Value Of Annuity Research Articles

Retirement Replacement Rates and RetirementWealth Inequality Among Baby Boomer and OtherBirth Cohorts

The retirement readiness of baby boomers has been a topic of considerable but inconclusive research. Using data from the Panel Study of Income Dynamics (PSID), the authors evaluate the relative retirement readiness of five discrete birth cohorts: Depression babies (born 1926–1935); World War II babies (born 1936–1945); two halves of the baby boom generation (older, born 1946–1955, and younger, born 1956–1965); and Gen-Xers (born 1966–1975). They construct a comprehensive measure of retirement wealth that combines both accumulated private net worth and the annuity values of Social Security and defined-benefit pensions at age 65. The authors then calculate replacement rates as the ratio of annuitized wealth at age 65 to average preretirement income. They find that median replacement rates decline steadily over the four birth cohorts from World War II babies to Gen-Xers and that younger generations appear to be considerably less well situated for retirement than baby boomers and earlier cohorts. By comparing ratios of replacement rates at the 99th and 50th percentile, the authors determine that retirement wealth inequality in the top half of the wealth distribution increases steadily across the five birth cohorts, reaching a peak among Gen-Xers.

The Effect of Longevity on Pensions in the Nigerian Pension Scheme

The old pension scheme pension were based on length of service and on a percentage of final salaries. In the new pension scheme contributions are invested till retirement. Accumulated contributions are used to purchase pension at retirement. The paper looks at the effect of longevity on the annuity values at retirement and the consequent pensions. Three lives age 25, 35 and 45 with 35, 25 and 15 years to retirement are considered. Five Life Tables with life expectancies of 13.48, 14.43, 15.61, 17.98 and 19.51 years at age 60 each were considered. We find that the new pension rate is considerably less than the old rate for each Life Table and longevity increases annuity value, thereby reducing pensions. The percentage goes from 100% to 82.8% taking the Life .Table with the least life expectancy as a base and for a life aged 25.The same result follows for each life considered,

Analysis of the Impact of the Economy on Pensions in a Defined Contribution Scheme

Retires depend solely on the final salaries and length of service in order to determine their pensions at retirement. In a defined contribution scheme the accumulated investments over the working life of the retiree is used to purchase pensions depending upon the annuity value at retirement. In a boom period the economy yields good investment returns. The investment return drops as the economy gets weak and also the discounting rate prevailing affects the annuity value calculated actuarially. This paper examines the relationship between pensions and the prevailing economic conditions considering investment returns and discounting rates. The assumed investment returns on all assets are 8%, 10%, 10% and 12% per annum and the discounting rates are 9%, 10%, 11%, 12% and 13% to reflect various states of the economy. The analysis is done for 3 lives aged 25, 35 and 45years with 35, 25, 15 years of service left before retirement. Comparisons are made. It is found that pension value is more than twice its value when investment return and discounting rates are 14% each compared to when investment return is 8% and discounting rate is 9% Retirees faces pension risk due to the state of the economy.

The determinants of mortality heterogeneity and implications for pricing annuities

Standard annuities are offered at one price to all individuals of the same age and gender. Individual mortality heterogeneity exposes insurers to adverse selection since only relatively healthy lives are expected to purchase annuities. As a result standard annuities are priced assuming above-average longevity, making them expensive for many individuals. In contrast underwritten annuity prices reflect individual risk factors based on underwriting information, as well as age and gender. While underwriting reduces heterogeneity, mortality risk still varies within each risk class due to unobservable individual risk factors, referred to as frailty. This paper quantifies the impact of heterogeneity due to underwriting factors and frailty on annuity values. Heterogeneity is quantified by fitting Generalized Linear Mixed Models to longitudinal data for a large sample of US males. The results show that heterogeneity remains after underwriting and that frailty significantly impacts the fair value of both standard and underwritten annuities. We develop a method to adjust annuity prices to allow for frailty.

Modelling and projecting mortality improvement rates using a cohort perspective

We investigate the feasibility of defining, modelling and projecting of (scaled) mortality improvement rates along cohort years-of-birth, that is, using a cohort perspective. This is in contrast to the approach in the literature which has considered mortality improvement rates that are defined by reference to changes in mortality rates over successive calendar years, that is, using a period perspective. In this paper, we offer a comparison of the 2 parallel approaches to modelling and forecasting using mortality improvement rates. Comparisons of simulated life expectancy and annuity value predictions (mainly by the cohort method) using the England & Wales population mortality experiences for males and females under a variety of controlled data trimming exercises are presented and comparisons are also made between the parallel cohort and period based approaches.

