IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v9y2021i1p20-d478258.html
   My bibliography  Save this article

On the Market-Consistent Valuation of Participating Life Insurance Heterogeneous Contracts under Longevity Risk

Author

Listed:
  • Anna Rita Bacinello

    (Department of Economics, Business, Mathematics and Statistics ‘B. de Finetti’, University of Trieste, Via dell’Università 1, 34100 Trieste, Italy)

  • An Chen

    (Faculty of Mathematics and Economics, University of Ulm, Helmholtzstrasse 20, 89069 Ulm, Germany)

  • Thorsten Sehner

    (Faculty of Mathematics and Economics, University of Ulm, Helmholtzstrasse 20, 89069 Ulm, Germany)

  • Pietro Millossovich

    (Department of Economics, Business, Mathematics and Statistics ‘B. de Finetti’, University of Trieste, Via dell’Università 1, 34100 Trieste, Italy
    Faculty of Actuarial Science and Insurance, The Business School (Formerly Cass), City, University of London, 106 Bunhill Row, London EC1Y 8TZ, UK)

Abstract

The purpose of this paper is to conduct a market-consistent valuation of life insurance participating liabilities sold to a population of partially heterogeneous customers under the joint impact of biometric and financial risk. In particular, the heterogeneity between groups of policyholders stems from their offered minimum interest rate guarantees and contract maturities. We analyse the effects of these features on the company’s insolvency while embracing the insurer’s goal to achieve the same expected return for different cohorts of policyholders. Within our extensive numerical analyses, we determine the fair participation rates and other key figures, and discuss the implications for the stakeholders, taking account of various degrees of conservativeness of the insurer when pricing the contracts.

Suggested Citation

  • Anna Rita Bacinello & An Chen & Thorsten Sehner & Pietro Millossovich, 2021. "On the Market-Consistent Valuation of Participating Life Insurance Heterogeneous Contracts under Longevity Risk," Risks, MDPI, vol. 9(1), pages 1-18, January.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:1:p:20-:d:478258
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/9/1/20/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/9/1/20/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Stéphane Loisel, 2010. "Understanding, Modeling and Managing Longevity Risk: Key Issues and Main Challenges," Post-Print hal-00517902, HAL.
    2. Tobias Burkhart, 2018. "Surrender Risk in the Context of the Quantitative Assessment of Participating Life Insurance Contracts under Solvency II," Risks, MDPI, vol. 6(3), pages 1-38, June.
    3. Anna Maria Gambaro & Riccardo Casalini & Gianluca Fusai & Alessandro Ghilarducci, 2019. "A market-consistent framework for the fair evaluation of insurance contracts under Solvency II," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(1), pages 157-187, June.
    4. Cheng, Chunli & Li, Jing, 2018. "Early default risk and surrender risk: Impacts on participating life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 30-43.
    5. Grosen, Anders & Løchte Jørgensen, Peter, 2001. "Life Insurance Liabilities at Market Value," Finance Working Papers 01-4, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    6. Martin Eling & Stefan Holder, 2013. "Maximum Technical Interest Rates in Life Insurance in Europe and the United States: An Overview and Comparison," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 38(2), pages 354-375, April.
    7. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    8. Dirk Broeders & An Chen & David Rijsbergen, 2013. "Valuation of liabilities in hybrid pension plans," Applied Financial Economics, Taylor & Francis Journals, vol. 23(15), pages 1215-1229, August.
    9. Carolina Orozco‐Garcia & Hato Schmeiser, 2019. "Is Fair Pricing Possible? An Analysis of Participating Life Insurance Portfolios," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 86(2), pages 521-560, June.
    10. Diana Dorobantu & Yahia Salhi & Pierre-E. Thérond, 2020. "Modelling Net Carrying Amount of Shares for Market Consistent Valuation of Life Insurance Liabilities," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 711-745, June.
    11. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, Francois, 2005. "Market value of life insurance contracts under stochastic interest rates and default risk," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 499-516, June.
    12. Bauer, Daniel & Bergmann, Daniela & Kiesel, Rüdiger, 2010. "On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 65-95, May.
    13. Sheldon, T. J. & Smith, A. D., 2004. "Market Consistent Valuation of Life Assurance Business," British Actuarial Journal, Cambridge University Press, vol. 10(3), pages 543-605, August.
    14. Chen, An & Suchanecki, Michael, 2007. "Default risk, bankruptcy procedures and the market value of life insurance liabilities," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 231-255, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Florian Gach & Simon Hochgerner & Eva Kienbacher & Gabriel Schachinger, 2023. "Mean-field Libor market model and valuation of long term guarantees," Papers 2310.09022, arXiv.org, revised Nov 2023.
    2. Annamaria Olivieri & Ermanno Pitacco, 2022. "Time Restrictions on Life Annuity Benefits: Portfolio Risk Profiles," Risks, MDPI, vol. 10(8), pages 1-18, August.

