Aggregate Mortality Risk Research Articles

VALUATION OF HYBRID FINANCIAL AND ACTUARIAL PRODUCTS IN LIFE INSURANCE BY A NOVEL THREE-STEP METHOD

AbstractFinancial products are priced using risk-neutral expectations justified by hedging portfolios that (as accurate as possible) match the product’s payoff. In insurance, premium calculations are based on a real-world best-estimate value plus a risk premium. The insurance risk premium is typically reduced by pooling of (in the best case) independent contracts. As hybrid life insurance contracts depend on both financial and insurance risks, their valuation requires a hybrid valuation principle that combines the two concepts of financial and actuarial valuation. The aim of this paper is to present a novel three-step projection algorithm to valuate hybrid contracts by decomposing their payoff in three parts: a financial, hedgeable part, a diversifiable actuarial part, and a residual part that is neither hedgeable nor diversifiable. The first two parts of the resulting premium are directly linked to their corresponding hedging and diversification strategies, respectively. The method allows for a separate treatment of unsystematic, diversifiable mortality risk and systematic, aggregate mortality risk related to, for example, epidemics or population-wide improvements in life expectancy. We illustrate our method in the case of CAT bonds and a pure endowment insurance contract with profit and compare the three-step method to alternative valuation operators suggested in the literature.

Annuitization and aggregate mortality risk

AbstractIt is well established that annuities can fully diversify idiosyncratic mortality risks. However, survival rates at the cohort level are changing, raising the question what is the scope of annuities in the presence of aggregate mortality risk? In an overlapping generations setting, we show that risk free annuities exist, but offer a return below the (fair) certainty equivalent return, and agents do not fully annuitize their savings. Higher aggregate mortality risk increases savings and thus the mean level of the capital stock. This lowers the mean rate of return on capital, the survival premium on annuities and the share of individual savings in annuities.

Different Shades of Risk: Mortality Trends Implied by Term Insurance Prices

To infer forward-looking, market-based mortality trends, we estimate a flexible affine stochastic mortality model based on a set of U.S. term life insurance prices using a generalized method of moments approach. We find that neither mortality shocks nor stochasticity in the aggregate trend seem to affect the prices. In contrast, allowing for heterogeneity in the mortality rates across carriers is crucial. We conclude that for life insurance, rather than aggregate mortality risk, the key risks emanate from the composition of the portfolio of policyholders. These findings have consequences for mortality risk management and emphasize important directions for mortality-related actuarial research.

Valuation of Hybrid Financial and Actuarial Products: A Universal 3-Step Method

Financial products are priced using risk-neutral expectations justified by hedging portfolios that (as accurate as possible) match the product’s payoff. In insurance, premium calculations are based on a real-world best-estimate value plus a risk premium. The insurance risk premium is typically reduced by pooling of (in the best case) independent contracts. As hybrid life insurance contracts depend on both financial and insurance risks, their valuation requires a hybrid valuation principle that combines the two concepts of financial and actuarial valuation. The aim of this paper is to present a novel three-step projection algorithm to valuate hybrid contracts by decomposing their payoff in three parts: a financial, hedgeable part, a diversifiable actuarial part, and a residual part that is neither hedgeable nor diversifiable. The first two parts of the resulting premium are directly linked to their corresponding hedging and diversification strategies, respectively. The method allows for a separate treatment of unsystematic, diversifiable mortality risk and systematic, aggregate mortality risk related to, for example, epidemics or population-wide improvements in life expectancy. We illustrate our method in the case of CAT bonds and a pure endowment insurance contract with profit and compare the three-step method to alternative valuation operators suggested in the literature.

Variable annuities and aggregate mortality risk

This paper explores the extent to which annuitants might be prepared to pay for protection against cohort-specific mortality risk, by comparing traditional indexed annuities with annuities whose payout rates are revised in response to differences between expected and actual mortality rates of the cohort in question. It finds that a man aged 65 with a coefficient of relative risk aversion of two would be prepared to pay 75p per £100 annuitised for protection against aggregate mortality risk while a man with risk aversion of twenty would be prepared to pay £5.75 per £100; studies put the actual cost at £2.70–£7 per £100, suggesting that unless annuitants are very risk averse it is likely that existing products tend to over-insure against cohort mortality risk.

