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MODELLING MORTALITY DEPENDENCE WITH REGIME-SWITCHING COPULAS

Published online by Cambridge University Press:  24 April 2019

Rui Zhou
Rui Zhou*
Affiliation:
Department of EconomicsUniversity of MelbourneParkville VIC 3010, Australia E-mail: [email protected]
*
E-mail: [email protected]
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Abstract

We propose a two-regime Markov switching copula to depict the evolution of mortality dependence. One regime represents periods of high dependence and the other regime represents periods of low dependence. Each regime features a regular vine (R-vine) copula that, built on bivariate copulas, provides great flexibility for modelling complex high-dimensional dependence. Our estimated model indicates that the years of recovery from extreme mortality deterioration and the years of health care reform more likely fall into the low regime, while the years in which extreme mortality deteriorating events break out and the peaceful years without major mortality-impacting events more likely fall into the high regime. We use a case study to illustrate how the regime-switching copula can be applied to assess the effectiveness of longevity risk hedge with different beliefs about future mortality dependence evolution incorporated.

Keywords

Mortality dependenceR-vine copularegime-switchinglongevity riskS-forward.
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 2 , May 2019 , pp. 373 - 407
Copyright
Copyright © Astin Bulletin 2019 

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References

Aas, K., Czado, C., Frigessi, A. and Bakken, H. (2009) Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics, 44,182–198.Google Scholar
Bedford, T. and Cooke, R.M. (2001) Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial Intelligence, 32, 245–268.CrossRefGoogle Scholar
Bedford, T. and Cooke, R.M. (2002) Vines—a new graphical model for dependent random variables. The Annals of Statistics, 30, 1031–1068.Google Scholar
Beltrán-Sánchez, H., Crimmins, E.M. and Finch, C.E. (2012) Early cohort mortality predicts the cohort rate of aging: an historical analysis. Journal of developmental origins of health and disease, 3, 380–386.CrossRefGoogle Scholar
Brechmann, E.C. and Czado, C. (2013) Risk management with high-dimensional vine copulas: an analysis of the euro stoxx 50. Statistics & Risk Modeling, 30, 307–342.CrossRefGoogle Scholar
Brechmann, E.C., Czado, C. and Aas, K. (2012) Truncated regular vines in high dimensions with application to financial data. Canadian Journal of Statistics, 40, 68–85.CrossRefGoogle Scholar
Cairns, A.J.G., 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.J.G., Blake, D., Dowd, K., Coughlan, G.D. and Khalaf-Allah, M. (2011) Bayesian stochastic mortality modelling for two populations. ASTIN Bulletin, 41, 29–59.Google Scholar
Chai, C.M.H., Kuen Siu, T. and Zhou, X. (2013) A double-exponential garch model for stochastic mortality. European Actuarial Journal, 3, 385–406.CrossRefGoogle Scholar
Chen, H., MacMinn, R. and Sun, T. (2015) Multi-population mortality models: a factor copula approach. Insurance: Mathematics and Economics, 63, 135–146.Google Scholar
Chen, H., MacMinn, R.D. and Sun, T. (2017) Mortality dependence and longevity bond pricing: A dynamic factor copula mortality model with the gas structure. Journal of Risk and Insurance, 84, 393–415.CrossRefGoogle Scholar
Chollete, L., Heinen, A. and Valdesogo, A. (2009) Modeling international financial returns with a multivariate regime-switching copula. Journal of Financial Econometrics, 7, 437–480.CrossRefGoogle Scholar
Chuliá, H., Guillén, M. and Uribe, J.M. (2016) Modeling longevity risk with generalized dynamic factor models and vine-copulae. ASTIN Bulletin, 46, 165–190.CrossRefGoogle Scholar
Dißmann, J., Brechmann, E.C., Czado, C. and Kurowicka, D. (2013) Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis, 59, 52–69.CrossRefGoogle Scholar
Dowd, K.,Cairns, A.J.G., Blake, D., Coughlan, G.D. and Khalaf-Allah, M. (2011) A gravity model of mortality rates for two related populations. North American Actuarial Journal, 15, 334–356.CrossRefGoogle Scholar
Engle, R.F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation. Econometrica, 50, 987–1007.CrossRefGoogle Scholar
