IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v58y2021i4d10.1007_s10614-020-09999-9.html
   My bibliography  Save this article

A Time Series Framework for Pricing Guaranteed Lifelong Withdrawal Benefit

Author

Listed:
  • Nitu Sharma

    (Indian Institute of Technology Delhi)

  • S. Dharmaraja

    (Indian Institute of Technology Delhi)

  • Viswanathan Arunachalam

    (Universidad Nacional de Colombia)

Abstract

In this work, the pricing problem of a variable annuity (VA) contract embedded with a guaranteed lifelong withdrawal benefit (GLWB) rider has been considered. VAs are annuities whose value is linked with a sub-account fund consisting of bonds and equities. The GLWB rider provides a series of regular payments to the policyholder during the policy duration when he is alive irrespective of the portfolio performance. Also, the remaining fund value is given to his nominee, at the time of death of the policyholder. The appropriate modelling of fund plays a crucial role in the pricing of VA products. In the literature, several authors model the fund value in a VA contract using a geometric Brownian motion (GBM) model with a constant variance. However, in real life, the financial assets returns are not Normal distributed. The returns have non-zero skewness, high kurtosis, and leverage effect. This paper proposes a discrete-time model for annuity pricing using generalized autoregressive conditional heteroscedastic (GARCH) models, which overcome the limitations of the GBM model. The proposed model is analyzed with numerical illustration along with sensitivity analysis.

Suggested Citation

  • Nitu Sharma & S. Dharmaraja & Viswanathan Arunachalam, 2021. "A Time Series Framework for Pricing Guaranteed Lifelong Withdrawal Benefit," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1225-1261, December.
    • Handle: RePEc:kap:compec:v:58:y:2021:i:4:d:10.1007_s10614-020-09999-9
    DOI: 10.1007/s10614-020-09999-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-020-09999-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-020-09999-9?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. 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.
    2. Gabriella Piscopo & Steven Haberman, 2011. "The Valuation of Guaranteed Lifelong Withdrawal Benefit Options in Variable Annuity Contracts and the Impact of Mortality Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(1), pages 59-76.
    3. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Ng, Andrew Cheuk-Yin & Li, Johnny Siu-Hang & Chan, Wai-Sum, 2011. "Modeling investment guarantees in Japan: A risk-neutral GARCH approach," International Review of Financial Analysis, Elsevier, vol. 20(1), pages 20-26, January.
    6. Zeileis, Achim & Leisch, Friedrich & Hornik, Kurt & Kleiber, Christian, 2002. "strucchange: An R Package for Testing for Structural Change in Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 7(i02).
    7. François Quittard-Pinon & Rivo Randrianarivony, 2011. "Impacts of Jumps and Stochastic Interest Rates on the Fair Costs of Guaranteed Minimum Death Benefit Contracts," Post-Print hal-02312495, HAL.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    9. Jingjiang Peng & Kwai Sun Leung & Yue Kuen Kwok, 2012. "Pricing guaranteed minimum withdrawal benefits under stochastic interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 12(6), pages 933-941, October.
    10. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    11. François Quittard-Pinon & Rivo Randrianarivony, 2011. "Impacts of Jumps and Stochastic Interest Rates on the Fair Costs of Guaranteed Minimum Death Benefit Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 36(1), pages 51-73, June.
    12. Ericsson, Jan & Huang, Xiao & Mazzotta, Stefano, 2016. "Leverage and asymmetric volatility: The firm-level evidence," Journal of Empirical Finance, Elsevier, vol. 38(PA), pages 1-21.
    13. Johnny Siu‐Hang Li & Mary R. Hardy & Ken Seng Tan, 2010. "On Pricing and Hedging the No‐Negative‐Equity Guarantee in Equity Release Mechanisms," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 77(2), pages 499-522, June.
    14. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    15. François Quittard-Pinon & Rivo Randrianarivony, 2011. "Impacts of Jumps and Stochastic Interest Rates on the Fair Costs of Guaranteed Minimum Death Benefit Contracts," Post-Print hal-02358451, HAL.
    16. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    17. Jungmin Choi, 2017. "Indifference Pricing of a GLWB Option in Variable Annuities," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(2), pages 281-296, April.
    18. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities1," ASTIN Bulletin, Cambridge University Press, vol. 38(2), pages 621-651, November.
    19. Forsyth, Peter & Vetzal, Kenneth, 2014. "An optimal stochastic control framework for determining the cost of hedging of variable annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 29-53.
    20. Min Dai & Yue Kuen Kwok & Jianping Zong, 2008. "Guaranteed Minimum Withdrawal Benefit In Variable Annuities," Mathematical Finance, Wiley Blackwell, vol. 18(4), pages 595-611, October.
    Full references (including those not matched with items on IDEAS)

