This is the submitted version of the paper.This version of the publication may differ from the final published version. Permanent repository link AbstractIn any country, mortality rates and indices such as life expectancy usually differ across subpopulations, for example, defined by gender, geographic area or socio-economic variables (e.g. occupation, level of education, income). These differentials, and in particular those related to socio-economic circumstances, pose important challenges for the design of public policies for tackling social inequalities, as well as for the design of pension systems and the management of longevity risk in pension funds and annuity portfolios. We discuss the suitability for the modelling and forecasting of socio-economic differences in mortality of several multiple population extensions of the Lee-Carter model, including a newly introduced relative model based on the modelling of the mortality in socio-economic subpopulations alongside the mortality of a reference population. Using England mortality data for socioeconomic subpopulations defined using a deprivation index, we show that this new relative model exhibits the best results in terms of goodness of fit and ex-post forecasting performance. We then use this model to derive projections of deprivation specific mortality rates and life expectancies at pensioner ages and analyse the impact of socio-economic differences in mortality on the valuation of annuities.

In this paper we mirror the framework of generalised (non-)linear models to define the family of generalised Age-Period-Cohort stochastic mortality models which encompasses the vast majority of stochastic mortality projection models proposed to date, including the well-known Lee-Carter and Cairns-Blake-Dowd models. We also introduce the R package StMoMo which exploits the unifying framework of the generalised Age-Period-Cohort family to provide tools for fitting stochastic mortality models, assessing their goodness of fit and performing mortality projections. We illustrate some of the capabilities of the package by performing a comparison of several stochastic mortality models applied to the England and Wales population.

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent repository link ABSTRACTLongevity 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.

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In this paper we mirror the framework of generalized (non-)linear models to define the family of generalized age-period-cohort stochastic mortality models which encompasses the vast majority of stochastic mortality projection models proposed to date, including the well-known Lee-Carter and Cairns-Blake-Dowd models. We also introduce the R package StMoMo which exploits the unifying framework of the generalized age-period-cohort family to provide tools for fitting stochastic mortality models, assessing their goodnessof-fit and performing mortality projections. We illustrate some of the capabilities of the package by performing a comparison of several stochastic mortality models applied to the England and Wales population.