Predicting Mortality Rates and Longevity Using Cains -Blake-Dowd Model
Article Sidebar
Main Article Content
Pension schemes and annuity providers frequently guarantee their retirement payouts until the retirees' deaths. As a result of longer life expectancies and declining rates of death in old age, trends in mortality and longevity have become evident. Academicians and actuaries have been forced to concentrate their research on mortality and longevity concerns in particular as a result of this. Instead of a provident fund, the new National Social Security Fund Act Number 45 of 2013 established a pension fund that is a requirement for every employee. Annuity service providers are exposed to the longevity risk when the scheme's participants retire. For pricing and reserving, appropriate modeling tools or projected life tables are required. In comparison to deterministic models, which were based on projected present values, stochastic models allow a variety of risk causes and components as well as pertinent effect on portfolio performance. The long term mean level of Longevity has become more uncertain exposing the annuity service providers such as assurance companies and states to the risk of uncertainty after retirement. Most industrialized countries' national security systems, pension plans, and annuity providers have revised their mortality tables to account for longevity risks due to decline mortality rates and rising life expectancy. Kenya is one of the developing nations that has seen a drop-in death rates and a rise in life expectancy recently. Since developing nations choose to take the longevity risk into account when pricing and reserving annuities because such long term mean level in mortality rates declines and increases life expectancy, particularly at retirement age, pose risks to annuity service providers and pension plans that has been pricing annuities based on mortality tables that do not take these trends into account. The stochastic aspect of mortality was ignored by earlier actuarial models used to estimate trends. The actuary will therefore likely be interested in knowing how the future mortality trend utilizing stochastic models affects annuity pricing and reserve. Demographers and actuaries have since employed a variety of stochastic methods to forecast mortality while examining a variety of stochastic model ranges. The CBD stochastic model, which was the first to take longer life expectancies into account, is now extensively used, and a number of expansions and adjustments have been suggested to stop the major characteristics of mortality intensity. The CBD model, developed by Andrew Cairn, David Blake, and Kevin Dowd, is being used in this study to fit mortality rates, forecast mortality trends, using least square method and then calculate projections for life expectancy. Regarding the longevity risk, we take into account the possibilities of computing annuity benefits by connecting the benefits to actual mortality and calculating the present value on annuities. The results of the study showed that, the CBD model can be used to forecast mortality rates where parameters estimating the CBD model are performed using the bivariate random walk (drift).
Downloads
Downloads
References
Cairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., & Balevich, I. (2009). A qualitative comparison of stochastic mortality models using data from England and Wales and the United States. Insurance: Mathematics and Economics, 44(3), 87-101. https://doi.org/10.1016/j.insmatheco.2008.09.004 DOI: https://doi.org/10.1016/j.insmatheco.2008.09.004
Antolin, P. (2007). Longevity risk and private pensions. OECD Working Papers on Insurance and Private Pensions, No. 3. OECD Publishing. https://doi.org/10.1787/261260613084 DOI: https://doi.org/10.1787/261260613084
Brockwell, P. J., & Davis, R. A. (2002). Introduction to time series and forecasting. Springer. DOI: https://doi.org/10.1007/b97391
Brouhns, N., Denuit, M., & Van Keilegom, I. (2005). Bootstrapping the Poisson log-bilinear model for mortality forecasting. Scandinavian Actuarial Journal, 2005(3), 212-224. https://doi.org/10.1080/03461230510007725 DOI: https://doi.org/10.1080/03461230510009754
Cairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., & Balevich, I. (2008). Modelling and management of mortality risk: A review. Risk & Insurance, 75(4), 671-699. https://doi.org/10.1111/j.1539-6975.2008.00261.
O'Brien, C. D. (2009). The U.K. with-profits life insurance industry: A market analysis. British Actuarial Journal, 15, 747-777. Https://doi.org/10.1017/S1357321700000275 DOI: https://doi.org/10.1017/S135732170000578X
Currie, I. D. (2011). Modelling and forecasting the mortality of the very old. Astin Bulletin, 41(1), 1-24. https://doi.org/10.2143/AST.41.1.2116790
Currie, I. D., Durban, M., & Eilers, P. H. C. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4(4), 279-298. https://doi.org/10.1191/1471082X04st073oa DOI: https://doi.org/10.1191/1471082X04st080oa
Eckart, C., & Young, G. (1936). The approximation of one matrix by another of lower rank. Psychometrika, 1(3), 211-218. https://doi.org/10.1007/BF02288367 DOI: https://doi.org/10.1007/BF02288367
Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11(2), 89-102. https://doi.org/10.1214/ss/1038425655 DOI: https://doi.org/10.1214/ss/1038425655
Pitacco, E. (2004). Longevity risk in living benefits. In E. Fornero & E. Luciano (Eds.), Developing an annuity market in Europe (pp. 132-167). Edward Elgar Publishing. DOI: https://doi.org/10.4337/9781035305049.00013
Booth, H., & Tickle, L. (2008). Mortality modelling and forecasting: A review of methods. Annals of Actuarial Science, 3(1), 3-43. https://doi.org/10.1017/S1748499500000440 DOI: https://doi.org/10.1017/S1748499500000440
Human Mortality Database. (2014). University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Retrieved from www.mortality.org
Hunt, A., & Blake, D. (2014). Identifiability in age/period mortality models. Journal of the Royal Statistical Society: Series A (Statistics in Society), 177(4), 919-937. https://doi.org/10.1111/rssa.12041 DOI: https://doi.org/10.1111/rssa.12041
Lee, R., & Carter, L. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659-671. https://doi.org/10.2307/2290201 DOI: https://doi.org/10.1080/01621459.1992.10475265
Macdonald, A. S., Gallop, A. P., Miller, K. A., Richards, S. J., Shah, R., & Willets, R. C. (2005). Projecting future mortality: Towards a proposal for a stochastic methodology. Continuous Mortality Investigation Bureau Working Paper No. 15.
Pitacco, E., Denuit, M., Haberman, S., & Oliveira, A. (2009). Modelling longevity dynamics for pensions and annuity business. Springer. DOI: https://doi.org/10.1093/oso/9780199547272.001.0001
This work is licensed under a Creative Commons Attribution 4.0 International License.
All articles published in our journal are licensed under CC-BY 4.0, which permits authors to retain copyright of their work. This license allows for unrestricted use, sharing, and reproduction of the articles, provided that proper credit is given to the original authors and the source.