Statistical models of mortality impact on the pricing and reserving of pensions
Submitting InstitutionsUniversity of Edinburgh,
Unit of AssessmentMathematical Sciences
Summary Impact TypeEconomic
Research Subject Area(s)
Mathematical Sciences: Statistics
Summary of the impact
Research carried out from 2003 by Currie (Maxwell Institute) and his PhD
students Djeundje, Kirkby and Richards (also Longevitas), and
international collaborators Eilers and Durban, created new, flexible
smoothing and forecasting methods. These methods are now widely used by
insurance and pension providers to forecast mortality when determining
pricing and reserving strategy for pensions. The methods were incorporated
by the SME Longevitas in its forecasting package Projections Toolkit
launched in 2009. This generated impact in the form of £400K turnover for
Longevitas in licensing and consultancy fees, with further impact on the
pricing and reserving strategies on Longevitas's customers. Since 2010 the
methods have been adopted by the Office for National Statistics (ONS) to
make the forecasts required to underpin public policy in pensions, social
care and health and by The Continuous Mortality Investigation (CMI) to
model and provide forecasts on mortality to the pensions and insurance
industries. As a result, the research has changed practices in these
advisory agencies and in the insurance industry.
Pensions and annuities are future liabilities that depend on the future
course of mortality. Research by a team led by Currie (Maxwell Institute,
MI) has provided a suite of solutions to several of the modelling
challenges facing the insurance and pensions industry in their forecasting
Statistical research. In 2004, Currie, Durban (Carlos III Madrid)
and Eilers (Leiden) proposed a new approach to forecasting mortality that
uses a 2-dimensional smoothing model to reveal the underlying pattern in
mortality by both age and time, and to forecast this pattern in time .
Fitting the 2-dimensional model in  is computationally intensive and in
2006 the authors formulated an algorithm that improves computational time
by orders of magnitude . Mortality data are usually indexed by age of
death and year of death, and the methods described in  and  provided
an immediate modelling solution to this scenario. Further research by
Richards (Longevitas), Kirkby (MI) and Currie showed how the 2-dimensional
model could also be applied when data are indexed by age at death and year
of birth and demonstrated the importance of cohort effects in the
modelling and forecasting of mortality rates . In another strand of
research, Richards and Currie  in 2009 showed how to produce more
regular forecasts with the Lee-Carter model — a benchmark model widely
used to forecast mortality — improving its actuarial performance. A common
feature of mortality data is overdispersion (where the observed mortality
rates are more variable in age and time than predicted by a simple random
model). Djeundje (MI) and Currie  showed how the techniques developed
in  and  could be extended to accommodate overdispersion. The
forecasting of the mortality of the very old is of particular interest to
annuity and pension providers but presents additional challenges since
data quality can be poor at such ages. Currie formulated a new solution to
this problem using the approach and computational methods in  and .
Implementation for users. All the techniques described above have
been incorporated in the commercial package Projections Toolkit
developed and licensed by Longevitas, a software and consulting company.
The techniques proposed in [1-3] have also been implemented in the freely
available R package MortalitySmooth, developed within the Max
Planck Institute for Demographic Research.
Attribution. I. D. Currie has been a member of the Maxwell
Institute since 1973. J. Kirkby (graduated in 2009) and V. Djeundje Biatat
(graduated in 2011) were PhD students, both supervised by I. D. Currie and
funded by EPSRC and CMI. S. J. Richards completed a part time PhD at HWU
in 2012. M. Durban was at Carlos III Madrid and P. H. C. Eilers at Leiden.
References to the research
References marked with a * best indicate the quality of the research.