Engle, R.F. and Granger, C.W.J. (1987) Co-integration and error correction: representation, estimation, and testing. Econometrica, 55, 251–276.CrossRefGoogle Scholar
Fink, H., Klimova, Y., Czado, C. and Stöber, J. (2017) Regime switching vine copula models for global equity and volatility indices. Econometrics, 5, 3. doi: 10.3390/econometrics5010003.CrossRefGoogle Scholar
Gao, Q. and Hu, C. (2009) Dynamic mortality factor model with conditional heteroskedasticity. Insurance: Mathematics and Economics, 45, 410-423.Google Scholar
Hamilton, J.D. (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57, 357–384.CrossRefGoogle Scholar
Janssen, F. (2005) Cohort patterns in mortality trends among the elderly in seven european countries, 1950–99. International Journal of Epidemiology, 34, 1149–1159.CrossRefGoogle ScholarPubMed
Jarner, S.F. and Kryger, E.M. (2011) Modelling adult mortality in small populations: the saint model. ASTIN Bulletin, 41, 377–418.Google Scholar
Joe, H. (1996) Families of m-variate distributions with given margins and m(m – 1)/2 bivariate dependence parameters. Lecture Notes–Monograph Series, pp. 120–141. Hayward, CA: Institute of Mathematical Statistics.Google Scholar
Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models. Econometrica, 59, 1551–1580.CrossRefGoogle Scholar
Jondeau, E. and Rockinger, M. (2006) The copula-garch model of conditional dependencies: an international stock market application. Journal of International Money and Finance, 25, 827–853.CrossRefGoogle Scholar
Kim, C.-J. (1994) Dynamic linear models with markov-switching. Journal of Econometrics, 60, 1–22.CrossRefGoogle Scholar
Kim, C.-J. and Nelson, C.R. (1999) State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications. Cambridge, Massachusetts: MIT Press.Google Scholar
Lee, R.D. and Carter, L.R. (1992) Modeling and forecasting u. s. mortality. Journal of the American Statistical Association, 87, 659–671.Google Scholar
Li, J.S.-H. and Hardy, M.R. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15, 177–200.CrossRefGoogle Scholar
Li, J.S.-H. Zhou, R. and Hardy, M. (2015) A step-by-step guide to building two-population stochastic mortality models. Insurance: Mathematics and Economics, 63, 121–134.Google 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
Lin, T., Wang, C.-W. and Tsai, C.C.-L. (2015) Age-specific copula-ar-garch mortality models. Insurance: Mathematics and Economics, 61, 110–124.Google Scholar
Nikoloulopoulos, A.K., Joe, H. and Li, H. (2012) Vine copulas with asymmetric tail dependence and applications to financial return data. Computational Statistics & Data Analysis, 56, 3659–3673.CrossRefGoogle Scholar
Osmond, C. (1985) Using age, period and cohort models to estimate future mortality rates. International Journal of Epidemiology, 14, 124–129.CrossRefGoogle ScholarPubMed
Sklar, A. (1959) Fonctions de répartition àn dimensions et leurs marges. Publications de l’Institut Statistique de l’Université de Paris, 8, 229–231.Google Scholar
Stöber, J. and Czado, C. (2014) Regime switches in the dependence structure of multidimensional financial data. Computational Statistics and Data Analysis, 76, 672–686.CrossRefGoogle Scholar
Wang, C.-W., Yang, S.S. and Huang, H.-C. (2015) Modeling multi-country mortality dependence and its application in pricing survivor index swaps—a dynamic copula approach. Insurance: Mathematics and Economics, 63, 30–39.Google Scholar
Wang, Z. and Li, J.S.-H. (2016) A dcc-garch multi-population mortality model and its applications to pricing catastrophic mortality bonds. Finance Research Letters, 16, 103–111.CrossRefGoogle Scholar
Wilmoth, J.R. (2005) On the relationship between period and cohort mortality. Demographic Research, S4, 231–280.CrossRefGoogle Scholar
Yang, S.S. and Wang, C.-W. (2013) Pricing and securitization of multi-country longevity risk with mortality dependence. Insurance: Mathematics and Economics, 52, 157–169.Google Scholar
Zhou, R., Li, J.S.-H. and Tan, K.S. (2013) Pricing standardized mortality securitizations: a two-population model with transitory jump effects. Journal of Risk and Insurance, 80, 733–774.CrossRefGoogle Scholar
Zhou, R., Wang, Y., Kaufhold, K., Li, J.S.-H. and Tan, K.S. (2014) Modeling period effects in multi-population mortality models: applications to Solvency II. North American Actuarial Journal, 18, 150–167.CrossRefGoogle Scholar