IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v78y2018icp30-43.html
   My bibliography  Save this article

Early default risk and surrender risk: Impacts on participating life insurance policies

Author

Listed:
  • Cheng, Chunli
  • Li, Jing

Abstract

We study the risk-neutral valuation of participating life insurance policies with surrender guarantees when an early default mechanism, forcing an insurance company to be liquidated once a solvency threshold is reached, is imposed by a regulator. The early default regulation affects the policies’ value not only directly via changing the policies’ payment stream but also indirectly via influencing policyholder’s surrender. In this paper, we endogenize surrender risk by assuming a representative policyholder’s surrender intensity bounded from below and from above and uncover the impact of the regulation on the policyholder’s surrender decision making. A partial differential equation is derived to characterize the price of a participating policy and solved with the finite difference method. We discuss the impacts of the early default regulation and insurance company’s reaction to the regulation in terms of its investment strategy on the policyholder’s surrender as well as on the contract value, which depend on the policyholder’s rationality level.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:78:y:2018:i:c:p:30-43
    DOI: 10.1016/j.insmatheco.2017.11.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668716303808
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2017.11.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jing Li & Alexander Szimayer, 2014. "The effect of policyholders' rationality on unit-linked life insurance contracts with surrender guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 327-342, February.
    2. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
    3. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
    4. Bacinello, Anna Rita, 2005. "Endogenous model of surrender conditions in equity-linked life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 270-296, October.
    5. 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.
    6. Dahl, Mikkel, 2004. "Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 113-136, August.
    7. Anna Rita Bacinello & Enrico Biffis & Pietro Millossovich, 2010. "Regression-based algorithms for life insurance contracts with surrender guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 1077-1090.
    8. Zaglauer, Katharina & Bauer, Daniel, 2008. "Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 29-40, August.
    9. Anna Rita Bacinello, 2003. "Pricing Guaranteed Life Insurance Participating Policies with Annual Premiums and Surrender Option," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(3), pages 1-17.
    10. Christiansen, Marcus C. & Steffensen, Mogens, 2013. "Safe-Side Scenarios For Financial And Biometrical Risk," ASTIN Bulletin, Cambridge University Press, vol. 43(3), pages 323-357, September.
    11. Bauer, Daniel & Kiesel, Rudiger & Kling, Alexander & Ru[ss], Jochen, 2006. "Risk-neutral valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 171-183, October.
    12. Eric Briys & François De Varenne, 1994. "Life Insurance in a Contingent Claim Framework: Pricing and Regulatory Implications," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 19(1), pages 53-72, June.
    13. Li, Jing & Szimayer, Alexander, 2011. "The uncertain mortality intensity framework: Pricing and hedging unit-linked life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 471-486.
    14. 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.
    15. Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
    16. 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.
    17. 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. Maria B. Chiarolla & Tiziano Angelis & Gabriele Stabile, 2022. "An analytical study of participating policies with minimum rate guarantee and surrender option," Finance and Stochastics, Springer, vol. 26(2), pages 173-216, April.
    2. 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.
    3. Chih-Te Yang & Yensen Ni & Mu-Hsiang Yu & Yuhsin Chen & Paoyu Huang, 2023. "Decoding the Profitability of Insurance Products: A Novel Approach to Evaluating Non-Participating and Participating Insurance Policies," Mathematics, MDPI, vol. 11(13), pages 1-16, June.
    4. 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).
    5. Fu-Wei Huang & Panpan Lin & Jyh-Horng Lin & Ching-Hui Chang, 2023. "The impact of war on insurer safety: a contingent claim model analysis," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-6, December.
    6. Srbinoski Bojan & Strozzi Fernanda & Poposki Klime & Born Patricia H., 2020. "Trends in Life Insurance Demand and Lapse Literature," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(2), pages 1-46, July.
    7. Cheng, Chunli & Hilpert, Christian & Miri Lavasani, Aidin & Schaefer, Mick, 2023. "Surrender contagion in life insurance," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1465-1479.
    8. Siti Nurasyikin Shamsuddin & Noriszura Ismail & Nur Firyal Roslan, 2022. "What We Know about Research on Life Insurance Lapse: A Bibliometric Analysis," Risks, MDPI, vol. 10(5), pages 1-19, May.
    9. 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.
    10. 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.

    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. Christian Hilpert & Jing Li & Alexander Szimayer, 2014. "The Effect of Secondary Markets on Equity-Linked Life Insurance With Surrender Guarantees," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 81(4), pages 943-968, December.
    2. Li, Jing & Szimayer, Alexander, 2010. "The effect of policyholders' rationality on unit-linked life insurance contracts with surrender guarantees," Bonn Econ Discussion Papers 22/2010, University of Bonn, Bonn Graduate School of Economics (BGSE).
    3. Cheng, Chunli & Hilpert, Christian & Miri Lavasani, Aidin & Schaefer, Mick, 2023. "Surrender contagion in life insurance," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1465-1479.
    4. 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).
    5. Christian Hilpert, 2020. "The Effect of Risk Aversion and Loss Aversion on Equity‐Linked Life Insurance With Surrender Guarantees," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 87(3), pages 665-687, September.
    6. Schmeiser, H. & Wagner, J., 2011. "A joint valuation of premium payment and surrender options in participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 580-596.
    7. 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.
    8. Martin Eling & Michael Kochanski, 2013. "Research on lapse in life insurance: what has been done and what needs to be done?," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 14(4), pages 392-413, August.
    9. Berdin, Elia, 2016. "Interest rate risk, longevity risk and the solvency of life insurers," ICIR Working Paper Series 23/16, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    10. 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.
    11. Srbinoski Bojan & Strozzi Fernanda & Poposki Klime & Born Patricia H., 2020. "Trends in Life Insurance Demand and Lapse Literature," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 14(2), pages 1-46, July.
    12. Eckhard Platen, 2009. "Real World Pricing of Long Term Contracts," Research Paper Series 262, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. 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.
    14. Ninna Reitzel Jensen & Kristian Juul Schomacker, 2015. "A Two-Account Life Insurance Model for Scenario-Based Valuation Including Event Risk," Risks, MDPI, vol. 3(2), pages 1-36, June.
    15. Marcos Escobar & Mikhail Krayzler & Franz Ramsauer & David Saunders & Rudi Zagst, 2016. "Incorporation of Stochastic Policyholder Behavior in Analytical Pricing of GMABs and GMDBs," Risks, MDPI, vol. 4(4), pages 1-36, November.
    16. Bruszas, Sandy & Kaschützke, Barbara & Maurer, Raimond & Siegelin, Ivonne, 2018. "Unisex pricing of German participating life annuities—Boon or bane for customer and insurance company?," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 230-245.
    17. Marco Di Francesco & Roberta Simonella, 2023. "A stochastic Asset Liability Management model for life insurance companies," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(1), pages 61-94, March.
    18. Bernard, Carole & MacKay, Anne & Muehlbeyer, Max, 2014. "Optimal surrender policy for variable annuity guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 116-128.
    19. Nordahl, Helge A., 2008. "Valuation of life insurance surrender and exchange options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 909-919, June.
    20. Nadine Gatzert & Gudrun Hoermann & Hato Schmeiser, 2009. "The Impact of the Secondary Market on Life Insurers’ Surrender Profits," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 887-908, December.

    More about this item

    Keywords

    Participating life insurance policies; Regulator’s intervention; Early default risk; Surrender risk; Partial rationality; Pricing partial differential equation;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

    Statistics

    Access and download statistics

    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:eee:insuma:v:78:y:2018:i:c:p:30-43. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.