lifelong annuity payments opposed to a lump sum. This discrimination of impaired insureds could be prevented if so-called enhanced annuities were offered, i.e. products where the annuity paid is the larger, the lower the person’s life expectancy. The article presents a quantitative comparison of the risk profile of insurance companies offering standard annuity contracts compared to enhanced annuities and an analysis of the impact of adverse selection on a standard insurer. By definition of individual mortality rates a heterogeneous insurance portfolio is specified. Besides we model the individual underwriting of enhanced annuities. A Monte Carlo Simulation provides results to compare the profit/loss situation of a portfolio of traditional annuity products and a portfolio of enhanced annuities with individual underwriting of different quality and to assess the impact of selection effects.     

Forecasting Longevity Gains for a Population with Short Time Series Using a Structural SUTSE Model: An Application to Brazilian Annuity Plans

In this article, a multivariate structural time series model with common stochastic trends is proposed to forecast longevity gains of a population with a short time series of observed mortality rates, using the information of a related population for which longer mortality time series exist. The state space model proposed here makes use of the seemingly unrelated time series equation and applies the concepts of related series and common trends to construct a proper model to predict the future mortality rates of a population with little available information. This common trends approach works by assuming the two populations’ mortality rates are affected by common factors. Further, we show how this model can be used by insurers and pension funds to forecast mortality rates of policyholders and beneficiaries. We apply the proposed model to Brazilian annuity plans where life expectancies and their temporal evolution are predicted using the forecast longevity gains. Finally, to demonstrate how the model can be used in actuarial practice, the best estimate of the liabilities and the capital based on underwriting risk are estimated by means of Monte Carlo simulation. The idiosyncratic risk effect in the process of calculating an amount of underwriting capital is also illustrated using that simulation.     

Developing Mortality Improvement Formulas

Abstract

Longevity improvements have contributed to widespread underfunding of pension plans and losses in insured annuity portfolios. Insurers might reasonably expect some upside from the effect of lower mortality on their life business. Although mortality improvement scales, such as the Society of Actuaries Scale AA, are widely employed in pension and annuity valuation, the derivation of these scales appears heuristic, leading to problems in deriving meaningful measures of uncertainty. We explore the evidence on mortality trends for the Canadian life insurance companies, data, using stochastic models. We use the more credible population data to benchmark the insured lives data. Finally, we derive a practical, model-based formula for actuaries to incorporate mortality improvement and the associated uncertainty into their calculations.     

How long might the younger-old live: A predictive model

Life expectancy amongst older people in industrialised countries has been improving over an extended period and still continues to do so. This has ramifications for providers of services to this population, thus necessitating a level of forward planning. Predictive models of remaining life expectancy for older age groups can assist long-term planning processes. This paper presents an extrapolative approach to forecasting remaining life expectancy. Based on logistic modelling of historic mortality and survivorship for the “younger-old” male population of England and Wales over the period 1970-2005, a parsimonious two-parameter model is derived. This model provides a close correspondence to published period life table data. Trends in these parameters are then fitted and extrapolated to enable projections of life expectancy up to 40 years into the future. Alternative assumptions are used to determine a range of future life expectancy trajectories for a 65-year-old male. Occupational pension scheme provision is identified as an area of particular concern in the context of increasing longevity. As an illustration, the life expectancy trajectories are combined with differing discount rate assumptions to generate a number of alternative pension liability scenarios for the extrapolation period.     

Converting Clinical Literature to an Insured Population: A Comparison of Models Using Nhanes

Abstract

The use of clinical literature to set risk classification standards for life insurance underwriting stems from the need to set the most accurate standards using the best available information. A necessary hurdle in this process is converting any excess mortality observed in a clinical study to the appropriate rating for use in underwriting. A widely accepted model in the insurance industry, the Excess Death Rate model, treats the excess as additive to the conditional probability of death for an insurance company’s unimpaired class.

