IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v7y2019i1p14-d202430.html
   My bibliography  Save this article

Changes of Relation in Multi-Population Mortality Dependence: An Application of Threshold VECM

Author

Listed:
  • Rui Zhou

    (Department of Economics, University of Melbourne, Parkville, VIC 3010, Australia)

  • Guangyu Xing

    (Manulife-Sinochem, Shanghai 200121, China)

  • Min Ji

    (Department of Mathematics, Towson University, Towson, MD 21252, USA)

Abstract

Standardized longevity risk transfers often involve modeling mortality rates of multiple populations. Some researchers have found that mortality indexes of selected countries are cointegrated, meaning that a linear relationship exists between the indexes. Vector error correction model (VECM) was used to incorporate this relation, thereby forcing the mortality rates of multiple populations to revert to a long-run equilibrium. However, the long-run equilibrium may change over time. It is crucial to incorporate these changes such that mortality dependence is adequately modeled. In this paper, we develop a framework to examine the presence of equilibrium changes and to incorporate these changes into the mortality model. In particular, we focus on equilibrium changes caused by threshold effect, the phenomenon that mortality indexes alternate between different VECMs depending on the value of a threshold variable. Our framework comprises two steps. In the first step, a statistical test is performed to examine the presence of threshold effect in the VECM for multiple mortality indexes. In the second step, threshold vector error correction model (TVECM) is fitted to the mortality indexes and model adequacy is evaluated. We illustrate this framework with the mortality data of England and Wales (EW) and Canadian populations. We further apply the TVECM to forecast future mortalities and price an illustrative longevity bond with multivariate Wang transform. Our numerical results show that TVECM predicted much faster mortality improvement for EW and Canada than single-regime VECM and thus the incorporation of threshold effect significant increases longevity bond price.

