Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-07T22:19:22.651Z Has data issue: false hasContentIssue false
  • English
  • Français

Using hierarchical Archimedean copulas for modelling mortality dependence and pricing mortality-linked securities

Published online by Cambridge University Press:  26 August 2020

Jackie Li ,
Uditha Balasooriya  and
Jia Liu
Jackie Li*
Affiliation:
Actuarial Studies and Business Analytics, Macquarie University, Sydney, New South Wales, 2109, Australia
Uditha Balasooriya
Affiliation:
Actuarial Studies and Business Analytics, Macquarie University, Sydney, New South Wales, 2109, Australia
Jia Liu
Affiliation:
Actuarial Studies and Business Analytics, Macquarie University, Sydney, New South Wales, 2109, Australia
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article, we explore the use of multivariate Archimedean copulas in modelling the mortality dependence between different countries and pricing mortality bonds. We study the fitting performance of multi-dimensional, fully nested, and partially nested Archimedean copulas and test 11 types of generators and two skewed distributions. To evaluate their practical usefulness, we adopt the fitted models to compute the market prices for some typical mortality bond structures. The results show that the copula assumption has a significant impact on the calculation of the prices of mortality-linked securities and the management of extreme mortality risks.

Keywords

Nested Archimedean copulasMortality dependenceMortality bond
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 15 , Issue 3 , November 2021 , pp. 505 - 518
Copyright
© Institute and Faculty of Actuaries 2020