Mortality after Inpatient Open Ventral Hernia Repair

BACKGROUND: 350,000 ventral hernia repairs (VHR) are performed yearly in the US, with open repairs comprising the majority of cases.1 The medical complexity of the hernia patient imparts higher risk for serious complications, poor quality of life, and higher costs. Mortality is a distinct reality, and while prior studies have identified risk factors for mortality, they have been limited to small series lacking generalizability.2 Furthermore, no study has stratified patients based upon risk. The purpose of this study is to utilize a widely-generalizable dataset (ACS-NSQIP) to develop a risk-stratification model for mortality based solely upon preoperative factors, with the hopes of improving decision-making, patient guidance, and minimizing perioperative mortality. METHODS: Patients undergoing inpatient open VHR were identified from the 2005-2012 ACS-NSQIP databases.3 Patient comorbidities and preoperative variables were analyzed to determine statistical correlation with mortality risk. A step-wise multivariate logistic regression of all factors with p value< 0.1 was conducted and resulting significant factors were entered into a bootstrap technique. Adjusted multivariate beta-coefficients were utilized to generate weighted risk scores for each factor. Subsequently, each patient was assigned an aggregate mortality risk score, yielding the risk-assessment tool for preoperative decision-making. RESULTS: 55,760 patients underwent inpatient open VHR with an overall mortality rate of 1.26% (n=704). Independent patient factors predictive of mortality included: partial/total dependent functional status (OR=2.32), cardiovascular (OR=1.23), pulmonary (OR=1.99), renal (OR=1.81), or liver disease (OR=3.19), anemia (OR=1.32), malnutrition (OR=1.83), age>65 years (OR=2.29), ASA 4 or higher (OR=3.83), metastatic cancer (OR=2.14), and systemic inflammation (OR=1.82)(Table 1).Table 1: F.S. – functional status, CV – cardiovascular, ASA – American Society of Anesthesiology, OR – Odds Ratio, CI – Confidence interval. *CV Disease not assigned a risk score because p value > 0.05.Operative factors included emergent case (OR=1.55), wound contamination (OR=1.71), and concurrent intra-abdominal procedure (OR=1.36). Patients were stratified into 4 groups according to mortality risk: low-risk (mortality=0.37%), moderate-risk (mortality=2.24%), high-risk (mortality=10.93%), and extreme-risk (mortality=32.65%) (Figure 1).Figure 1: Additionally, length of stay, unplanned reoperations, and medical complications all increased across the 4 patient groups. The bootstrap model demonstrated high sensitivity and specificity for discriminating mortality risk with a C-statistic=0.87.CONCLUSIONS: This study is the first to provide an accurate model to predict mortality risk based upon preoperative risk factors in patients undergoing open VHR. The strongest predictors were ASA 4 or higher, liver disease, functional status, and older age. This tool allows surgeons to better counsel patients preoperatively and improve clinical decision-making to reduce complication rates and optimize outcomes, patient satisfaction, and cost-efficacy.

Platelet-monocyte aggregate formation and mortality risk in older patients with severe sepsis and septic shock.

Aging-related changes in platelet and monocyte interactions may contribute to adverse outcomes in sepsis but remain relatively unexamined. We hypothesized that differential platelet-monocyte aggregate (PMA) formation in older septic patients alters inflammatory responses and mortality. We prospectively studied 113 septic adults admitted to the intensive care unit with severe sepsis or septic shock. Patients were dichotomized a priori into one of two groups: older (age ≥ 65 years, n = 28) and younger (age < 65 years, n = 85). PMA levels were measured in whole blood via flow cytometry within 24 hours of admission. Plasma levels of IL-6 and IL-8, proinflammatory cytokines produced by monocytes upon PMA formation, were determined by commercial assays. Patients were followed for the primary outcome of 28-day, all-cause mortality. Elevated PMA levels were associated with an increased risk of mortality in older septic patients (hazard ratio for mortality 5.64, 95% confidence interval 0.64-49.61). This association remained after adjusting for potential confounding variables in multivariate regression. Receiver operating curve analyses demonstrated that PMA levels greater than or equal to 8.43% best predicted 28-day mortality in older septic patients (area under the receiver operating curve 0.82). Plasma IL-6 and IL-8 levels were also significantly higher in older nonsurvivors. In younger patients, neither PMA levels nor plasma monokines were significantly associated with mortality. Increased PMA formation, and associated proinflammatory monokine synthesis, predicts mortality in older septic patients. Although larger studies are needed, our findings suggest that heightened PMA formation in older septic patients may contribute to injurious inflammatory responses and an increased risk of mortality.