Decision usefulness of whole-asset operating lease capitalizations

Monson (2001) and Hepp and Scoles (2012) argue that some leased assets should be capitalized at the assets' purchase price (whole-asset value) rather than at the present value of future minimum lease payments (right-of-use asset value). The argument is based in part on the notion that the assets under lease generate future income not the obligation related to future lease payments. To test the notion we compare associations between capitalizations representing whole asset values and current and future return on assets (ROA) and return on equity (ROE) with capitalizations representing right-of-use asset values and current and future ROA and ROE. Our results indicate that the whole-asset annuity values are incrementally associated with future ROA and ROE over right-of-use asset values. We interpret our results to suggest that the current practice of capitalizing future lease payments does not fully reflect the income generation provided by leased assets.

Approximations for quantiles of life expectancy and annuity values using the parametric improvement rate approach to modelling and projecting mortality

In this paper, we develop accurate approximations for medians of life expectancy and life annuity pure premiums viewed as functions of future mortality trends as predicted by parametric models of the improvement rates in mortality. Numerical illustrations show that the comonotonic approximations perform well in this case, which suggests that they can be used in practice to evaluate the consequences of the uncertainty in future death rates. Prediction intervals based on 5 and 95 % quantiles are also considered but appear to be wider compared to simulated ones. This provides the practitioner with a conservative shortcut, thereby avoiding the problem of simulations within simulations in, for instance, Solvency 2 calculations.

The Determinants of Mortality Heterogeneity and Implications for Pricing Underwritten Annuities

It is widely accepted that mortality risk varies across individuals within age-sex bands of a population. This heterogeneity exposes insurers to adverse selection if only the healthiest lives purchase annuities, so standard annuities are priced with a mortality table that assumes above-average longevity. This makes standard annuities expensive for many individuals. To address this issue there has been a shift to underwriting annuities in order to offer lower prices to individuals with below-average longevity. While underwriting reduces heterogeneity, mortality risk still varies within each risk class due to unobservable individual-specific factors, referred to as frailty. This paper quantifies the financial impact of frailty on underwritten annuities. The heterogeneity implied by underwriting factors and frailty is quantified by fitting Generalized Linear Mixed Models to longitudinal data for a large sample of US males. The results show that heterogeneity remains after underwriting, creating signi ficant variation in the fair value of underwritten annuities. We develop a method to adjust annuity prices to allow for frailty.

Decision Usefulness of Whole-Asset Operating Lease Capitalizations

Monson (2001) and Hepp and Scoles (2012) argue that some leased assets should be capitalized at the assets’ purchase price (whole-asset value) rather than at the present value of future minimum lease payments (right-of-use asset value). The argument is based in part on the notion that the assets under lease generate future income not the obligation related to future lease payments. To test the notion we compare associations between capitalizations representing whole asset values and current and future return on assets (ROA) and return on equity (ROE) with capitalizations representing right-of-use asset values and current and future ROA and ROE. Our results indicate that the whole-asset annuity values are incrementally associated with future ROA and ROE over right-of-use asset values. We interpret our results suggest that the current practice of capitalizing future lease payments does not fully reflect the income generation provided by leased assets.

Pricing European options on deferred annuities

This paper considers the pricing of European call options written on pure endowment and deferred life annuity contracts, also known as guaranteed annuity options. These contracts provide a guaranteed value at the maturity of the option. The contract valuation is dependent on the stochastic interest rate and mortality processes. We assume single-factor stochastic square-root processes for both the interest rate and mortality intensity, with mortality being a time-inhomogeneous process. We then derive the pricing partial differential equation (PDE) and the corresponding transition density PDE for options written on the pure endowment and deferred annuity contracts. The general solution of the pricing PDE is derived as a function of the transition density function. We solve the transition density PDE by first transforming it to a system of characteristic PDEs using Laplace transform techniques and then applying the method of characteristics. Once an explicit expression for the density function is found, we then use sparse grid quadrature techniques to generate European call option prices on the pure endowment and deferred annuity contracts. This approach can easily be generalised to other contracts which are driven by similar stochastic processes presented in this paper. We test the sensitivity of the option prices by varying independent parameters in our model. As option maturity increases, the corresponding option prices significantly increase. The effect of mispricing the guaranteed annuity value is analysed, as is the benefit of replacing the whole-life annuity with a term annuity to remove volatility of the old age population.

