scholarly journals Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives

Risks ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 2 ◽  
Author(s):  
Man Chung Fung ◽  
Katja Ignatieva ◽  
Michael Sherris
Keyword(s):  
Risk Premium ◽  
Mortality Data ◽  
Longevity Risk ◽  
Stochastic Mortality ◽  
Life Annuity ◽  
Analytical Formulae ◽  
Life Annuities ◽  
Longevity Swap ◽  
Stochastic Mortality Model ◽  
Benefits And Costs

This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap for a life annuity portfolio. Although longevity swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, provide more effective downside protection. A tractable stochastic mortality model with age dependent drift and volatility is developed and analytical formulae for prices of longevity derivatives are derived. The model is calibrated using Australian mortality data. The hedging of the life annuity portfolio is comprehensively assessed for a range of assumptions for the longevity risk premium, the term to maturity of the hedging instruments, as well as the size of the underlying annuity portfolio. The results compare the risk management benefits and costs of longevity derivatives with linear and nonlinear payoff structures.

scholarly journals Mortality data reliability in an internal model

2020 ◽  
Vol 14 (2) ◽  
pp. 420-444
Author(s):  
Fabrice Balland ◽  
Alexandre Boumezoued ◽  
Laurent Devineau ◽  
Marine Habart ◽  
Tom Popa
Keyword(s):  
Data Quality ◽  
Internal Model ◽  
Mortality Rates ◽  
Solvency Ii ◽  
West Germany ◽  
Mortality Data ◽  
Longevity Risk ◽  
Capital Requirement ◽  
Stochastic Mortality ◽  
The Impact

AbstractIn this paper, we discuss the impact of some mortality data anomalies on an internal model capturing longevity risk in the Solvency 2 framework. In particular, we are concerned with abnormal cohort effects such as those for generations 1919 and 1920, for which the period tables provided by the Human Mortality Database show particularly low and high mortality rates, respectively. To provide corrected tables for the three countries of interest here (France, Italy and West Germany), we use the approach developed by Boumezoued for countries for which the method applies (France and Italy) and provide an extension of the method for West Germany as monthly fertility histories are not sufficient to cover the generations of interest. These mortality tables are crucial inputs to stochastic mortality models forecasting future scenarios, from which the extreme 0.5% longevity improvement can be extracted, allowing for the calculation of the solvency capital requirement. More precisely, to assess the impact of such anomalies in the Solvency II framework, we use a simplified internal model based on three usual stochastic models to project mortality rates in the future combined with a closure table methodology for older ages. Correcting this bias obviously improves the data quality of the mortality inputs, which is of paramount importance today, and slightly decreases the capital requirement. Overall, the longevity risk assessment remains stable, as well as the selection of the stochastic mortality model. As a collateral gain of this data quality improvement, the more regular estimated parameters allow for new insights and a refined assessment regarding longevity risk.

scholarly journals Comparison of Stochastic Mortality Model for Wider Age Range

MATEMATIKA ◽  
2018 ◽  
Vol 34 (2) ◽  
pp. 227-233
Author(s):  
Siti Rohani Mohd Nor ◽  
Fadhilah Yusof ◽  
Arifah Bahar
Keyword(s):  
Risk Exposure ◽  
Longevity Risk ◽  
Model Structure ◽  
Research Directions ◽  
Linear Pattern ◽  
Stochastic Mortality ◽  
Mortality Model ◽  
New Research ◽  
Age Range ◽  
Stochastic Mortality Model

The incorporation of non-linear pattern of early ages has opened new research directions on improving the existing stochastic mortality model structure. Several authors have outlined the importance of encompassing the full age range in dealing with longevity risk exposure by not to ignore the dependence between young and old age. In this study, we consider the two extensions of Cairns, Blake and Dowd model that incorporate the irregularity profile seen at the mortality of lower ages which are Plat and O’Hare and Li. The models’ performances in terms of in-sample fitting and out-sample forecasts were examined and compared. The results indicated that O’Hare and Li model performs better as compared to Plat model

Portfolio choice and longevity risk in the late seventeenth century: a re-examination of the first English tontine

2014 ◽  
Vol 21 (3) ◽  
pp. 225-258 ◽  
Author(s):  
Moshe A. Milevsky
Keyword(s):  
Seventeenth Century ◽  
Portfolio Choice ◽  
Survival Rates ◽  
Optimal Choice ◽  
First Century ◽  
Longevity Risk ◽  
Empirical Examination ◽  
Pension Income ◽  
Life Annuity ◽  
Life Annuities

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.

Mortality and smoking prevalence: An empirical investigation in ten developed countries

2013 ◽  
Vol 18 (2) ◽  
pp. 452-466 ◽  
Author(s):  
Torsten Kleinow ◽  
Andrew J.G. Cairns
Keyword(s):  
Smoking Prevalence ◽  
Empirical Investigation ◽  
Developed Countries ◽  
Mortality Rates ◽  
Mortality Data ◽  
Death Rates ◽  
Stochastic Mortality ◽  
Mortality Model ◽  
Stochastic Mortality Model ◽  
Country Specific

AbstractWe investigate the link between death rates and smoking prevalence in ten developed countries with the aim of using smoking prevalence data to explain differences in country-specific death rates. A particular problem in building a stochastic mortality model based on smoking prevalence is that there are in general no separate mortality data for smokers and non-smokers available. We show how we can estimate mortality rates for smokers and non-smokers using information about the smoking prevalence in a number of developed countries, and making an additional assumption about the death rates of smokers. We consider this empirical investigation to be the first step towards a consistent mortality model for multiple populations, which will require modelling of country specific differences in mortality, as well as non-smokers’ and smokers’ mortality rates.

