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A Two-Population Mortality Model to Assess Longevity Basis Risk

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  • Selin Ozen
  • c{S}ule c{S}ahin

Abstract

Index-based hedging solutions are used to transfer the longevity risk to the capital markets. However, mismatches between the liability of the hedger and the hedging instrument cause longevity basis risk. Therefore, an appropriate two-population model to measure and assess the longevity basis risk is required. In this paper, we aim to construct a two-population mortality model to provide an effective hedge against the longevity basis risk. The reference population is modelled by using the Lee-Carter model with the renewal process and exponential jumps proposed by \"Ozen and \c{S}ahin (2020) and the dynamics of the book population are specified. The analysis based on the UK mortality data indicates that the proposed model for the reference population and the common age effect model for the book population provide a better fit compared to the other models considered in the paper. Different two-population models are used to investigate the impact of the sampling risk on the index-based hedge as well as to analyse the risk reduction regarding hedge effectiveness. The results show that the proposed model provides a significant risk reduction when mortality jumps and the sampling risk are taken into account.

Suggested Citation

  • Selin Ozen & c{S}ule c{S}ahin, 2021. "A Two-Population Mortality Model to Assess Longevity Basis Risk," Papers 2101.06690, arXiv.org.
    • Handle: RePEc:arx:papers:2101.06690
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    1. 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.
    2. Andrew J.G. Cairns & Kevin Dowd & David Blake & Guy D. Coughlan, 2014. "Longevity hedge effectiveness: a decomposition," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 217-235, February.
    3. Jarner, Søren Fiig & Kryger, Esben Masotti, 2011. "Modelling Adult Mortality in Small Populations: The Saint Model," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 377-418, November.
    4. Koissi, Marie-Claire & Shapiro, Arnold F. & Hognas, Goran, 2006. "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 1-20, February.
    5. Coughlan, Guy & Khalaf-Allah, Marwa & Ye, Yijing & Kumar, Sumit & Cairns, Andrew & Blake, David & Dowd, Kevin, 2011. "Longevity hedging 101: A framework for longevity basis risk analysis and hedge effectiveness," MPRA Paper 35743, University Library of Munich, Germany.
    6. Ngai, Andrew & Sherris, Michael, 2011. "Longevity risk management for life and variable annuities: The effectiveness of static hedging using longevity bonds and derivatives," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 100-114, July.
    7. Hua Chen & Samuel H. Cox, 2009. "Modeling Mortality With Jumps: Applications to Mortality Securitization," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 727-751, September.
    8. 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.
    9. Renshaw, A.E. & Haberman, S., 2008. "On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 797-816, April.
    10. 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.
    11. 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.
    12. Hatzopoulos, P. & Haberman, S., 2013. "Common mortality modeling and coherent forecasts. An empirical analysis of worldwide mortality data," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 320-337.
    13. 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.
    14. Kogure Atsuyuki & Kitsukawa Kenji & Kurachi Yoshiyuki, 2009. "A Bayesian Comparison of Models for Changing Mortalities toward Evaluating Longevity Risk in Japan," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 3(2), pages 1-22, April.
    15. Guy Coughlan & Marwa Khalaf-Allah & Yijing Ye & Sumit Kumar & Andrew Cairns & David Blake & Kevin Dowd, 2011. "Longevity Hedging 101," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 150-176.
    16. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    17. 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.
    18. Li, Jackie, 2014. "A quantitative comparison of simulation strategies for mortality projection," Annals of Actuarial Science, Cambridge University Press, vol. 8(2), pages 281-297, September.
    19. 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.
    20. Li, Johnny Siu-Hang & Zhou, Rui & Hardy, Mary, 2015. "A step-by-step guide to building two-population stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 121-134.
    21. Johnny Li & Mary Hardy, 2011. "Measuring Basis Risk in Longevity Hedges," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 177-200.
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