The Impact of Aggregate Mortality Risk on Defined Benefit Pension Plans

We calculate the risk faced by defined benefit plan providers arising from uncertain aggregate mortality — the risk that the average participant will live longer than expected. First, comparing the widely cited Lee-Carter model to industry benchmarks, we show that plan providers appear to substantially underestimate the longevity of their employees. The resultant understatement of liabilities is 15.2 percent, when weighted by the characteristics of typical male participants in defined benefit plans, and reaches as much as 25.2 percent for male workers aged 22. Next, we consider the substantial mortality risk that arises even if plan providers were to use the Lee-Carter model or other unbiased forecasts of mortality reductions. We calculate the consequences for plan liabilities if aggregate mortality declines unexpectedly faster than is predicted by an unbiased projection. There is a 5 percent chance that liabilities of a terminated plan would be 2.9 to 5.1percent higher than what is expected, depending on the mix of workers covered. Lastly, we explain how longevity bonds might be used to transfer mortality risk from defined benefit plans to the capital markets, and we calculate a risk premium for a hypothetical frozen plan.

The impact of aggregate mortality risk on defined benefit pension plans

AbstractWe calculate the risk faced by defined benefit plan providers arising from uncertain aggregate mortality – the risk that the average participant will live longer than expected. First, comparing the widely cited Lee–Carter model to industry benchmarks that are commonly employed by plan providers, we show that these benchmarks appear to substantially underestimate longevity. The resultant understatement of liabilities may reach 12.2% for typical male participants in defined benefit plans and may reach 22.4% for male workers aged 22. Next, we consider consequences for plan liabilities if aggregate mortality declines unexpectedly faster than is predicted by a putatively unbiased projection. There is a 5% chance that liabilities of a terminated plan would be 3.1% to 5.3% higher than what is expected, depending on the mix of workers covered.

Stochastic Mortality: Experience-Based Modeling and Application Issues Consistent with Solvency 2

This paper is motivated by the need to have appropriate tools for the valuation of mortality risks when carrying out an internal assessment of the insurance business, such as a portfolio valuation or a solvency investigation based on internal models. The case of life annuities is in particular addressed, due to the importance of mortality on the cost of living benefits for the elderly. Our aim is to describe a stochastic mortality model calibrated on the best-estimate life table available to the insurer and to the mortality experienced in the insurer's portfolio. As we address life annuities, uncertainty of future mortality improvements, i.e. the aggregate mortality risk, needs in particular to be accounted for. Following Olivieri and Pitacco (2009), we extend some classical results about the modeling of the number of deaths joint to the modeling of parameter uncertainty. We explore the features of two alternative approaches: a Beta-Binomial and a Poisson-Gamma setting; we then focus on the latter only. Thanks to a Bayesian inferential procedure, the parameters, initially assigned referring to the best-estimate life table, are updated according to the mortality experienced in the portfolio. Extending a traditional tool-kit, the framework we define is in particular suitable for practical work. Due to calibration, clearly the scope of the model is within internal assessments. To provide an example of application of the model, we perform a capital assessment. Solvency rules which could be adopted as an alternative to a standard, regulatory requirement are tested. The Solvency 2 requirement for longevity risk is referred to for the design of an internal rule which could get validation for replacing the standard one.

Individual Annuity Demand Under Aggregate Mortality Risk

Aggregate mortality risk—the risk that the mortality trend in a population changes in a nondeterministic way—and its implications for corporate decisions has recently been the subject of lively scientific discussion. We show that aggregate mortality risk is also a key determinant for individual annuitization decisions. Aggregate mortality risk appears to be a risk very difficult to transfer for individuals. Whether its existence leads to a higher or lower annuity demand depends on objective factors (e.g., insurers’ vulnerability to aggregate mortality changes). Subjective factors (i.e., individuals’ preferences) determine only the intensity of the annuity demand reaction to aggregate mortality risk. Our results are of significant importance not only for financial planning approaches of individual annuity buyers but also for strategic decisions in insurance companies and for solvency regulators. Furthermore, consideration of aggregate mortality risk may alleviate, but also intensify, the annuity puzzle.