In this paper we test the validity of that model versus other common predictive models of excess mortality in an insured population. Applying these models to National Health and Nutrition Examination Survey (NHANES) data, we derive estimates for excess mortality from three commonly seen underwriting impairments in what could be considered a clinical population. These estimates are added to an estimate of an insurance company’s unimpaired mortality class and then used to predict deaths in an “insurable” subset of that clinical population.

The Excess Death Rate model performed the best of all models, having the smallest cumulative difference of actual to predicted deaths. The use of publicly available data, such as that in NHANES, could help bridge the gap between clinical literature and its application in insurance underwriting if insurable cohorts can be reliably identified from these generally healthy, ambulatory groups.     

How to prepare a life expectancy report for an attorney in a tort case

The purpose of this methodology article is to describe a suitable format for a legally acceptable report on the life expectancy of the principal in a tort case that is being advocated or defended by an attorney. Life insurance medical directors and underwriters are clearly skilled and experienced in mortality risk classification for life insurance. However, the judicial system is accustomed to measuring excess mortality only in terms of reduced life expectancy. The analyst preparing the report must convert the excess mortality into a figure for reduced life expectancy and compare this with the life expectancy of persons matched by age, sex and race in the latest Decennial US Life Tables. This process is different from the life insurance underwriting process. A life table projected to age 109 must be constructed as an essential part of the report, and the entire process must be presented clearly and convincingly. There are good reasons why the excess death rate (EDR) should be used as the index of excess mortality in constructing the life table, in preference to the mortality ratio (MR), which is used most of the time in life insurance risk classification. All of these considerations are discussed in this article, which is based on a sample of 40 cases handled by the author, a retired life insurance medical director.     

A Model for Analyzing the Impact of Selective Lapsation on Mortality

Abstract

This paper presents a model for examining the effect of various relationships between mortality rates and lapse rates on the mortality experience of a cohort of insured lives. The approach is individual rather than the aggregate traditionally used in analyzing selective lapsation. The model assumes that insured lives are healthy at policy issue, but later may move to an impaired state from which the lapse rate is zero. Associated with each insured is an unobservable “risk level” random variable, which reflects the heterogeneity of the insured group. Individual mortality and lapse rates are functions of the risk level. A numerical illustration provides some interesting results obtained by using this model.     

Life expectancy--a commentary on this life table variable

In 1992, I wrote an article on a method of modifying the Decennial US Life Table to accommodate any pattern of excess mortality expressed in terms of excess death rate (EDR), for the specific purpose of calculating the reduced life expectancy, e. I believe this was the first article published in the Journal of Insurance Medicine (JIM) that dealt specifically with life expectancy as an index of survival and risk appraisal, never used in the classification of extra mortality risk in applicants for life insurance. In this commentary, I discuss the 1989-91 US Decennial Life Table in detail. I link the subject matter of the 1992 article with several more recent articles that also focus on the utility of life expectancy in underwriting structured settlement annuities and preparing reports on life expectancy for an attorney in a tort case. A few references are given for further reading on life table methodology and its use in the most accurate estimate of life expectancy, given the inherent limitations of the life table and the limited duration of follow-up studies.     

The evolution of death rates and life expectancy in Denmark

From 1835 to date Denmark has experienced an increase in life expectancy at birth of about 40 years for both sexes. Over the course of the last 170 years, life expectancy at birth has increased from 40 to 80 years for women and from 36 to 76 years for men, and it continues to rise. Using a new methodology, we show that about half of the total historic increase can be attributed to the sharp decline in infant and young age death rates up to 1950. However, life expectancy gains from 1950 to date can be primarily attributed to improvements in the age-specific death rates for the age group from 50 to 80, although there is also a noticeable contribution from the further decline in infant mortality over this period. With age-specific death rates up to age 60 now at a very low absolute level, substantial future life expectancy improvements must necessarily arise from improvements in age-specific death rates for ages 60 and above. Using the developed methodology, we quantify the impact of further reductions in age-specific mortality. Despite being one of countries with the highest life expectancy at the beginning of the 20th century, and despite the spectacular historic increase in life expectancy since then, Denmark is, in fact, lagging behind compared to many other countries, notably the other Nordic countries. The main reason is an alarming excess mortality for cause-specific death rates related to ischaemic heart diseases and, in particular, a number of cancer diseases. Age-specific death rates continue to improve in most countries, and a likely scenario is that in the future Denmark will experience improvement rates at the international level or perhaps even higher as a result of a catch-up effect.     

