Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T14:14:06.500Z Has data issue: false hasContentIssue false
  • English
  • Français

Mortality data reliability in an internal model

Published online by Cambridge University Press:  03 August 2020

Fabrice Balland ,
Alexandre Boumezoued Open the ORCID record for Alexandre Boumezoued [Opens in a new window] ,
Laurent Devineau ,
Marine Habart  and
Tom Popa
Fabrice Balland
Affiliation:
GIE AXA, 21 Avenue Matignon, 75008Paris, France
Alexandre Boumezoued*
Affiliation:
Milliman, 14 Avenue de la Grande Armée, 75017Paris, France
Laurent Devineau
Affiliation:
Milliman, 14 Avenue de la Grande Armée, 75017Paris, France
Marine Habart
Affiliation:
GIE AXA, 21 Avenue Matignon, 75008Paris, France
Tom Popa
Affiliation:
GIE AXA, 21 Avenue Matignon, 75008Paris, France
*
*Corresponding author. Email: alexandre.boumezoued@milliman.com
Get access Rights & Permissions [Opens in a new window]

Abstract

In 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.

Keywords

MortalityLongevityCohort effectSolvency 2Internal model
Type
Paper
Information
Annals of Actuarial Science , Volume 14 , Issue 2 , September 2020 , pp. 420 - 444
Copyright
© Institute and Faculty of Actuaries 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Boumezoued, A. (2020). Improving HMD mortality estimates with HFD fertility data. North American Actuarial Journal, 1–25.CrossRefGoogle Scholar
Boumezoued, A. & Devineau, L. (2017). Enjeux de fiabilité dans la construction des tables de mortalité nationales. L’Actuariel, janvier 2017.Google Scholar
Cairns, A.J.G., Blake, D. & Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73(4), 687–718.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A. & Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13(1), 1–35.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D., Dowd, K. & Kessler, A.R. (2016). Phantoms never die: living with unreliable population data. Journal of the Royal Statistical Society: Series A (Statistics in Society), 179(4), 975–1005.CrossRefGoogle Scholar
CEIOPS’ Advice for Level 2 Implementing Measures on Solvency II - Annex B Longevity risk calibration analysis. CEIOPS-DOC-42/09.Google Scholar
Currie, I.D., Durban, M. & Eilers, P.H.C. (2004). Smoothing and forecasting mortality rates. Statistical modelling, 4(4), 279–298. https://doi.org/10.1191/1471082X04st080oaCrossRefGoogle Scholar
Human Fertility Database. Max Planck Institute for Demographic Research (Germany) and Vienna Institute of Demography (Austria).). Available online at the address www.humanfertility.org [data downloaded on Jul-2016].Google Scholar
Human Mortality Database. University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Available online at the address www.mortality.org or www.humanmortality.de [data downloaded on 1-Sep-2015].Google Scholar
Lee, R.D. & Carter, L.R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
Plat, R. (2011). One-year value-at-risk for longevity and mortality. Insurance: Mathematics and Economics, 49(3), 462–470.Google Scholar
Quashie, A. & Denuit, M. (2005). Modèles d’extrapolation de la mortalité aux grands âges. Institut des Sciences Actuarielles et Institut de Statistique, Université Catholique de Louvain.Google Scholar
Renshaw, A.E. & Haberman, S. (2006). A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38(3), 556–570.Google Scholar
Richards, S.J. (2008). Detecting year-of-birth mortality patterns with limited data. Journal of the Royal Statistical Society, Series A, 171(1), 279–298.Google Scholar
Wilmoth, J.R., Andreev, K., Jdanov, D. & Glei, D.A. (2017). Methods Protocol for the Human Mortality Database. University of California, Berkeley, and Max Planck Institute for Demographic Research, Rostock. Available online at the address http://mortality.org [accessed 27-Nov-2017].Google Scholar