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

Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171–178.Google Scholar
Azzalini, A. & Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. Journal of the Royal Statistical Society: Series B, 65(2), 367–389.CrossRefGoogle Scholar
Brouhns, N., Denuit, M. & Vermunt, J.K. (2002). A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31, 373–393.Google Scholar
Cairns, A.J.G., Blake, D. & Dowd, K. (2006). A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73(4), 687–718.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D. & Dowd, K. (2008). Modelling and management of mortality risk: a review. Scandinavian Actuarial Journal, 2008(2–3), 79–113.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D. & Khalaf-Allah, M., (2011). Bayesian stochastic mortality modelling for two populations. ASTIN Bulletin, 41(1), 29–59.Google Scholar
Carter, L.R. & Lee, R.D. (1992). Modeling and forecasting US sex differentials in mortality. International Journal of Forecasting, 8(3), 393–411.CrossRefGoogle Scholar
Chen, H. & Cox, S.H. (2009). Modeling mortality with jumps: applications to mortality securitization. Journal of Risk and Insurance, 76(3), 727–751.CrossRefGoogle Scholar
Chen, H., MacMinn, R. & 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. & 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(S1R), 393–415.CrossRefGoogle Scholar
Coughlan, G.D., Epstein, D., Sinha, A. & Honig, P. (2007). Q-forwards: Derivatives for Transferring Longevity and Mortality Risk. JPMorgan. https://www.researchgate.net/publication/256109844_q-Forwards_Derivatives_for_Transferring_Longevity_and_Mortality_Risks.Google Scholar
Embrechts, P., Lindskog, F. & McNeil, A. (2001). Modelling Dependence with Copulas and Applications to Risk Management. Department of Mathematics, ETHZ.Google Scholar
Gaiduchevici, G. (2014). Post-crisis CDO valuation with Archimedean copulas. Procedia Economics and Finance, 15(2014), 19–26.CrossRefGoogle Scholar
Guégan, D. & Ladoucette, S.A. (2004). Dependence modelling of the joint extremes in a portfolio using Archimedean copulas: application to MSCI indices. Institutions et Dynamiques Historiques de l’Economie (IDHE).Google Scholar
Human Mortality Database (HMD). (2018). University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). www.mortality.orgGoogle Scholar
Hyndman, R.J., Booth, H. & Yasmeen, F. (2013). Coherent mortality forecasting: the product-ratio method with functional time series models. Demography, 50(1), 261–283.CrossRefGoogle ScholarPubMed
Joe, H. (1997). Multivariate Models and Dependence Concepts. Chapman & Hall, London.Google Scholar
Lee, R.D. & Carter, L.R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
Li, J. (2013). A Poisson common factor model for projecting mortality and life expectancy jointly for females and males. Population Studies, 67(1), 111–126.CrossRefGoogle ScholarPubMed
Li, J. & Liu, J. (2018). A logistic two-population mortality projection model for modelling mortality at advanced ages for both sexes. Scandinavian Actuarial Journal. https://doi.org/10.1080/03461238.2018.1511464Google Scholar
Li, J.S.H., Chan, W.S. & Cheung, S.H. (2011). Mortality indexes: detection and implications. North American Actuarial Journal, 15(1), 13–31.CrossRefGoogle Scholar
Li, J.S.H. & Hardy, M.R. (2011). Measuring basis risk in longevity hedges. North American Actuarial Journal, 15(2), 177–200.CrossRefGoogle Scholar
Li, N. & Lee, R. (2005). Coherent mortality forecasts for a group of populations: an extension of the Lee-Carter method. Demography, 42(3), 575–594.CrossRefGoogle ScholarPubMed
Lin, Y. & Cox, S.H. (2008). Securitization of catastrophe mortality risks. Insurance: Mathematics and Economics, 42(2), 628–637.Google Scholar
Luciano, E., Spreeuw, J. & Vigna, E. (2008). Modelling stochastic mortality for dependent lives. Insurance: Mathematics and Economics, 43(2), 234–244.Google Scholar
Luciano, E., Spreeuw, J. & Vigna, E. (2016). Spouses’ dependence across generations and pricing impact on reversionary annuities. Risks, 4(2), 16.CrossRefGoogle Scholar
Milidonis, A., Lin, Y. & Cox, S.H. (2011). Mortality regimes and pricing. North American Actuarial Journal, 15(2), 266–289.CrossRefGoogle Scholar
Nelsen, R.B. (1999). An Introduction to Copulas. Springer-Verlag, New York.CrossRefGoogle Scholar
Okhrin, O., Okhrin, Y. & Schmid, W. (2013). On the structure and estimation of hierarchical Archimedean copulas. Journal of Econometrics, 173(2), 189–204.CrossRefGoogle Scholar
Okhrin, O. & Ristig, A. (2014). Hierarchical Archimedean copulae: the HAC package. Journal of Statistical Software, 58(4), 1–20.CrossRefGoogle Scholar
Plat, R. (2009). Stochastic portfolio specific mortality and the quantification of mortality basis risk. Insurance: Mathematics and Economics, 45, 123–132.Google Scholar
Savu, C. & Trede, M. (2008). Goodness-of-fit tests for parametric families of Archimedean copulas. Quantitative Finance, 8(2), 109–116.CrossRefGoogle Scholar
Sklar, A. (1959). Fonctions de répartition à n dimensions et leurs marges. Institut Statistique de l’Université de Paris, 8, 229–231.Google Scholar
Tsay, R.S. (2002). Analysis of Financial Time Series. John Wiley & Sons, New York.CrossRefGoogle Scholar
Villegas, A.M., Haberman, S., Kaishev, V.K. & Millossovich, P. (2017). A comparative study of two-population models for the assessment of basis risk in longevity hedges. ASTIN Bulletin, 47(3), 631–679.CrossRefGoogle Scholar
Wang, C.W., Yang, S.S. & Huang, H.C. (2015). Modeling multi-country mortality experience and its application in pricing survivor index swaps – a dynamic copula approach. Insurance: Mathematics and Economics, 63, 30–39.Google Scholar
Wang, S.S. (2000). A class of distortion operations for pricing financial and insurance risks. Journal of Risk and Insurance, 67(1), 15–36.CrossRefGoogle Scholar
Wang, S.S. (2004). Cat bond pricing using probability transforms. Geneva Papers: Etudes et Dossiers (Special Issue on Insurance and the State of the Art in Cat Bond Pricing), 278, 19–29.Google Scholar
Zhou, R. (2019). Modelling mortality dependence with regime-switching copulas. ASTIN Bulletin, 49(2), 373–407.CrossRefGoogle Scholar
Zhu, W., Tan, K.S. & Wang, C.W. (2017). Modeling multicountry longevity risk with mortality dependence: a Lévy subordinated hierarchical Archimedean copulas approach. Journal of Risk and Insurance, 84(S1), 477–493.CrossRefGoogle Scholar