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Analytical calculation of risk measures for variable annuity guaranteed benefits

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  • Feng, Runhuan
  • Volkmer, Hans W.

Abstract

With the increasing complexity of investment options in life insurance, more and more life insurers have adopted stochastic modeling methods for the assessment and management of insurance and financial risks. The most prevalent approach in market practice, Monte Carlo simulation, has been observed to be time consuming and sometimes extremely costly. In this paper we propose alternative analytical methods for the calculation of risk measures for variable annuity guaranteed benefits on a stand-alone basis. The techniques for analytical calculations are based on the study of geometric Brownian motion and its integral. Another novelty of the paper is to propose a quantitative model which assesses both market risk on the liability side and revenue risk on the asset side in the same framework from the viewpoint of risk management. As we demonstrate by numerous examples on quantile risk measure and conditional tail expectation, the methods and numerical algorithms developed in this paper appear to be both accurate and computationally efficient.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:3:p:636-648
    DOI: 10.1016/j.insmatheco.2012.09.007
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    References listed on IDEAS

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    1. Yor, Marc, 1993. "From planar Brownian windings to Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 13(1), pages 23-34, September.
    2. 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.
    3. Mary Hardy, 2001. "A Regime-Switching Model of Long-Term Stock Returns," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 41-53.
    4. De Schepper, A. & Goovaerts, M. & Delbaen, F., 1992. "The Laplace transform of annuities certain with exponential time distribution," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 291-294, December.
    5. van Haastrecht, Alexander & Plat, Richard & Pelsser, Antoon, 2010. "Valuation of guaranteed annuity options using a stochastic volatility model for equity prices," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 266-277, December.
    6. 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.
    7. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    8. Coleman, Thomas F. & Li, Yuying & Patron, Maria-Cristina, 2006. "Hedging guarantees in variable annuities under both equity and interest rate risks," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 215-228, April.
    9. 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.
    10. De Schepper, A. & De Vylder, F. & Goovaerts, M. & Kaas, R., 1992. "Interest randomness in annuities certain," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 271-281, December.
    11. Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 195-214, February.
    12. Wang, Yumin, 2009. "Quantile hedging for guaranteed minimum death benefits," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 449-458, December.
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    Cited by:

    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 & Shimizu, Yasutaka, 2016. "Applications of central limit theorems for equity-linked insurance," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 138-148.
    3. Steinorth, Petra & Mitchell, Olivia S., 2015. "Valuing variable annuities with guaranteed minimum lifetime withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 246-258.
    4. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(06), pages 1-24.
    5. 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.
    6. 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.
    7. 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.
    8. Pirjol, Dan & Zhu, Lingjiong, 2016. "Discrete sums of geometric Brownian motions, annuities and Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 19-37.
    9. Wentao Hu & Cuixia Chen & Yufeng Shi & Ze Chen, 2022. "A Tail Measure With Variable Risk Tolerance: Application in Dynamic Portfolio Insurance Strategy," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 831-874, June.
    10. Runhuan Feng & Pingping Jiang & Hans Volkmer, 2020. "Geometric Brownian motion with affine drift and its time-integral," Papers 2012.09661, arXiv.org.
    11. Feng, Runhuan & Jiang, Pingping & Volkmer, Hans, 2021. "Geometric Brownian motion with affine drift and its time-integral," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    12. Runhuan Feng & Alexey Kuznetsov & Fenghao Yang, 2016. "Exponential functionals of Levy processes and variable annuity guaranteed benefits," Papers 1610.00577, arXiv.org.
    13. 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.
    14. Kirkby, J. Lars & Nguyen, Duy, 2021. "Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 408-428.
    15. Emilio Russo, 2020. "A Discrete-Time Approach to Evaluate Path-Dependent Derivatives in a Regime-Switching Risk Model," Risks, MDPI, vol. 8(1), pages 1-22, January.
    16. 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.
    17. 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.
    18. Runhuan Feng & Hans W. Volkmer, 2013. "An identity of hitting times and its application to the valuation of guaranteed minimum withdrawal benefit," Papers 1307.7070, arXiv.org.
    19. Feng, Runhuan & Kuznetsov, Alexey & Yang, Fenghao, 2019. "Exponential functionals of Lévy processes and variable annuity guaranteed benefits," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 604-625.
    20. Brignone, Riccardo & Kyriakou, Ioannis & Fusai, Gianluca, 2021. "Moment-matching approximations for stochastic sums in non-Gaussian Ornstein–Uhlenbeck models," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 232-247.
    21. Daniel Doyle & Chris Groendyke, 2018. "Using Neural Networks to Price and Hedge Variable Annuity Guarantees," Risks, MDPI, vol. 7(1), pages 1-19, December.
    22. Dan Pirjol & Lingjiong Zhu, 2016. "Discrete Sums of Geometric Brownian Motions, Annuities and Asian Options," Papers 1609.07558, arXiv.org.
    23. Runhuan Feng & Hans W. Volkmer, 2015. "Conditional Asian Options," Papers 1505.06946, arXiv.org.
    24. Yoo Byoung Hark & Ko Bangwon & Kwon Hyuk-Sung, 2016. "On the Bayesian Risk Evaluation of Minimum Guarantees in Variable Annuities," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 10(1), pages 21-43, January.

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