Suggested Citation

  • Rui Zhou & Guangyu Xing & Min Ji, 2019. "Changes of Relation in Multi-Population Mortality Dependence: An Application of Threshold VECM," Risks, MDPI, vol. 7(1), pages 1-18, February.
  • Handle: RePEc:gam:jrisks:v:7:y:2019:i:1:p:14-:d:202430
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/7/1/14/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-9091/7/1/14/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hansen, Bruce E. & Seo, Byeongseon, 2002. "Testing for two-regime threshold cointegration in vector error-correction models," Journal of Econometrics, Elsevier, vol. 110(2), pages 293-318, October.
    2. Kevin Dowd & Andrew Cairns & David Blake & Guy Coughlan & Marwa Khalaf-Allah, 2011. "A Gravity Model of Mortality Rates for Two Related Populations," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 334-356.
    3. Andreas Milidonis & Yijia Lin & Samuel Cox, 2011. "Mortality Regimes and Pricing," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 266-289.
    4. Shaun Wang, 2007. "Normalized Exponential Tilting," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(3), pages 89-99.
    5. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    6. Weiyu Kuo & Chenghsien Tsai & Wei‐Kuang Chen, 2003. "An Empirical Study on the Lapse Rate: The Cointegration Approach," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(3), pages 489-508, September.
    7. Mitchell, Daniel & Brockett, Patrick & Mendoza-Arriaga, Rafael & Muthuraman, Kumar, 2013. "Modeling and forecasting mortality rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 275-285.
    8. Yang, Sharon S. & Wang, Chou-Wen, 2013. "Pricing and securitization of multi-country longevity risk with mortality dependence," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 157-169.
    9. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    10. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
    11. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Khalaf-Allah, Marwa, 2011. "Bayesian Stochastic Mortality Modelling for Two Populations," ASTIN Bulletin, Cambridge University Press, vol. 41(1), pages 29-59, May.
    12. Johnny Li & Mary Hardy, 2011. "Measuring Basis Risk in Longevity Hedges," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 177-200.
    13. Samuel H. Cox & Yijia Lin & Shaun Wang, 2006. "Multivariate Exponential Tilting and Pricing Implications for Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 719-736, December.
    14. Villegas, Andrés M. & Haberman, Steven & Kaishev, Vladimir K. & Millossovich, Pietro, 2017. "A Comparative Study Of Two-Population Models For The Assessment Of Basis Risk In Longevity Hedges," ASTIN Bulletin, Cambridge University Press, vol. 47(3), pages 631-679, September.
    15. Lin, Yijia & Cox, Samuel H., 2008. "Securitization of catastrophe mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 628-637, April.
    16. Nan Li & Ronald Lee, 2005. "Coherent mortality forecasts for a group of populations: An extension of the lee-carter method," Demography, Springer;Population Association of America (PAA), vol. 42(3), pages 575-594, August.
    17. Chen, Chung & Tiao, George C, 1990. "Random Level-Shift Time Series Models, ARIMA Approximations, and Level-Shift Detection," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 83-97, January.
    18. Rui Zhou & Yujiao Wang & Kai Kaufhold & Johnny Li & Ken Tan, 2014. "Modeling Period Effects in Multi-Population Mortality Models: Applications to Solvency II," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 150-167.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    2. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    3. Li, Jackie & Haberman, Steven, 2015. "On the effectiveness of natural hedging for insurance companies and pension plans," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 286-297.
    4. Jarner, Søren F. & Jallbjørn, Snorre, 2020. "Pitfalls and merits of cointegration-based mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 90(C), pages 80-93.
    5. David Blake & Marco Morales & Enrico Biffis & Yijia Lin & Andreas Milidonis, 2017. "Special Edition: Longevity 10 – The Tenth International Longevity Risk and Capital Markets Solutions Conference," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(S1), pages 515-532, April.
    6. de Jong, Piet & Tickle, Leonie & Xu, Jianhui, 2016. "Coherent modeling of male and female mortality using Lee–Carter in a complex number framework," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 130-137.
    7. Hunt, Andrew & Blake, David, 2015. "Modelling longevity bonds: Analysing the Swiss Re Kortis bond," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 12-29.
    8. Li, Hong & Lu, Yang, 2017. "Coherent Forecasting Of Mortality Rates: A Sparse Vector-Autoregression Approach," ASTIN Bulletin, Cambridge University Press, vol. 47(2), pages 563-600, May.
    9. Chen, Hua & MacMinn, Richard & Sun, Tao, 2015. "Multi-population mortality models: A factor copula approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 135-146.
    10. Liu, Yanxin & Li, Johnny Siu-Hang, 2016. "It’s all in the hidden states: A longevity hedging strategy with an explicit measure of population basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 301-319.
    11. Hunt, Andrew & Blake, David, 2018. "Identifiability, cointegration and the gravity model," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 360-368.
    12. Ahmadi, Seyed Saeed & Li, Johnny Siu-Hang, 2014. "Coherent mortality forecasting with generalized linear models: A modified time-transformation approach," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 194-221.
    13. Chen, Fen-Ying & Yang, Sharon S. & Huang, Hong-Chih, 2022. "Modeling pandemic mortality risk and its application to mortality-linked security pricing," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 341-363.
    14. de Jong, Piet & Tickle, Leonie & Xu, Jianhui, 2020. "A more meaningful parameterization of the Lee–Carter model," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 1-8.
    15. Yang, Sharon S. & Wang, Chou-Wen, 2013. "Pricing and securitization of multi-country longevity risk with mortality dependence," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 157-169.
    16. Katrien Antonio & Anastasios Bardoutsos & Wilbert Ouburg, 2015. "Bayesian Poisson log-bilinear models for mortality projections with multiple populations," Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven 485564, KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven.
    17. Selin Özen & Şule Şahin, 2021. "A Two-Population Mortality Model to Assess Longevity Basis Risk," Risks, MDPI, vol. 9(2), pages 1-19, February.
    18. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2021. "Addressing the life expectancy gap in pension policy," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 200-221.
    19. Rui Zhou & Johnny Siu-Hang Li & Ken Seng Tan, 2013. "Pricing Standardized Mortality Securitizations: A Two-Population Model With Transitory Jump Effects," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(3), pages 733-774, September.
    20. Zhou, Rui & Ji, Min, 2021. "Modelling mortality dependence: An application of dynamic vine copula," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 241-255.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:7:y:2019:i:1:p:14-:d:202430. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.