Effective Underwriting in the Genetic Testing Era

This paper notes that prior to the availability of genetic test results, conventional life insurance underwriting had produced satisfactory mortality results even though a number of applicants insured at standard or better must have had serious genetic markers. The paper discusses the problems that may affect underwriting when an applicant is aware of a genetic risk factor.

The paper suggests use of pre-genetic testing era underwriting methodology, including medical history and family history, with strict financial underwriting to control antiselection. A set of underwriting rules is provided. The need for a sales organization that can produce a substantial amount of business is cited as necessary for success.

To spread equitably any excess cost on account of insuring persons with genetic markers, a risk pool is suggested. The pool manager would also inform a company of additional applications to other companies by genetically impaired applicants.

The purpose of the proposal is to deflect ill-advised political solutions and, at the same time, to control expenses by ensuring a high ratio of paid-for policies to applications.     

Mortality,Health, and Marriage: A Study Based on Taiwan's Population Data

Life expectancy has been increasing significantly since the start of the 20th century, and mortality improvement trends are likely to continue in the 21st century. Stochastic mortality models are used frequently to predict the expansion in life expectancy. In addition to gender, age, period, and cohort are the three main risk factors considered in constructing mortality models. Other than these factors, it is also believed that marital status is related to health and longevity, and many studies have found that married persons have a lower mortality rate than the unmarried. In this study, we have used Taiwan's marital data for the whole population (married, unmarried, divorced/widowed) to evaluate if the marital status can be a preferred criteria. Furthermore, we also want to know whether the preferred criteria will be valid in the future. We chose two popular mortality models, the Lee-Carter and age-period-cohort, to model the mortality improvements for various marital statuses. Because of a linear dependence in the parameters of the age-period-cohort model, we used a computer simulation to choose the appropriate estimation method. Based on Taiwan's marital data, we found that married persons have significantly lower mortality rates than the single, and if converting the difference into a life insurance policy, the discount amount is even larger than that for smokers/nonsmokers.     

On systematic mortality risk and risk-minimization with survivor swaps

A new market for so-called mortality derivatives is now appearing with survivor swaps (also called mortality swaps), longevity bonds and other specialized solutions. The development of these new financial instruments is triggered by the increased focus on the systematic mortality risk inherent in life insurance contracts, and their main focus is thus to allow the life insurance companies to hedge their systematic mortality risk. At the same time, this new class of financial contract is interesting from an investor's point of view, since it increases the possibility for an investor to diversify the investment portfolio. The systematic mortality risk stems from the uncertainty related to the future development of the mortality intensities. Mathematically, this uncertainty is described by modeling the underlying mortality intensities via stochastic processes. We consider two different portfolios of insured lives, where the underlying mortality intensities are correlated, and study the combined financial and mortality risk inherent in a portfolio of general life insurance contracts. In order to hedge this risk, we allow for investments in survivor swaps and derive risk-minimizing strategies in markets where such contracts are available. The strategies are evaluated numerically.     

Mind the Gap: A Study of Cause-Specific Mortality by Socioeconomic Circumstances

Socioeconomic groups may be exposed to varying levels of mortality; this is certainly the case in the United Kingdom, where the gaps in life expectancy, differentiated by socioeconomic circumstances, are widening. The reasons for such diverging trends are yet unclear, but a study of cause-specific mortality may provide rich insight into this phenomenon. Therefore, we investigate the relationship between socioeconomic circumstances and cause-specific mortality using a unique dataset obtained from the U.K. Office for National Statistics. We apply a multinomial logistic framework; the reason is twofold. First, covariates such as socioeconomic circumstances are readily incorporated, and, second, the framework is able to handle the intrinsic dependence amongst the competing causes. As a consequence of the dataset and modeling framework, we are able to investigate the impact of improvements in cause-specific mortality by socioeconomic circumstances. We assess the impact using (residual) life expectancy, a measure of aggregate mortality. Of main interest are the gaps in life expectancy among socioeconomic groups, the trends in these gaps over time, and the ability to identify the causes most influential in reducing these gaps. This analysis is performed through the investigation of different scenarios: first, by eliminating one cause of death at a time; second, by meeting a target set by the World Health Organization (WHO), called WHO 25 × 25; and third, by developing an optimal strategy to increase life expectancy and reduce inequalities.     

