Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-22T13:10:08.287Z Has data issue: false hasContentIssue false
  • English
  • Français

MODELING THE MORTALITY TREND UNDER MODERN SOLVENCY REGIMES

Published online by Cambridge University Press:  10 October 2013

Matthias Börger ,
Daniel Fleischer  and
Nikita Kuksin
Matthias Börger*
Affiliation:
Institute of Insurance, Ulm University & Institute for Finance and Actuarial Sciences (ifa), Ulm Helmholtzstraße 22, 89081 Ulm, Germany Phone: +49 731 50 31257, Fax: +49 731 50 31239
Daniel Fleischer
Affiliation:
Swiss Reinsurance Company Ltd Mythenquai 50/60, 8022 Zurich, Switzerland
Nikita Kuksin
Affiliation:
Swiss Reinsurance Company Ltd Mythenquai 50/60, 8022 Zurich, Switzerland
*
E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Stochastic modeling of mortality/longevity risks is necessary for internal models of (re)insurers under the new solvency regimes, such as Solvency II and the Swiss Solvency Test. In this paper, we propose a mortality model which fulfills all requirements imposed by these regimes. We show how the model can be calibrated and applied to the simultaneous modeling of both mortality and longevity risk for several populations. The main contribution of this paper is a stochastic trend component which explicitly models changes in the long-term mortality trend assumption over time. This allows to quantify mortality and longevity risk over the one-year time horizon prescribed by the solvency regimes without relying on nested simulations. We illustrate the practical ability of our model by calculating solvency capital requirements for some example portfolios, and we compare these capital requirements with those from the Solvency II standard formula.

Keywords

Stochastic mortalitymortality trend risklongevity risksolvencyone-year view
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 44 , Issue 1 , January 2014 , pp. 1 - 38
Copyright
Copyright © ASTIN Bulletin 2013 

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

Börger, M. (2010) Deterministic shock vs. stochastic value-at-risk – an analysis of the Solvency II standard model approach to longevity risk. Blätter der DGVFM, 31, 225–259.CrossRefGoogle Scholar
Cairns, A., Blake, D. and Dowd, K. (2006) A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance, 73, 687–718.CrossRefGoogle Scholar
Cairns, A., Blake, D. and Dowd, K. (2008) Modelling and management of mortality risk: A review. Scandinavian Actuarial Journal, 2, 79–113.CrossRefGoogle Scholar
Cairns, A., Blake, D., Dowd, K., Coughlan, G. and Khalaf-Allah, M. (2011) Bayesian stochastic mortality modelling for two populations. ASTIN Bulletin, 41, 29–59.Google Scholar
Coughlan, G., Khalaf-Allah, M., Ye, Y., Kumar, S., Cairns, A., Blake, D. and Dowd, K. (2011) Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness. North American Actuarial Journal, 15, 150–176.CrossRefGoogle Scholar
Currie, I., Durban, M. and Eilers, P. (2004) Smoothing and forecasting mortality rates. Statistical Modelling, 4, 279–298.CrossRefGoogle Scholar
Devineau, L. and Loisel, S. (2009) Risk aggregation in Solvency II: How to converge the approaches of the internal models and those of the standard formula? Bulletin Français d'Actuariat, 18, 107–145.Google Scholar
Doff, R. (2008) A critical analysis of the Solvency II proposals. The Geneva Papers on Risk and Insurance Issues and Practice, 33, 193–206.CrossRefGoogle Scholar
Dowd, K., Cairns, A., Blake, D., Coughlan, G. and Khalaf-Allah, M. (2011) A gravity model of mortality rates for two related populations. North American Actuarial Journal, 15, 334–356.CrossRefGoogle Scholar
Eling, M., Gatzert, N. and Schmeiser, H. (2008) The Swiss Solvency Test and its market implications. The Geneva Papers on Risk and Insurance Issues and Practice, 33, 418–439.CrossRefGoogle Scholar
Eling, M., Schmeiser, H. and Schmit, J. (2007) The Solvency II process: Overview and critical analysis. Risk Management and Insurance Review, 10, 69–85.CrossRefGoogle Scholar
Engle, R. and Granger, C. (1987) Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55, 251–276.CrossRefGoogle Scholar
Gardner, E. (2006) Exponential smoothing: The state of the art – Part II. International Journal of Forecasting, 22, 637–666.CrossRefGoogle Scholar
Hari, N., De Waegenaere, A., Melenberg, B. and Nijman, T. (2008) Longevity risk in portfolios of pension annuities. Insurance: Mathematics and Economics, 42, 505–519.Google Scholar
Holzmüller, I. (2009) The United States RBC standards, Solvency II and the Swiss Solvency Test: A comparative assessment. The Geneva Papers on Risk and Insurance Issues and Practice, 34, 56–77.CrossRefGoogle Scholar
Hunt, A. and Blake, D. (2013) A general procedure for constructing mortality models. Working Paper n. 1301, Pensions Institute.Google Scholar
Hyndman, R., Booth, H. and Yasmeen, F. (2011) Coherent mortality forecasting: The product-ratio method with functional time series models. Working Paper n. 01/11, Monash University.Google Scholar
Jarner, S. and Kryger, E. (2011) Modelling adult mortality in small populations: The SAINT model. ASTIN Bulletin, 41, 377–418.Google Scholar
Lee, R. and Miller, T. (2001) Evaluating the performance of the Lee-Carter method for forecasting mortality. Demography, 38, 537–549.CrossRefGoogle ScholarPubMed
Li, J. and Hardy, M. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15, 177–200.CrossRefGoogle Scholar
Li, N. and Lee, R. (2005) Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 42, 575–594.CrossRefGoogle ScholarPubMed
Olivieri, A. (2011) Stochastic mortality: Experience-based modeling and application issues consistent with Solvency 2. European Actuarial Journal, 1, 101–125.CrossRefGoogle Scholar
Olivieri, A. and Pitacco, E. (2008a) Solvency requirements for life annuities: Some comparisons. Working Paper, University of Parma and University of Trieste.Google Scholar
Olivieri, A. and Pitacco, E. (2008b) Stochastic mortality: The impact on target capital. CARFIN Research Paper, University Bocconi.Google Scholar
Plat, R. (2009) On stochastic mortality modeling. Insurance: Mathematics and Economics, 45, 393–404.Google Scholar
Plat, R. (2011) One-year value-at-risk for longevity and mortality. Insurance: Mathematics and Economics, 49.Google Scholar
Richards, S., Currie, I. and Ritchie, G. (2012) A value-at-risk framework for longevity trend risk. Working Paper, Longevitas Ltd, Edinburgh.Google Scholar
Steffen, T. (2008) Solvency II and the work of CEIOPS. The Geneva Papers on Risk and Insurance Issues and Practice, 33, 60–65.CrossRefGoogle Scholar
Stevens, R., De Waegenaere, A. and Melenberg, B. (2010) Calculating capital requirements for longevity risk in life insurance products. Using an internal model in line with Solvency II. Working Paper, Tilburg University.Google Scholar
Swiss Federal Office of Private Insurance. (2006) Technical Document on the Swiss Solvency Test. Available at www.finma.ch.Google Scholar