    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. Muhammad Surajo Sanusi, 2017. "Investigating the sources of Black’s leverage effect in oil and gas stocks," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1318812-131, January.
    2. Ender Su & John Bilson, 2011. "Trading asymmetric trend and volatility by leverage trend GARCH in Taiwan stock index," Applied Economics, Taylor & Francis Journals, vol. 43(26), pages 3891-3905.
    3. Wu, Guojun & Xiao, Zhijie, 2002. "A generalized partially linear model of asymmetric volatility," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 287-319, August.
    4. Halunga, Andreea G. & Orme, Chris D., 2009. "First-Order Asymptotic Theory For Parametric Misspecification Tests Of Garch Models," Econometric Theory, Cambridge University Press, vol. 25(2), pages 364-410, April.
    5. Amare Wubishet Ayele & Emmanuel Gabreyohannes & Yohannes Yebabe Tesfay, 2017. "Macroeconomic Determinants of Volatility for the Gold Price in Ethiopia: The Application of GARCH and EWMA Volatility Models," Global Business Review, International Management Institute, vol. 18(2), pages 308-326, April.
    6. Siddique, Akhtar R., 2003. "Common asset pricing factors in volatilities and returns in futures markets," Journal of Banking & Finance, Elsevier, vol. 27(12), pages 2347-2368, December.
    7. Jaleel, Fazeel M. & Samarakoon, Lalith P., 2009. "Stock market liberalization and return volatility: Evidence from the emerging market of Sri Lanka," Journal of Multinational Financial Management, Elsevier, vol. 19(5), pages 409-423, December.
    8. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Dong, Bing & Xu, Wei & Sevic, Aleksandar & Sevic, Zeljko, 2020. "Efficient willow tree method for variable annuities valuation and risk management☆," International Review of Financial Analysis, Elsevier, vol. 68(C).
    10. Awartani, Basel M.A. & Corradi, Valentina, 2005. "Predicting the volatility of the S&P-500 stock index via GARCH models: the role of asymmetries," International Journal of Forecasting, Elsevier, vol. 21(1), pages 167-183.
    11. Mehmet Sahiner, 2022. "Forecasting volatility in Asian financial markets: evidence from recursive and rolling window methods," SN Business & Economics, Springer, vol. 2(10), pages 1-74, October.
    12. Jorge Caiado, 2004. "Modelling And Forecasting The Volatility Of The Portuguese Stock Index Psi-20," Portuguese Journal of Management Studies, ISEG, Universidade de Lisboa, vol. 9(1), pages 3-21.
    13. A. B. M. Rabiul Alam Beg & Sajid Anwar, 2014. "Detecting volatility persistence in GARCH models in the presence of the leverage effect," Quantitative Finance, Taylor & Francis Journals, vol. 14(12), pages 2205-2213, December.
    14. Turan Bali, 2007. "Modeling the dynamics of interest rate volatility with skewed fat-tailed distributions," Annals of Operations Research, Springer, vol. 151(1), pages 151-178, April.
    15. John D. Levendis, 2018. "Time Series Econometrics," Springer Texts in Business and Economics, Springer, number 978-3-319-98282-3, August.
    16. Geoffrey F. Loudon & Wing H. Watt & Pradeep K. Yadav, 2000. "An empirical analysis of alternative parametric ARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 117-136.
    17. Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
    18. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," International Economics, CEPII research center, issue 157, pages 179-202.
    19. Nam Kiseok, 2003. "The Asymmetric Reverting Property of Stock Returns," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(4), pages 1-18, March.
    20. Louzis, Dimitrios P. & Xanthopoulos-Sisinis, Spyros & Refenes, Apostolos P., 2011. "Are realized volatility models good candidates for alternative Value at Risk prediction strategies?," MPRA Paper 30364, University Library of Munich, Germany.

    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:kap:compec:v:58:y:2021:i:4:d:10.1007_s10614-020-09999-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.