IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20150008.html
   My bibliography  Save this paper

Comonotonic Approximations of Risk Measures for Variable Annuity Guaranteed Benefits with Dynamic Policyholder Behavior

Author

Listed:
  • Runhuan Feng

    (University of Illinois at Urbana-Champaign, United States)

  • Xiaochen Jing

    (University of Illinois at Urbana-Champaign, United States)

  • Jan Dhaene

    (Katholieke Universiteit Leuven, Belgium)

Abstract

The computation of various risk metrics is essential to the quantitative risk management of variable annuity guaranteed bene ts. The current market practice of Monte Carlo simulation often requires intensive computations, which can be very costly for insurance companies to implement and take so much time that they cannot obtain information and take actions in a timely manner. In an attempt to nd low-cost and ecient alternatives, we explore the techniques of comonotonic bounds to produce closed-form approximation of the risk measures for variable annuity guaranteed bene ts. The techniques are further developed in this paper to address in a systematic way risk measures for death bene ts with the consideration of dynamic policyholder behavior.

Suggested Citation

  • Runhuan Feng & Xiaochen Jing & Jan Dhaene, 2015. "Comonotonic Approximations of Risk Measures for Variable Annuity Guaranteed Benefits with Dynamic Policyholder Behavior," Tinbergen Institute Discussion Papers 15-008/IV/DSF85, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20150008
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/15008.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Feng, Runhuan & Volkmer, Hans W., 2014. "Spectral Methods For The Calculation Of Risk Measures For Variable Annuity Guaranteed Benefits," ASTIN Bulletin, Cambridge University Press, vol. 44(3), pages 653-681, September.
    2. Costabile, M., 2013. "Analytical valuation of periodical premiums for equity-linked policies with minimum guarantee," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 597-600.
    3. Bacinello, Anna Rita & Millossovich, Pietro & Olivieri, Annamaria & Pitacco, Ermanno, 2011. "Variable annuities: A unifying valuation approach," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 285-297.
    4. David Hobson & Peter Laurence & Tai-Ho Wang, 2005. "Static-arbitrage upper bounds for the prices of basket options," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 329-342.
    5. Runhuan Feng, 2014. "A Comparative Study of Risk Measures for Guaranteed Minimum Maturity Benefits by a PDE Method," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(4), pages 445-461, October.
    6. J. Dhaene & S. Vanduffel & M. Goovaerts, 2007. "Comonotonicity," Review of Business and Economic Literature, KU Leuven, Faculty of Economics and Business (FEB), Review of Business and Economic Literature, vol. 0(2), pages 265-278.
    7. Simon, S. & Goovaerts, M. J. & Dhaene, J., 2000. "An easy computable upper bound for the price of an arithmetic Asian option," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 175-183, May.
    8. Delong, Łukasz, 2014. "Pricing and hedging of variable annuities with state-dependent fees," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 24-33.
    9. Ulm, Eric R., 2014. "Analytic solution for ratchet guaranteed minimum death benefit options under a variety of mortality laws," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 14-23.
    10. Ulm, Eric R., 2008. "Analytic Solution for Return of Premium and Rollup Guaranteed Minimum Death Benefit Options Under Some Simple Mortality Laws," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 543-563, November.
    11. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    12. Claymore Marshall & Mary Hardy & David Saunders, 2010. "Valuation of a Guaranteed Minimum Income Benefit," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(1), pages 38-58.
    13. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    14. J. Dhaene & S. Vanduffel & M. J. Goovaerts & R. Kaas & D. Vyncke, 2005. "Comonotonic Approximations for Optimal Portfolio Selection Problems," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(2), pages 253-300, June.
    15. J. Marin-Solano (Universitat de Barcelona) & O. Roch (Universitat de Barcelona) & J. Dhaene (Katholieke Univerisiteit Leuven) & C. Ribas (Universitat de Barcelona) & M. Bosch-Princep (Universitat de B, 2009. "Buy-and-Hold Strategies and Comonotonic Approximations," Working Papers in Economics 213, Universitat de Barcelona. Espai de Recerca en Economia.
    16. 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.
    17. Feng, Runhuan & Volkmer, Hans W., 2012. "Analytical calculation of risk measures for variable annuity guaranteed benefits," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 636-648.
    18. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities 1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 621-651, November.
    19. Vanduffel, Steven & Shang, Zhaoning & Henrard, Luc & Dhaene, Jan & Valdez, Emiliano A., 2008. "Analytic bounds and approximations for annuities and Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1109-1117, June.
    20. 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.
    21. Chen, X. & Deelstra, G. & Dhaene, J. & Vanmaele, M., 2008. "Static super-replicating strategies for a class of exotic options," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1067-1085, June.
    22. Chi, Yichun & Lin, X. Sheldon, 2012. "Are Flexible Premium Variable Annuities Under-Priced?," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 559-574, November.
    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. Jin Sun & Pavel V. Shevchenko & Man Chung Fung, 2018. "The Impact of Management Fees on the Pricing of Variable Annuity Guarantees," Risks, MDPI, vol. 6(3), pages 1-20, September.
    2. Raj Kumari Bahl & Sotirios Sabanis, 2017. "General Price Bounds for Guaranteed Annuity Options," Papers 1707.00807, arXiv.org.

