IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v8y2018icp231-249.html
   My bibliography  Save this article

A two-decrement model for the valuation and risk measurement of a guaranteed annuity option

Author

Listed:
  • Zhao, Yixing
  • Mamon, Rogemar
  • Gao, Huan

Abstract

The lapse risk arising from the termination of policies, due to a variety of causes, has significant influence on the prices of contracts, liquidity of an insurer, and the reserves necessary to meet regulatory capital. The aim is to address in an integrated manner the problem of pricing and determining the capital requirements for a guaranteed annuity option when lapse risk is embedded in the modelling framework. In particular, two decrements are considered in which death and policy lapse occurrences with their correlations to the financial risk are explicitly modelled. A series of probability measure changes is employed and the corresponding forward, survival, and risk-endowment measures are constructed. This approach superbly circumvents the rather slow “simulation-within-simulation” pricing procedure under a stochastic setting. Implementation results illustrate that the proposed approach cuts down the Monte-Carlo simulation technique’s average computing time by 99%. Risk measures are computed using the moment-based density method and benchmarked against the Monte-Carlo-based numerical findings. Depending on the risk metric used (e.g., VaR, CVaR, various forms of distortion risk measures) and the correlation between the interest and lapse rates, the capital requirement may substantially change, which could be either an increase or decrease of up to 50%.

Suggested Citation

  • Zhao, Yixing & Mamon, Rogemar & Gao, Huan, 2018. "A two-decrement model for the valuation and risk measurement of a guaranteed annuity option," Econometrics and Statistics, Elsevier, vol. 8(C), pages 231-249.
    • Handle: RePEc:eee:ecosta:v:8:y:2018:i:c:p:231-249
    DOI: 10.1016/j.ecosta.2018.06.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306218300340
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2018.06.004?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. Gao, Huan & Mamon, Rogemar & Liu, Xiaoming & Tenyakov, Anton, 2015. "Mortality modelling with regime-switching for the valuation of a guaranteed annuity option," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 108-120.
    2. Bruce Jones & Ričardas Zitikis, 2003. "Empirical Estimation of Risk Measures and Related Quantities," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 44-54.
    3. Loisel, Stéphane & Milhaud, Xavier, 2011. "From deterministic to stochastic surrender risk models: Impact of correlation crises on economic capital," European Journal of Operational Research, Elsevier, vol. 214(2), pages 348-357, October.
    4. repec:eme:jrfpps:v:14:y:2013:i:2:p:392-413 is not listed on IDEAS
    5. Barsotti, Flavia & Milhaud, Xavier & Salhi, Yahia, 2016. "Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 317-331.
    6. Stéphane Loisel, 2011. "Surrender risk and correlation crises," Post-Print hal-00671919, HAL.
    7. Changki Kim, 2005. "Modeling Surrender and Lapse Rates With Economic Variables," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(4), pages 56-70.
    8. Barsotti, Flavia & Milhaud, Xavier & Salhi, Yahia, 2016. "Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 317-331.
    9. Xiaojing Xi & Rogemar Mamon, 2014. "Capturing the Regime-Switching and Memory Properties of Interest Rates," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 307-337, October.
    10. Robert J. Elliott & John van der Hoek, 2001. "Stochastic flows and the forward measure," Finance and Stochastics, Springer, vol. 5(4), pages 511-525.
    11. Marianito R. Rodrigo & Rogemar S. Mamon, 2014. "An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1961-1970, November.
    12. Gao, Huan & Mamon, Rogemar & Liu, Xiaoming, 2017. "Risk measurement of a guaranteed annuity option under a stochastic modelling framework," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 100-119.
    13. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    14. 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.
    15. Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
    16. Anna Rita Bacinello, 2003. "Fair Valuation of a Guaranteed Life Insurance Participating Contract Embedding a Surrender Option," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(3), pages 461-487, September.
    17. Marianito Rodrigo & Rogemar Mamon, 2011. "A unified approach to explicit bond price solutions under a time-dependent affine term structure modelling framework," Quantitative Finance, Taylor & Francis Journals, vol. 11(4), pages 487-493.
    18. Christina Erlwein & Rogemar Mamon, 2009. "An online estimation scheme for a Hull–White model with HMM-driven parameters," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(1), pages 87-107, March.
    19. 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, vol. 14(4), pages 392-413, August.
    20. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    21. Zhao, Yixing & Mamon, Rogemar, 2018. "An efficient algorithm for the valuation of a guaranteed annuity option with correlated financial and mortality risks," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 1-12.
    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. Huang, Yiming & Mamon, Rogemar & Xiong, Heng, 2022. "Valuing guaranteed minimum accumulation benefits by a change of numéraire approach," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 1-26.
    2. Yixing Zhao & Rogemar Mamon & Heng Xiong, 2021. "Claim reserving for insurance contracts in line with the International Financial Reporting Standards 17: a new paid-incurred chain approach to risk adjustments," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-26, December.