PRICING AND SOLVENCY OF VALUE-MAXIMIZING LIFE ANNUITY PROVIDERS

2013 ◽  
Vol 44 (1) ◽  
pp. 39-61 ◽  
Author(s):  
Maathumai Nirmalendran ◽  
Michael Sherris ◽  
Katja Hanewald
Keyword(s):  
Solvency Ii ◽  
Default Probability ◽  
Product Demand ◽  
Stochastic Mortality ◽  
Life Insurers ◽  
Life Annuity ◽  
Product Pricing ◽  
One Year ◽  
Life Annuities ◽  
The Impact

AbstractThis paper provides a detailed quantitative assessment of the impact of capital and default probability on product pricing and shareholder value for a life insurer providing life annuities. A multi-period cash flow model, allowing for stochastic mortality and asset returns, imperfectly elastic product demand, as well as frictional costs, is used to derive value-maximizing capital and pricing strategies for a range of one-year default probability levels reflecting differences in regulatory regimes including Solvency II. The model is calibrated using realistic assumptions. The sensitivity of results is assessed. The results show that value-maximizing life insurers should target higher solvency levels than the Solvency II regulatory one-year 99.5% probability under assumptions of reasonable levels of policyholder's aversion to insolvency risk. Even in the case of less restrictive solvency probabilities, policyholder price elasticity and solvency preferences are shown to be important factors for a life insurer's value-maximizing strategy.

scholarly journals Mandatory annuitization and money's worth: evidence from Singapore

2021 ◽  
pp. 1-20
Author(s):  
Joelle H. Fong ◽  
Jackie Li
Keyword(s):  
Expected Value ◽  
Longevity Risk ◽  
Future Trends ◽  
The Past ◽  
The Future ◽  
Population Mortality ◽  
Mortality Improvement ◽  
Life Annuities ◽  
Compulsory Purchase ◽  
The Impact

Abstract This paper examines the impact of uncertainties in the future trends of mortality on annuity values in Singapore's compulsory purchase market. We document persistent population mortality improvement trends over the past few decades, which underscores the importance of longevity risk in this market. Using the money's worth framework, we find that the life annuities delivered expected payouts valued at 1.019–1.185 (0.973–1.170) per dollar of annuity premium for males (females). Even in a low mortality improvement scenario, the annuities provide an expected value exceeding 0.950. This suggests that participants in the national annuity pool have access to attractively priced annuities, regardless of sex, product, and premium invested.

scholarly journals The Reciprocal Generalized Inverse Gaussian Frailty with Application in Life Annuity Business

2020 ◽  
pp. 112-131
Author(s):  
Walter Onchere ◽  
Richard Tinega ◽  
Patrick Weke ◽  
Jam Otieno
Keyword(s):  
Simulation Study ◽  
Unobserved Heterogeneity ◽  
Survival Curve ◽  
Gaussian Model ◽  
Frailty Models ◽  
Residual Lifetime ◽  
Longevity Risk ◽  
Inverse Gaussian ◽  
Life Annuity ◽  
Valuation Of Life

Aims: As shown in literature, several authors have adopted various individual frailty mixing distributions as a way of dealing with possible heterogeneity due to unobserved covariates in a group of insurers. This research contribution is to generalize the frailty mixing distribution to nest other classes of frailty distributions not in literature and apply the proposed distributions in valuation of life annuity business. Methodology: A simulation study is done to assess the performance of the aforementioned models. The baseline parameters is estimated using Bayesian Inference and a better model is suggested for valuation of life annuity business. Results: As a result of generalizing the frailty some new classes of frailty distributions are constructed such as; the Reciprocal Inverse Gaussian Frailty, the Inverse Gamma Frailty, the Harmonic Frailty and the Positive Hyperbolic Frailty. From the simulation study, the proposed new frailty models shows that ignoring frailty leads to an underestimation of future residual lifetime since the survival curve shifts to the right when heterogeneity is accounted for. This is consistent with frailty literature. The Reciprocal Inverse Gaussian model closely represents the Association of Kenya Insurers graduated rates with a slight increase in survival due to longevity risk. Conclusion: The proposed new frailty models show an increase in the insurers expected liability when unobserved heterogeneity is accounted for. This is consistent with frailty literature and thus can be applied to avoid underestimating the insurer’s liability in the context of life annuity business. The RIG model as proposed in estimating future liability by directly adjusting the AKI mortality rates shows an increase in longevity risk. The extent of heterogeneity of the insured group determines the level of risk. The RIG frailties should be considered for multivariate cases where the insureds are clustered in groups.

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