Heart Failure Due to Systolic Dysfunction and Mortality in Diabetes: Pooled Analysis of 39,505 Subjects

Background Despite recent successes in improving mortality from congestive heart failure (CHF) with drugs and devices, several reports suggest increased mortality among CHF subjects with diabetes. Our objective was to conduct a meta-analysis to determine aggregate risk of mortality and hospitalization in CHF from systolic dysfunction and diabetes. Methods and Results Observational and randomized trials reporting on CHF and mortality in diabetes since 2001 were identified through MEDLINE and Cochrane database searches and hand searching of cross-references. Minimum follow-up of the study cohort should have been at least 6 months. Studies with very small sample size (n < 200) were excluded. Major outcome measure of mortality and secondary outcome measure of CHF hospitalization were extracted from published results. Analysis was done for composite mortality and hospitalization risk, heterogeneity, robustness, and publication bias. A total of 17 trials (n = 39,505 subjects) were eligible. There were a total of 10,068 deaths, with 3615 among diabetics, from available data. The relative risk was significantly higher for diabetics by 28% (95% CI 1.22-1.34, P < .0001). Similarly pooled relative risk for hospitalization was significantly higher for diabetics by 36% (95% CI 1.26-1.48, P < .0001). Heterogeneity was present ( P < .01) and accounted for by observational studies. There was no significant publication bias and lack of robustness was not obvious. Conclusions Aggregate mortality and recurrent hospitalization risk for diabetic subjects with CHF is 28% and 36% higher than for nondiabetic subjects. Future trials should specifically focus on improving survival in these subjects.

Assessing Investment and Longevity Risks within Immediate Annuities

Life annuities provide a guaranteed income for the remainder of the recipient’s lifetime, and therefore, annuitization presents an important option when choosing an adequate investment strategy for the retirement ages. While there are numerous research articles studying annuities from a pensioner’s point of view, thus far there have been few contributions considering annuities from the provider’s perspective. In particular, to date there are no surveys of the general risks within annuity books. The present paper aims at filling this gap: Using a simulation framework, it provides a long-term analysis of the risks within annuity books. In particular, the joint impact of mortality risks and investment risks as well as their respective influences on the insurer’s financial situation are studied. The key finding is that, under the model specifications and using annuity data from the United Kingdom, the risk premium charged for aggregate mortality risk seems to be very large relative to its characteristics. Possible reasons as well as economic implications are provided, and potential caveats are discussed.

Individual Annuity Demand under Aggregate Mortality Risk

Aggregate mortality risk - the risk that the mortality trend in a population changes in a nondeterministic way - and its implications for corporate decisions has recently been the subject of lively scientific discussion. We show that aggregate mortality risk is also a key determinant for individual annuitization decisions. Aggregate mortality risk appears to be a risk very difficult to transfer for individuals. Whether its existence leads to a higher or lower annuity demand depends on objective factors (e.g., insurers' vulnerability to aggregate mortality changes). Subjective factors (i.e., individuals' preferences) determine only the intensity of the annuity demand reaction to aggregate mortality risk. Our results are of significant importance not only for financial planning approaches of individual annuity buyers, but also for strategic decisions in insurance companies and for solvency regulators. Furthermore, consideration of aggregate mortality risk may both alleviate, but also intensify, the annuity puzzle.

Life Is Cheap: Using Mortality Bonds to Hedge Aggregate Mortality Risk

Abstract Insurance companies, employer pension plans, and the U.S. government all provide annuities and therefore assume aggregate mortality risk. Using the widely-cited Lee-Carter mortality model, we quantify aggregate mortality risk as the risk that the average annuitant lives longer than is predicted by the model, and we determine that annuities expose providers to substantial risk. We also find that other recent actuarial forecasts lie at the edge or outside of Lee-Carter's 95% confidence interval, suggesting even more uncertainty about future mortality.We then evaluate the implications of aggregate mortality risk for insurance companies; this analysis can be extended to private pension providers and Social Security. Given the forecasts of the Lee-Carter model, we calculate that a markup of 3.9% on an annuity premium (or shareholders' capital equal to 3.9% of the expected present value of annuity payments) would be required to reduce the probability of insolvency resulting from aggregate mortality shocks to 5%, and a markup of 5.7% would reduce the probability of insolvency to 1%. Based on the same model, we find that a projection scale commonly referred to by the insurance industry underestimates aggregate mortality improvements and would leave annuities underpriced.Annuity providers could manage aggregate mortality risk more efficiently by transferring it to financial markets through mortality-contingent bonds. We calculate the returns that one recently proposed mortality bond would have paid had it been available over a long period. Using both the Capital and the Consumption Capital Asset Pricing Models, we determine the risk premium that investors would have required to hold the bond. At plausible coefficients of risk aversion, annuity providers should be able to hedge aggregate mortality risk via such bonds at very low cost.