Estimation of future mortality rates and life expectancy in chronic medical conditions

Estimates of old-age mortality are necessary for the construction of life tables and computation of life expectancy, and are essential in the growing area of life insurance for the elderly. Two common assumptions are that either the excess death rate (EDR) or the relative risk (RR) stays constant with increasing age. It is known, however, that for most medical conditions the former underestimates the risk and the latter overestimates it. A third popular method is that of rating up: a subject is said to be "rated up k years" if his future mortality rates are assumed to be those of a person in the general population who is k years older. It is shown here that this method generally leads to gross overestimates of old-age mortality. We consider two less-commonly used models, log-linear declining relative risk (LDR) and constant proportional life expectancy (PLE), and compare them to the methods of constant EDR, constant RR and rating up. Although slightly more complicated to employ than the other methods, both LDR and PLE generally give better estimates of mortality and life expectancy. When mortality rates for chronic conditions are known within a certain age range, and estimates outside of the range are required, the LDR and PLE methods may be preferable to the more familiar methods of constant EDR, constant RR, or rating up.     

Minimum Death Rates and Maximum Life Expectancy: The Role of Concordant Ages

Only five populations have achieved maximum life expectancy (or best practice population) more than occasionally since 1900. The aim of this article is to understand how maximum life expectancy is achieved in the context of mortality transition. We explore this aim using the concepts of potential life expectancy, based on minimum rates at each age among all high longevity populations, and concordant ages. Concordant ages are defined as ages at which the minimum death rate occurs in the population with the maximum life expectancy. The results show the extent to which maximum life expectancy could increase through the realization of demonstrably achievable minimum rates. Concordant ages are concentrated at increasingly older ages over time, but they have produced more than half of the change in maximum life expectancy in almost all periods since 1900. This finding is attributed to their quantity and position whereby concordant ages are concentrated at the ages that have the greatest impact on mortality decline in a particular period. Based on mortality forecasts, we expect that concordant ages will continue to lead increases in female maximum life expectancy, but that they will play a weaker role in male maximum life expectancy.     

Evaluating Life Expectancy Evaluations

The quality of life expectancy estimates is one key consideration for an investor in life settlements. The predominant metric for assessing this quality is the so-called A-to-E ratio, which relies on a comparison of the actual to the predicted number of deaths. In this article, we explain key issues with this metric: In the short run, it is subject to estimation uncertainty for small and moderately sized portfolios; and, more critically, in the long run, it converges to 100% even if the underwriting is systematically biased. As an alternative, we propose and discuss a set of new metrics based on the difference in (temporary) life expectancies. We examine the underwriting quality of a leading U.S. life expectancy provider based on this new methodology.     

Select mortality and other durational effects modelled by partially observed Markov Chains

Abstract

In a recent paper Norberg explained select mortality tables for insured lives by a simple Markov model where the lives are classified as active/disabled and insured/not insured, and where no return is possible to previously visited states. The present paper extends the set-up and its results to more complex state spaces and patterns of transition, the key tool being the Kolmogorov backward differential equations.     

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.     

The mortality among industrial insured lives in Norway during the war

In the Norwegian life insurance company Fram a continuous mortality investigation takes place in connection with the yearly valuation of policies issued with weekly premiums. The investigation gives the aggregate mortality, the unit is the policy and the year of observation is the calendar year. A detailed account of the method used has been given by Fredrik Borch in his paper: “The mortality among industrial insured lives in Norway 1931–1940” in this journal 1943. The most important results of the investigation from the years 1940–1946 are rendered below.