    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. Francesca Biagini & Tobias Huber & Johannes G. Jaspersen & Andrea Mazzon, 2021. "Estimating extreme cancellation rates in life insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 971-1000, December.
    2. Mark Kiermayer, 2021. "Modeling surrender risk in life insurance: theoretical and experimental insight," Papers 2101.11590, arXiv.org, revised Aug 2021.
    3. 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.
    4. Barsotti, Flavia & Milhaud, Xavier & Salhi, Yahia, 2016. "Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 317-331.
    5. 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.
    6. Debbie Kusch Falden & Anna Kamille Nyegaard, 2021. "Retrospective Reserves and Bonus with Policyholder Behavior," Risks, MDPI, vol. 9(1), pages 1-28, January.
    7. Berdin, Elia & Gründl, Helmut & Kubitza, Christian, 2017. "Rising interest rates, lapse risk, and the stability of life insurers," ICIR Working Paper Series 29/17, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    8. Christian Knoller & Gunther Kraut & Pascal Schoenmaekers, 2016. "On the Propensity to Surrender a Variable Annuity Contract: An Empirical Analysis of Dynamic Policyholder Behavior," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 83(4), pages 979-1006, December.
    9. Barsotti, Flavia & Milhaud, Xavier & Salhi, Yahia, 2016. "Lapse risk in life insurance: Correlation and contagion effects among policyholders’ behaviors," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 317-331.
    10. Feodoria, Mark & Förstemann, Till, 2015. "Lethal lapses: How a positive interest rate shock might stress German life insurers," Discussion Papers 12/2015, Deutsche Bundesbank.
    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. 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.
    13. Mathias Valla & Xavier Milhaud & Anani Ayodélé Olympio, 2023. "Including individual Customer Lifetime Value and competing risks in tree-based lapse management strategies," Post-Print hal-03903047, HAL.
    14. Abdul-Fatawu Majeed, 2020. "Accelerated Failure Time Models: An Application in Insurance Attrition [Modèles de temps de défaillance accéléré: une application dans l'attrition de l'assurance]," Post-Print hal-02953269, HAL.
    15. Huang, Yiming & Mamon, Rogemar & Xiong, Heng, 2022. "Valuing guaranteed minimum accumulation benefits by a change of numéraire approach," Insurance: Mathematics and Economics, Elsevier, vol. 103(C), pages 1-26.
    16. 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.
    17. Mathias Valla & Xavier Milhaud & Anani Ayodélé Olympio, 2023. "Including individual Customer Lifetime Value and competing risks in tree-based lapse management strategy," Working Papers hal-03903047, HAL.
    18. Xavier Milhaud & Christophe Dutang, 2018. "Lapse tables for lapse risk management in insurance: a competing risk approach," Post-Print hal-01727669, HAL.
    19. Renuka Sane & Susan Thomas, 2020. "From Participation To Repurchase: Low Income Households And Micro‐insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 87(3), pages 783-814, September.
    20. J. François Outreville, 2013. "The Relationship Between Insurance and Economic Development: 85 Empirical Papers for a Review of the Literature," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 16(1), pages 71-122, March.

    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:ecosta:v:8:y:2018:i:c:p:231-249. 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: https://www.journals.elsevier.com/econometrics-and-statistics .

    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.