Annuities and Aggregate Mortality Uncertainty

This paper explores the effect of aggregate mortality risk on the pricing of annuities. It uses a two-period model; in the second period people face a constant but initially unknown risk of death. Old people can either carry the aggregate emortality risk for themselves or buy annuities which are sold by young people. A market-clearing price for such annuities is established. It is found that old people would, given the choice, decide to carry a considerable part of aggregate mortality risk for themselves.

The Political Economy of Government‐Issued Longevity Bonds

AbstractThis article explores the trade‐offs associated with government issuance of longevity bonds as a way of stimulating private annuity supply in the presence of aggregate mortality risk. We provide new calculations suggesting a 5 percent chance that aggregate mortality risk could ex post raise annuity costs for private insurers by as much as 5–10 percentage points, with the most likely effect based on historical patterns toward the lower end of that range. While we suspect that aggregate mortality risk does exert some upward pressure on annuity prices, evidence from private market pricing suggests that, to the extent that private insurers are accurately pricing this risk, the effect is less than 5 percentage points. We discuss ways that the private market can spread this risk, while emphasizing that the government has the unique ability to spread aggregate risk across generations. We note factors that might hamper such an efficient allocation of risk, including potential political incentives for the government to shift more than the optimal amount of risk onto future generations, and the possibility that government fiscal policy might allocate risk less efficiently within each generation than would private markets. We also discuss how large‐scale longevity bond issuance might affect government borrowing costs, as well as political economy aspects of how the proceeds from such a bond issuance might be used.

Killing the Law of Large Numbers: Mortality Risk Premiums and the Sharpe Ratio

AbstractWe provide an overview of how the law of large numbers breaks down when pricing life‐contingent claims under stochastic as opposed to deterministic mortality (probability, hazard) rates. In a stylized situation, we derive the limiting per‐policy risk and show that it goes to a non‐zero constant. This is in contrast to the classical situation when the underlying mortality decrements are known with certainty, per policy risk goes to zero. We decompose the standard deviation per policy into systematic and non‐systematic components, akin to the analysis of individual stock (equity) risk in a Markowitz portfolio framework. Finally, we draw upon the financial analogy of the Sharpe Ratio to develop a premium pricing methodology under aggregate mortality risk.

Do economic cycles have a permanent effect on population health? Revisiting the Brenner hypothesis.

The Brenner hypothesis is essentially that economic cycles, characterized by unemployment and fluctuations in per capita income can have profound negative implications for population health. A number of subsequent studies have identified shortcomings in Brenner's model and have reported results that for the most part contradict his results. This paper argues that the failure to account for the time-series properties (i.e. the potential for unit root behaviour) of macro level data is a key omission in Brenner's and other subsequent studies. To address this omission an error correction model specification was applied to American data for the period 1948-1996. The findings suggest that economic cycles do have a permanent effect on population health. Paradoxically, they also suggest that economic growth and increases in unemployment reduce aggregate mortality risk. A need for measures of economic change that are perhaps more sensitive to the effects of economic cycles on groups that may be at greater risk of unemployment was identified.

Survivor Bonds: Helping to Hedge Mortality Risk

One of the key problems facing annuity providers is mortality risk, the risk of underestimating mortality improvements. The authors argue that the government could help the issuers of annuities to hedge aggregate mortality risk by introducing a new type of bond, which the authors call a survivor bond. The future coupons on this bond depend on the percentage of the population of retirement age on the issue date who are still alive on the future coupon payment dates. The coupons on the bond therefore decline over time but continue in payment until the last members of this population cohort have died. The government would therefore be assuming a risk that has hitherto been borne by the private sector. However, governments now issue inflation-indexed bonds, and the authors would argue that inflation risk is a much greater risk than mortality risk in aggregate. Furthermore, governments directly contribute to mortality risk: for example, they promote public health campaigns that, if successful, lead to mortality improvements that are difficult to predict many years ahead. Survivor bonds enable pension provision to be a shared responsibility between the public and private sectors.