Actuarial present values of annuities under stochastic interest rate

Actuarial present values of annuities under stochastic interest rate

AN INTERNATIONAL COMPARISON OF LIFETIME INEQUALITY: HOW CONTINENTAL EUROPE RESEMBLES NORTH AMERICA

We compare earnings inequality and mobility across the United States, Canada, France, Germany and the United Kingdom during the late 1990s. A flexible model of earnings dynamics that isolates positional mobility within a stable earnings distribution is estimated. Earnings trajectories are then simulated, and lifetime annuity value distributions are constructed. Earnings mobility and employment risk are found to be positively correlated with base-year inequality. Taken together they produce more equalization in countries with high cross-section inequality such that the countries in our sample have more similar lifetime inequality levels than cross-section measures suggest.

Defined Benefit and Defined Contribution Retirement Plan Simulations

The focus of this paper is the effect of changes to employer sponsored retirement plans on employee retirement benefits. Today’s retirement benefits consist mainly of three types of plans: defined benefit (DB), defined contribution (DC), and “hybrid” plans. Many employers have changed the type of plan they offered in recent years. Specifically, there is a shift from DB plans to DC plans. A retirement benefit comparison is made between a DB plan and a DC plan under different scenarios which depend on years of work, market yield, interest rates, and predicted wage increases. Using simulation modeling, DB and DC benefits are compared over different career lengths for a worker with a starting salary of $50,000. Simulated fluctuations in annual market yield and average national wage increases are used to project DC balances. DB benefits are simulated using random fluctuations in both wage increases and interest rates used for lump sum conversions. The resulting simulated benefits show that DC plans are generally inferior to DB plans. In addition, simulated DC retirement account balances have a much higher standard deviation than the present value of traditional DB plan annuities. However, DB benefits that are converted to lump sums have standard deviations closer to those of DC lump sums due to the variability of interest rates used in the conversion of DB annuities to a lump sum.

Selecting stochastic mortality models for the Italian population

The future revision of capital requirements and a market-consistent valuation of non-hedgeable liabilities lead to an increasing attention on forecasting longevity trends. In this field, many methodologies focus on either modeling mortality or pricing mortality-linked securities (as longevity bonds). Following Lee–Carter method (proposed in 1992), actuarial literature has provided several extensions in order to consider different trends observed in European data set (e.g., the cohort effect). The purpose of the paper is to compare the features of main mortality models proposed over the years. Model selection became indeed a primary task with the aim to identify the “best” model. What is meant by best is controversial, but good selection techniques are usually based on a good balance between goodness of fit and simplicity. In this regard, different criteria, mainly based on residual and projected rates analysis, are here used. For the sake of comparison, main forecasting methods have been applied to deaths and exposures to risk of male Italian population. Weaknesses and strengths have been emphasized, by underlying how various models provide a different goodness of fit according to different data sets. At the same time, the quality and the variability of forecasted rates have been compared by evaluating the effect on annuity values. Results confirm that some models perform better than others, but no single model can be defined as the best method.

Interchangeability of the median operator with the present value operator

It is well known that the expected present value of a life annuity is smaller than the present value of an annuity certain with term equal to life expectancy. This result can be viewed as a consequence of the lack of interchangeability between the present value operator and the mathematical expectation operation. However, we prove that the median and present value operators can be interchanged; that is, the median of the present value of a life annuity equals the present value of an annuity certain whose term is the median additional years of life. At young ages and through late middle age, median additional years of life exceed life expectancy. Therefore, the median value of a life annuity exceeds an annuity certain paid to life expectancy which exceeds the expected present value of a life annuity - the fair price of a life annuity.

