Solvency analysis and demographic risk measures

Assessing the cost of capital for longevity risk

Assessing Longevity Risk in a Portfolio of Life Annuities

Approximations for life annuity contracts in a stochastic financial environment

Tontines and life annuities both insure against longevity risk by guaranteeing (pension) income for life. The optimal choice between these two mortality-contingent claims depends on personal preferences for consumption and risk. And, while pure tontines are unavailable in the twenty-first century, the first longevity-contingent claim (and debt) issued by the English government in the late seventeenth century offered a choice between the two. This article analyzes financial and economic aspects of King William's 1693 tontine that have not received attention in the literature. In particular, it compares the stochastic present value (SPV) of the tontine vs the life annuity and discusses characteristics of investors who selected one versus the other. Finally, the article examines the issue of whether high reported tontine survival rates should be attributed to anti-selection or fraud. In sum, this article is an empirical examination of annuitization decisions made by actual investors in the late seventeenth century.

The paper deals with the solvency analysis through internal models in the case of a portfolio of life annuities, focusing on the interplay between stochastic interest rate dynamics and the survival evolution in time. This specific aspect is investigated basing the survival death rates on Poisson Lee Carter model approached according to the Iterative Procedure and two simulated approaches on the Poisson Lee Carter: the Standard Procedure and the Stratified Sampling Procedure. The financial aspect, particularly notable in portfolios with long duration and multiplicity of payments as in the considered case, is tackled assuming different stochastic hypotheses on the interest rates evolution. Aim of the paper is to deepen the reaction of solvency measures as the surplus index and the ruin probability to the specific financial and demographic scenario. The indexes are studied in different loading factor assumptions and several numerical applications illustrate the model setup.

From 'Benefits' to 'Guarantees': Looking at Life Insurance Products in a New Framework

Longevity risk is an important risk factor for payments of pension annuities. Securitization of this risk can offer great opportunities for hedging. The purpose of this article is to design longevity bonds, payments of which depend on the survival index of a certain population. Considering characteristics of the people survival and interest rates market, Feller process with jumps is used to model the death intensity to get a survival function. And the interest rate is described with Cox-Ingersoll-Ross(CIR) model. Due to the CAPM pricing methods rarely suit to the hypotheses of complete market, the paper uses Wang transform to value the bond in an incomplete market framework Finally, empirical study is conducted with data of Chinese life table.

Forward Mortality Rates in Discrete Time II: Longevity Risk and Hedging Strategies

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.

In life insurance analysis, weighing insured’s benefits and contributions which occur over time requires discounting those amounts to present value equivalents. Therefore, the choice of discount rate can be consequential for the valuation of insurance policies. Out of the functions making up the life insurance products, there seems to be no closed form numerical estimates for the interest rate intensity and present value functions. This identified problem may either be in favour of the insured or ortherwise. However, the practice favours the life insurer most in actuarial valuation under the deterministic parsimonious setting. Empirical evidence suggests that new theoretical model advances given the future uncertainty likely suggesting lower long-term rates. This evidence generally supports lowering discount rates under a feasible best guess based on the available financial information. This necessitates deriving a discount rate which can adjust for the fact that benefits are more valuable at present than in the future if policyholders prefer to buy cover now rather than wait or if insurers could be earning a positive return on invested incomes. In this study, the objectives is to develop model for the present value function under the Chebyshev polynomial series framework within the interval of orthogonality and then define some life table structures on the model. From our analytical constructions, as the argument of the polynomial series tends to, we obtain the present value function, which attempts to balance the interests of the policyholders and the life insurers.

This paper explores the extent to which retirees can and do insure themselves against longevity risk in private pension plans. We first review the theoretical and empirical results on the value of annuities, and discuss reasons why households may choose not to further insure themselves against longevity risk. We then analyze current trends in the private pension market, and find that the shift from defined benefit plans to defined contribution plans is likely to reduce annuitization rates among future retirees. This is driven primarily by the fact that the majority of DC plans, such as 401(k) plans, do not even offer participants a life annuity option at retirement. Thus, individuals who wish to annuitize generally must do so in the individual market where payouts are lower due to a healthier mortality pool. Hence, we can forecast that in the coming decades, absent institutional and regulatory changes, overall annuitization rates may fall and households may be increasingly exposed to the risk of outliving their financial resources, while the currently small private individual annuity market may witness significant growth. Finally, we discuss several policy options designed to increase annuitization of retirement resources.

We introduce a model for the mortality rates of multiple populations. To build the proposed model we investigate to what extent a common age effect can be found among the mortality experiences of several countries and use a common principal component analysis to estimate a common age effect in an age–period model for multiple populations. The fit of the proposed model is then compared to age–period models fitted to each country individually, and to the fit of the model proposed by Li and Lee (2005).Although we do not consider stochastic mortality projections in this paper, we argue that the proposed common age effect model can be extended to a stochastic mortality model for multiple populations, which allows to generate mortality scenarios simultaneously for all considered populations. This is particularly relevant when mortality derivatives are used to hedge the longevity risk in an annuity portfolio as this often means that the underlying population for the derivatives is not the same as the population in the annuity portfolio.

‘If there be one point free from obscurity in the Act of 1842 it is this, that the Legislature intended all traders, whether in groceries, annuities or other articles of commerce, to be assessed upon the same footing.’ Lord Watson in The Gresham Life Assurance Society υ. Styles.The main object is to discuss principles and therefore many points of detail will be omitted, however intrinsically interesting they may be. Satisfactory consideration of principles entails reference to all classes of business which involve an actuarial valuation (viz. life assurance and annuity business, sinking fund business and permanent sickness insurance business). Reference will be made to the National Defence Contribution and the Excess Profits Tax, which are based upon income-tax legislation. The subject in mind is the relation of such taxation to insurance business and funds of the classes mentioned, as distinct from other aspects of income tax which an insurance office encounters, and it will be considered solely from the point of view of an office established in the United Kingdom which transacts business only in the United Kingdom. In view of the paper by Messrs S. J. Rowland and F. H. Wales on ‘The Taxation of the Annuity Fund’ (March 1937, J.I.A. Vol. LXVIII), only brief reference will be made to annuity business, and it will be assumed that it is unnecessary, in describing taxation processes, to include explanations or qualifying phrases on account of annuity business.

Longevity risk in portfolios of pension annuities

Improving Longevity and Mortality Risk Models with Common Stochastic Long-Run Trends