    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. Olivier Le Courtois & François Quittard-Pinon & Xiaoshan Su, 2020. "Pricing and hedging defaultable participating contracts with regime switching and jump risk," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 303-339, June.
    2. Cheng, Chunli & Li, Jing, 2018. "Early default risk and surrender risk: Impacts on participating life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 30-43.
    3. An Chen & Xia Su, 2009. "Knightian uncertainty and insurance regulation decision," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 32(1), pages 13-33, May.
    4. Bernard, Carole & Boyle, Phelim P., 2011. "A Natural Hedge for Equity Indexed Annuities," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 211-230, September.
    5. 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.
    6. 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.
    7. Florian Gach & Simon Hochgerner & Eva Kienbacher & Gabriel Schachinger, 2023. "Mean-field Libor market model and valuation of long term guarantees," Papers 2310.09022, arXiv.org, revised Nov 2023.
    8. Broeders, Dirk & Chen, An & Koos, Birgit, 2011. "A utility-based comparison of pension funds and life insurance companies under regulatory constraints," Insurance: Mathematics and Economics, Elsevier, vol. 49(1), pages 1-10, July.
    9. Kevin Fergusson & Eckhard Platen, 2013. "Real World Pricing of Long Term Cash-Linked Annuities and Equity-Linked Annuities with Cash-Linked Guarantees," Research Paper Series 338, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Cheng, Chunli, 2022. "Beyond death: The impact of a population-wide health shock on life insurance," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    11. Olivieri, Annamaria & Pitacco, Ermanno, 2008. "Assessing the cost of capital for longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1013-1021, June.
    12. Olivier Le Courtois & François Quittard-Pinon, 2008. "Fair Valuation of Participating Life Insurance Contracts with Jump Risk," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 33(2), pages 106-136, December.
    13. Broeders, Dirk & Chen, An, 2010. "Pension regulation and the market value of pension liabilities: A contingent claims analysis using Parisian options," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1201-1214, June.
    14. Eling, Martin & Holder, Stefan, 2013. "The value of interest rate guarantees in participating life insurance contracts: Status quo and alternative product design," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 491-503.
    15. Li, Xin & Liu, Haibo & Tang, Qihe & Zhu, Jinxia, 2020. "Liquidation risk in insurance under contemporary regulatory frameworks," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 36-49.
    16. Shi Chen & Jyh-Horng Lin & Wenyu Yao & Fu-Wei Huang, 2019. "CEO Overconfidence and Shadow-Banking Life Insurer Performance Under Government Purchases of Distressed Assets," Risks, MDPI, vol. 7(1), pages 1-25, March.
    17. Ilja Boelaars & Dirk Broeders, 2019. "Fair Pensions," DNB Working Papers 630, Netherlands Central Bank, Research Department.
    18. Tat Wing Wong & Mei Choi Chiu & Hoi Ying Wong, 2017. "Managing Mortality Risk With Longevity Bonds When Mortality Rates Are Cointegrated," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(3), pages 987-1023, September.
    19. Chen, An & Suchanecki, Michael, 2006. "Default Risk, Bankruptcy Procedures and the Market Value of Life Insurance Liabilities," Bonn Econ Discussion Papers 8/2006, University of Bonn, Bonn Graduate School of Economics (BGSE).
    20. Feng, Runhuan & Yi, Bingji, 2019. "Quantitative modeling of risk management strategies: Stochastic reserving and hedging of variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 60-73.

    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:9:y:2021:i:1:p:20-:d:478258. 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.