Pricing European Options on Deferred Insurance Contracts

This paper considers the pricing of European call options written on pure endowment and deferred life annuity contracts, also known as guaranteed annuity options. These contracts provide a guaranteed value at the maturity of the option. The contract valuation is dependent on the stochastic interest rate and mortality processes. We assume single-factor stochastic square-root processes for both the interest rate and mortality intensity, with mortality being a time-inhomogeneous process. We then derive the pricing partial differential equation (PDE) and the corresponding transition density PDE for options written on the pure endowment and deferred annuity contracts. The general solution of the pricing PDE is derived as a function of the transition density function. We solve the transition density PDE by first transforming it to a system of characteristic PDEs using Laplace transform techniques and then applying the method of characteristics. Once an explicit expression for the density function is found, we then use sparse grid quadrature techniques to generate European call option prices on the pure endowment and deferred annuity contracts. This approach can easily be generalised to other contracts which are driven by similar stochastic processes presented in this paper. We test the sensitivity of the option prices by varying independent parameters in our model. As option maturity increases, the corresponding option prices significantly increase. The effect of mispricing the guaranteed annuity value is analysed, as is the benefit of replacing the whole-life annuity with a term annuity to remove volatility of the old age population.

Medicaid Insurance in Old Age

Medicaid was primarily designed to protect and insure the poor. However, the poor tend to live much shorter lifespans and thus incur much lower medical expenses before death. In this paper we assess the insurance and redistributive properties of Medicaid, taking these dimensions of heterogeneity into account, for single retirees. The Medicaid recipiency rate for those at the bottom income quintile stays around 60%-70% throughout their retirement. In contrast, Medicaid recipiency by higher-income retirees is much lower but increases by age, especially after age 90. Our preliminary results show that the annuity value of Medicaid payments is a hump-shaped function of permanent income. People in the middle of the income distribution receive more than those at the top or the bottom. Once one takes into account that the rich live longer, Medicaid is even less redistribu- tive: in terms of present discounted value, the richest people receive almost as much the poorest ones, and the middle income people still benefit the most. Accounting for risk makes Medicaid less redistributive further still. Compensating differential calculations show that Medicaid insurance is valued most highly by the most rich, who have the most to lose.

Optimal commutable annuities to minimize the probability of lifetime ruin

We find the minimum probability of lifetime ruin of an investor who can invest in a market with a risky and a riskless asset and who can purchase a commutable life annuity. The surrender charge of a life annuity is a proportion of its value. Ruin occurs when the total of the value of the risky and riskless assets and the surrender value of the life annuity reaches zero. We find the optimal investment strategy and optimal annuity purchase and surrender strategies in two situations: (i) the value of the risky and riskless assets is allowed to be negative, with the imputed surrender value of the life annuity keeping the total positive; (ii) the value of the risky and riskless assets is required to be non-negative. In the first case, although the individual has the flexibility to buy or sell at any time, we find that the individual will not buy a life annuity unless she can cover all her consumption via the annuity and she will never sell her annuity. In the second case, the individual surrenders just enough annuity income to keep her total assets positive. However, in this second case, the individual’s annuity purchasing strategy depends on the size of the proportional surrender charge. When the charge is large enough, the individual will not buy a life annuity unless she can cover all her consumption, the so-called safe level. When the charge is small enough, the individual will buy a life annuity at a wealth lower than this safe level.

Fractional mortality rate based on rational interpolating method and its application in actuarial science

This paper attempts to introduce a new method with adjustable parameter for estimating the mortality of fractional age based on rational interpolating theory. The efficiency analysis of the method is given and some conditions the adjustable parameter should satisfy are given in order to meet the need of actuarial practice. We also analyze the relationship between our estimating method and the one based on UDD assumption—the most commonly used in actuarial study and practice. The result shows that the latter is just a special case of our results. Finally we apply our method to the calculations of actuarial present value of life insurance and annuities. Simulations are also done to give a clear comparison between traditional method and our method specified in this paper.

Markovian Approaches to Joint-Life Mortality

Many insurance products provide benefits that are contingent on the combined survival status of two lives. To value such benefits accurately, we require a statistical model for the impact of the survivorship of one life on another. In this paper we first set up two models, one Markov and one semi-Markov, to model the dependence between the lifetimes of a husband and wife. From the models we can measure the extent of three types of dependence: (1) the instantaneous dependence due to a catastrophic event that affect both lives, (2) the short-term impact of spousal death, and (3) the long-term association between lifetimes. Then we apply the models to a set of jointlife and last-survivor annuity data from a large Canadian insurance company. Given the fitted models, we study the impact of dependence on annuity values and examine the potential inaccuracy in pricing if we assume lifetimes are independent. Finally, we compare our Markovian models with two copula models considered in previous research on modeling joint-life mortality.