* Currie, I.D., Durban, M. and Eilers, P.H.C., Generalized linear
array models with applications to multidimensional smoothing, Journal
of the Royal Statistical Society, Series B, 68, 259-280
 Richards, S. J., Kirkby, J.G. and Currie, I.D., The importance of
year of birth in two-dimensional mortality data (with Discussion), British
Actuarial Journal, 12, 5-61 (2006). http://dx.doi.org/10.1017/S1357321700004682
 Richards, S.J., Currie, I.D. and Ritchie, G.P., A value-at-risk
framework for longevity trend risk. (with Discussion) Read before the
Institute and Faculty of Actuaries in Edinburgh and London (November
2012), British Actuarial Journal, Available on CJO 2013 http://dx.doi.org/10.1017/S1357321712000451
The work was supported by two PhD studentships (J. Kirkby, 2003-2006 and
V. Djeundje Biatat, 2008-2011) both jointly funded by the EPSRC and the
CMI (total funding £156K); EPSRC grant numbers GR/P02912 and EP/P504570/1
respectively. The work of Iain Currie was supported by four grants from
the Actuarial Profession during 2003-09, total value: £25K.
Details of the impact
Projections Toolkit. Significant impact has been achieved in the
form of increased turnover for Longevitas, an SME formed in 2006, which
offers its customers leading-edge software for modelling and analysing
demographic risks, including mortality, longevity and critical illness.
The increased turnover results from the licensing and marketing of a
software application — Projections Toolkit — which was developed
by Longevitas staff from code originally written by Currie. The Projections
Toolkit is an important tool in the service provided by Longevitas
to the pensions and insurance industry and embodies a wide range of
forecasting models — specifically the 2- dimensional models [1-3, 5] and
the Lee-Carter models . [text removed for publication.]
Impact on practices of advisory agencies. The research has
generated further impact through the uptake of the smoothing and
forecasting methods described in Section 2 by two bodies, the Office for
National Statistics and the Continuous Mortality Investigation, whose
respective remits includes the provision of statistical analyses for use
by government and by the pensions and insurance industries.
The Office for National Statistics (ONS) provides official
statistics on behalf of the UK government including the National
Population Projections (NPP) which impact strongly on government policy on
pensions, social care and health. Since 2006 the ONS has used the 2-
dimensional smoothing model to remove fluctuations from age to age and
year to year in formulating smoothed mortality surfaces for each gender
. During development of the new methodology, Currie provided direct
support to the Principal Methodologist involved at ONS. Our contribution
to the work of ONS is described in  which states (p4) that "Mortality
rates for the UK in each calendar year in the period 1961 to 2009 have
been smoothed to remove fluctuations from age to age and year to year,
using a new methodology" — a direct reference to their use of our 2-
dimensional smoothing model as described by them on p5: "A p-spline model
was then applied to the resulting crude mortality rates to produce a
fitted, smoothed mortality surface to the historical data for each
The Continuous Mortality Investigation (CMI) is funded by the
insurance industry and actuarial consultancies and has two main functions:
(i) the collection of claims and exposed-to-risk data from across the
insurance industry and pension schemes, the collation of these data by
source (for example, by type of insurance), and the creation of a
repository of the resulting mortality data sets; (ii) the modelling and
forecasting of the data in (i).
The underpinning research, which has been partially supported by the CMI
(see section 2), is now incorporated into their forecasting methodology
. Specifically, the research has provided the methods used in the CMI
model for smoothing the data by fitting a 2-dimensional P-spline age-cohort
model, as described in ; see the CMI 2010 Working paper .
The final model is used extensively by many insurance companies to assess
pricing and reserving for various classes of assurance and annuities, and
by pension schemes in valuing their liabilities for funding or risk
Sources to corroborate the impact
 Projections Toolkit: Board Member, Longevitas, will confirm the
central role played by the research in [1-6] in Projections Toolkit.
 Senior Methodologist, Office for National Statistics: will confirm
the use of the methodology by ONS.
 National Population Projections, 2010-based reference volume: Series
PP2, published by the ONS. See Chapter 4, `Mortality' for a description of
how the research is used by the ONS. http://www.ons.gov.uk/ons/rel/npp/national-population-projections/2010-based-reference-volume--series-pp2/mortality.html
 Continuous Mortality Investigation: Senior actuary with Barnett
Waddingham will confirm the use of the methodology by CMI.
 Continuous Mortality Investigation , The CMI mortality projections
model, `CMI 2010', Working Paper 49, November (2010).
See under CMI working papers on the CMI web site above; in particular,
section 5, p20.