Stochastic modeling of financing longevity risk in pension insurance
This 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.
|Date of creation:||25 May 2012|
|Date of revision:|
|Contact details of provider:|| Postal: Bank of Finland, P.O. Box 160, FI-00101 Helsinki, Finland|
Web page: http://www.suomenpankki.fi/en/
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- Philippe Robert-Demontrond & R. Ringoot, 2004. "Introduction," Post-Print halshs-00081823, HAL.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Alho, Juha M., 1990. "Stochastic methods in population forecasting," International Journal of Forecasting, Elsevier, vol. 6(4), pages 521-530, December.
- 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.
- Juha M. Alho, 2008. "Annuity-Based Assessment of Uncertainty in Mortality," Revue économique, Presses de Sciences-Po, vol. 59(5), pages 927-940.
- Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
- 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.
- Hans-Ulrich Derlien & B. Guy Peters, 2008. "Introduction," Chapters, in: The State at Work, Volume 2, chapter 1 Edward Elgar Publishing.
- 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.
- Engle, Robert & Granger, Clive, 2015.
"Co-integration and error correction: Representation, estimation, and testing,"
Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
- 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.
- 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.
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