Bayesian Poisson Log-Bilinear Mortality Projections

Mortality projections are major concerns for public policy, social security and private insurance. This paper implements a Bayesian log-bilinear Poisson regression model to forecast mortality. Computations are carried out using Markov Chain Monte Carlo methods in which the degree of smoothing is learnt from the data. Comparisons are made with the approach proposed by Brouhns, Denuit & Vermunt (2002a,b), as well as with the original model of Lee & Carter (1992)

On age-period-cohort parametric mortality rate projections

An enhanced version of the Lee–Carter modelling approach to mortality forecasting, which has been extended to include an age modulated cohort index in addition to the standard age modulated period index, is described and tested for prediction robustness. Life expectancy and annuity value predictions, at pensioner ages and for various periods are compared, both with and without the age modulated cohort index, for the England & Wales male mortality experience. The simulation of prediction intervals for these indices of interest is discussed in detail

Forecasting mortality in subpopulations using Lee-Carter type models: A comparison

The relative performance of multipopulation stochastic mortality models is investigated. When targeting mortality rates, we consider five extensions of the well known Lee–Carter single population extrapolative approach. As an alternative, we consider similar structures when mortality improvement rates are targeted. We use a dataset of deaths and exposures of Italian regions for the years 1974–2008 to conduct a comparison of the models, running a battery of tests to assess the relative goodness of fit and forecasting capability of different approaches. Results show that the preferable models are those striking a balance between complexity and flexibility

On the effectiveness of natural hedging for insurance companies and pension plans

Natural hedging is one possible method to reduce longevity risk exposure for an annuity provider or a pension plan. In this paper, we provide an assessment of the effectiveness of natural hedging between annuity and life products, using the correlated Poisson Lee–Carter model, Poisson common factor model, product-ratio model, and historical simulation. Our analysis is based on the mortality experience of UK assured lives, pensioners, and annuitants, and the national population of England and Wales. We consider a range of different scenarios, and find that the level of risk reduction is significant in general, with an average of around 60%. These results have important implications for those insurers, reinsurers, and pension plan sponsors who are seeking ways to hedge their unwanted risk exposures

Sex-specific mortality forecasting for UK countries: a coherent approach

This paper introduces a gender specific model for the joint mortality projection of three countries (England and Wales combined, Scotland, and Northern Ireland) of the United Kingdom. The model, called 2-tier Augmented Common Factor model, extends the classical Lee and Carter [26] and Li and Lee [32] models, with a common time factor for the whole UK population, a sex specific period factor for males and females, and a specific time factor for each country within each gender. As death counts in each subpopulation are modelled directly, a Poisson framework is used. Our results show that the 2-tier ACF model improves the in-sample fitting compared to the use of independent LC models for each subpopulation or of independent Li and Lee models for each couple of genders within each country. Mortality projections also show that the 2-tier ACF model produces coherent forecasts for the two genders within each country and different countries within each gender, thus avoiding the divergence issues arising when independent projections are used. The 2-tier ACF is further extended to include a cohort term to take into account the faster improvements of the UK ‘golden generation’

A comparative study of two population models for the assessment of basis risk in longevity hedges

Longevity swaps have been one of the major success stories of pension scheme derisking in recent years. However, with some few exceptions, all of the transactions to date have been bespoke longevity swaps based upon the mortality experience of a portfolio of named lives. In order for this market to start to meet its true potential, solutions will ultimately be needed that provide protection for all types of members, are cost effective for large and smaller schemes, are tradable, and enable access to the wider capital markets. Index-based solutions have the potential to meet this need; however concerns remain with these solutions. In particular, the basis risk emerging from the potential mismatch between the underlying forces of mortality for the index reference portfolio and the pension fund/annuity book being hedged is the principal issue that has, to date, prevented many schemes progressing their consideration of index-based solutions. Two-population stochastic mortality models offer an alternative to overcome this obstacle as they allow market participants to compare and project the mortality experience for the reference and target populations and thus assess the amount of demographic basis risk involved in an index-based longevity hedge. In this paper, we systematically assess the suitability of several multi-population stochastic mortality models for assessing basis risks and provide guidelines on how to use these models in practical situations paying particular attention to the data requirements for the appropriate calibration and forecasting of such models

Pricing reverse mortgages in Spain

[EN] In Spain, as in other European countries, the continuous ageing of the population creates a need for long-term care services and their financing. However, in Spain the development of this kind of services is still embryonic. The aim of this article is to obtain a calculation method for reverse mortgages in Spain based on the fit and projection of dynamic tables for Spanish mortality, using the Lee and Carter model. Mortality and life expectancy for the next 20 years are predicted using the fitted model, and confidence intervals are obtained from the prediction errors of parameters for the mortality index of the model. The last part of the article illustrates an application of the results to calculate the reverse mortgage model promoted by the Spanish Instituto de Crédito Oficial (Spanish State Financial Agency), for which the authors have developed a computer application.The authors are indebted to Jose Garrido, whose suggestions improved the original manuscript, and to the anonymous referee for his/her valuable comments. This work was partially supported by grants from the MEyC (Ministerio de Educacio´n y Ciencia, Spain), projects MTM2010- 14961 and MTM2008-05152.Debón Aucejo, AM.; Montes, F.; Sala, R. (2013). Pricing reverse mortgages in Spain. European Actuarial Journal. 3:23-43. https://doi.org/10.1007/s13385-013-0071-yS23433Blay-Berrueta D (2007) Sistemas de cofinaciaciación de la dependencia: seguro privado frente a hipoteca inversa. Cuadernos de la Fundación, Fundación Mapfre Estudios, Madrid.Booth H (2006) Demographic forecasting: 1980 to 2005 in review. 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Bayesian mortality forecasting with overdispersion

The ability to produce accurate mortality forecasts, accompanied by a set of representative uncertainty bands, is crucial in the planning of public retirement funds and various life-related businesses. In this paper, we focus on one of the drawbacks of the Poisson Lee–Carter model (Brouhns et al., 2002) that imposes mean–variance equality, restricting mortality variations across individuals. Specifically, we present two models to potentially account for overdispersion. We propose to fit these models within the Bayesian framework for various advantages, but primarily for coherency. Markov Chain Monte Carlo (MCMC) methods are implemented to carry out parameter estimation. Several comparisons are made with the Bayesian Poisson Lee–Carter model (Czado et al., 2005) to highlight the importance of accounting for overdispersion. We demonstrate that the methodology we developed prevents over-fitting and yields better calibrated prediction intervals for the purpose of mortality projections. Bridge sampling is used to approximate the marginal likelihood of each candidate model to compare the models quantitatively