    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. Feng, Runhuan & Huang, Huaxiong, 2016. "Statutory financial reporting for variable annuity guaranteed death benefits: Market practice, mathematical modeling and computation," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 54-64.
    2. 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.
    3. Raj Kumari Bahl & Sotirios Sabanis, 2017. "General Price Bounds for Guaranteed Annuity Options," Papers 1707.00807, arXiv.org.
    4. Daniël Linders & Jan Dhaene & Wim Schoutens, 2015. "Option prices and model-free measurement of implied herd behavior in stock markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-35.
    5. H. Albrecher & P. A. Mayer & W. Schoutens, 2008. "General Lower Bounds for Arithmetic Asian Option Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 123-149.
    6. Liang, Xiaoqing & Tsai, Cary Chi-Liang & Lu, Yi, 2016. "Valuing guaranteed equity-linked contracts under piecewise constant forces of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 150-161.
    7. Daniel Doyle & Chris Groendyke, 2018. "Using Neural Networks to Price and Hedge Variable Annuity Guarantees," Risks, MDPI, vol. 7(1), pages 1-19, December.
    8. Hansjörg Albrecher & Philipp Mayer, 2010. "Semi-Static Hedging Strategies For Exotic Options," World Scientific Book Chapters, in: Rüdiger Kiesel & Matthias Scherer & Rudi Zagst (ed.), Alternative Investments And Strategies, chapter 14, pages 345-373, World Scientific Publishing Co. Pte. Ltd..
    9. Wang, Gu & Zou, Bin, 2021. "Optimal fee structure of variable annuities," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 587-601.
    10. Wenlong Hu, 2020. "Risk management of guaranteed minimum maturity benefits under stochastic mortality and regime-switching by Fourier space time-stepping framework," Papers 2006.15483, arXiv.org, revised Dec 2020.
    11. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2020. "Model-free bounds for multi-asset options using option-implied information and their exact computation," Papers 2006.14288, arXiv.org, revised Jan 2022.
    12. Huang, H. & Milevsky, M.A. & Salisbury, T.S., 2014. "Optimal initiation of a GLWB in a variable annuity: No Arbitrage approach," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 102-111.
    13. He, Junnan & Tang, Qihe & Zhang, Huan, 2016. "Risk reducers in convex order," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 80-88.
    14. Zhenyu Cui & Anne MacKay & Marie-Claude Vachon, 2022. "Analysis of VIX-linked fee incentives in variable annuities via continuous-time Markov chain approximation," Papers 2207.14793, arXiv.org.
    15. Xu, Guoping & Zheng, Harry, 2009. "Approximate basket options valuation for a jump-diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 188-194, October.
    16. Tavin, Bertrand, 2015. "Detection of arbitrage in a market with multi-asset derivatives and known risk-neutral marginals," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 158-178.
    17. J. Marin-Solano (Universitat de Barcelona) & O. Roch (Universitat de Barcelona) & J. Dhaene (Katholieke Univerisiteit Leuven) & C. Ribas (Universitat de Barcelona) & M. Bosch-Princep (Universitat de B, 2009. "Buy-and-Hold Strategies and Comonotonic Approximations," Working Papers in Economics 213, Universitat de Barcelona. Espai de Recerca en Economia.
    18. Gan Guojun & Valdez Emiliano A., 2017. "Valuation of large variable annuity portfolios: Monte Carlo simulation and synthetic datasets," Dependence Modeling, De Gruyter, vol. 5(1), pages 354-374, December.
    19. Kouritzin, Michael A. & MacKay, Anne, 2018. "VIX-linked fees for GMWBs via explicit solution simulation methods," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 1-17.
    20. Evangelia Dragazi & Shuaiqiang Liu & Antonis Papapantoleon, 2024. "Improved model-free bounds for multi-asset options using option-implied information and deep learning," Papers 2404.02343, arXiv.org.

    More about this item

    Keywords

    Variable annuity guaranteed benefit; risk measures; value at risk; conditional tail expectation; geometric Brownian motion; comonotonicity; dynamic policyholder behavior;
    All these keywords.

    JEL classification:

    • G19 - Financial Economics - - General Financial Markets - - - Other
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tin:wpaper:20150008. 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: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.html .

    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.