Stochastic modeling of financing longevity risk in pension insurance
AbstractThis work studies and develops tools to quantify and manage the risks and uncertainty relating to the pricing of annuities in the long run. To this end, an idealized Monte-Carlo simulation model is formulated, estimated and implemented, which enables one to investigate some typical pension and life insurance products. The main risks in pension insurance relate to investment performance and mortality/longevity development. We first develop stochastic models for equity and bond returns. The S&P 500 yearly total return is modeled by an uncorrelated and Normally distributed process to which exogenous Gamma distributed negative shocks arrive with Geometrically distributed interarrival times. This regime switching jump model takes into account the empirical observations of infrequent exceptionally large losses. The 5-year US government bond yearly total return is modeled as an ARMA(1,1) process after suitably log-transforming the returns. This model is able to generate long term interest rate cycles and allows rapid year-to-year corrections in the returns. We also address the parameter uncertainty in these models. We then develop a stochastic model for mortality. The chosen mortality forecasting model is the well-known model of Lee and Carter (1992), in which we use the Bayesian MCMC methods in the inference concerning the time index. Our analysis with a local version of the model showed that the assumptions of the Lee-Carter model are not fully compatible with Finnish mortality data. In particular we found that mortality has been lower than average for the cohort born in wartime. However, because the forecasts of these two models were not significantly different, we chose the more parsimonious Lee-Carter model. Although our main focus is on the total population data, we also analysed the data for males and females separately. Finally we build a flexible model for the dependence structure that allows us to generate stochastic scenarios in which mortality and economic processes are either uncorrelated, correlated or shock-correlated. By using the simulation model to generate stochastic pension cash-flows, we are then able to analyse the financing of longevity risk in pension insurance and the resulting risk management issues. This is accomplished via three case studies. Two of these concentrate on the pricing and solvency questions of a pension portfolio. The first study covers a single cohort of different sizes, and the second allows for multiple cohorts of annuitants. The final case study discusses individual pension insurance from the customer and long-term points of view. Realistic statistical long-term risk measurement is the key theme of this work, and so we compare our simulation results with the Value-at-Risk or VaR approach. The results show that the limitations of basic VaR approach must be carefully accounted for in applications. The VaR approach is the most commonly used risk measurement methodology in insurance and finance applications. For instance, it underlies the solvency capital requirement in Solvency II, which we also discuss in this work.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Bank of Finland in its series Scientific Monographs with number E:44/2012.
Length: 124 pages
Date of creation: 25 May 2012
Date of revision:
equities; stocks; jump model; bond; longevity; Lee-Carter model; stochastic mortality; cohort mortality; dependence model; asymmetric dependence; parameter uncertainty; stochastic annuity; pension; cohort size; solvency; internal model;
Find related papers by JEL classification:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
This paper has been announced in the following NEP Reports:
- NEP-AGE-2012-11-11 (Economics of Ageing)
- NEP-ALL-2012-11-11 (All new papers)
- NEP-DEM-2012-11-11 (Demographic Economics)
- NEP-FOR-2012-11-11 (Forecasting)
- NEP-HEA-2012-11-11 (Health Economics)
- NEP-IAS-2012-11-11 (Insurance Economics)
- NEP-ORE-2012-11-11 (Operations Research)
- NEP-RMG-2012-11-11 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer, vol. 38(4), pages 537-549, November.
- Greenberg,Edward, 2008.
"Introduction to Bayesian Econometrics,"
Cambridge University Press, number 9780521858717, October.
- Merton, Robert C., 1975.
"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
- Kroner, Kenneth F & Ng, Victor K, 1998. "Modeling Asymmetric Comovements of Asset Returns," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 817-44.
- Wu, Yangru & Zhang, Hua, 1996. "Mean Reversion in Interest Rates: New Evidence from a Panel of OECD Countries," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(4), pages 604-21, November.
- Chen, Joseph & Hong, Harrison & Stein, Jeremy C., 2001.
"Forecasting crashes: trading volume, past returns, and conditional skewness in stock prices,"
Journal of Financial Economics,
Elsevier, vol. 61(3), pages 345-381, September.
- Joseph Chen & Harrison Hong & Jeremy C. Stein, 2000. "Forecasting Crashes: Trading Volume, Past Returns and Conditional Skewness in Stock Prices," NBER Working Papers 7687, National Bureau of Economic Research, Inc.
- Alho, Juha M., 1990. "Stochastic methods in population forecasting," International Journal of Forecasting, Elsevier, vol. 6(4), pages 521-530, December.
- Juha M. Alho, 2008. "Annuity-Based Assessment of Uncertainty in Mortality," Revue économique, Presses de Sciences-Po, vol. 59(5), pages 927-940.
- Costantini, Mauro & Lupi, Claudio, 2007. "An analysis of inflation and interest rates. New panel unit root results in the presence of structural breaks," Economics Letters, Elsevier, vol. 95(3), pages 408-414, June.
- Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228 Elsevier.
- Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
- Alho, Juha M. & Hougaard Jensen, Svend E. & Lassila, Jukka & Valkonen, Tarmo, 2005. "Controlling the effects of demographic risks: the role of pension indexation schemes," Journal of Pension Economics and Finance, Cambridge University Press, vol. 4(02), pages 139-153, July.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Minna Nyman) or (Päivi Määttä).
If references are entirely missing, you can add them using this form.