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A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities

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  • Seyed Amir Hejazi
  • Kenneth R. Jackson
  • Guojun Gan

Abstract

Variable Annuity (VA) products expose insurance companies to considerable risk because of the guarantees they provide to buyers of these products. Managing and hedging these risks requires insurers to find the value of key risk metrics for a large portfolio of VA products. In practice, many companies rely on nested Monte Carlo (MC) simulations to find key risk metrics. MC simulations are computationally demanding, forcing insurance companies to invest hundreds of thousands of dollars in computational infrastructure per year. Moreover, existing academic methodologies are focused on fair valuation of a single VA contract, exploiting ideas in option theory and regression. In most cases, the computational complexity of these methods surpasses the computational requirements of MC simulations. Therefore, academic methodologies cannot scale well to large portfolios of VA contracts. In this paper, we present a framework for valuing such portfolios based on spatial interpolation. We provide a comprehensive study of this framework and compare existing interpolation schemes. Our numerical results show superior performance, in terms of both computational efficiency and accuracy, for these methods compared to nested MC simulations. We also present insights into the challenge of finding an effective interpolation scheme in this framework, and suggest guidelines that help us build a fully automated scheme that is efficient and accurate.

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  • Seyed Amir Hejazi & Kenneth R. Jackson & Guojun Gan, 2017. "A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities," Papers 1701.04134, arXiv.org.
    • Handle: RePEc:arx:papers:1701.04134
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    References listed on IDEAS

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    1. Boyle, Phelim P. & Hardy, Mary R., 1997. "Reserving for maturity guarantees: Two approaches," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 113-127, November.
    2. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    3. Ron Dembo & Dan Rosen, 1999. "The practice of portfolio replication. A practical overview of forward and inverse problems," Annals of Operations Research, Springer, vol. 85(0), pages 267-284, January.
    4. Boyle, Phelim & Tian, Weidong, 2008. "The design of equity-indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 303-315, December.
    5. Eric R. Ulm, 2006. "The Effect of the Real Option to Transfer on the Value of Guaranteed Minimum Death Benefits," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(1), pages 43-69, March.
    6. Chen, Z. & Vetzal, K. & Forsyth, P.A., 2008. "The effect of modelling parameters on the value of GMWB guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 165-173, August.
    7. A. C. Belanger & P. A. Forsyth & G. Labahn, 2009. "Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(6), pages 451-496.
    8. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    9. Gan, Guojun, 2013. "Application of data clustering and machine learning in variable annuity valuation," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 795-801.
    10. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2012. "Valuing equity-linked death benefits and other contingent options: A discounted density approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 73-92.
    11. 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.
    12. 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.
    13. Bauer, Daniel & Reuss, Andreas & Singer, Daniela, 2012. "On the Calculation of the Solvency Capital Requirement Based on Nested Simulations," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 453-499, November.
    14. Gan, Guojun & Lin, X. Sheldon, 2015. "Valuation of large variable annuity portfolios under nested simulation: A functional data approach," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 138-150.
    15. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    16. 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.
    17. 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.
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    Cited by:

    1. Daniel Doyle & Chris Groendyke, 2018. "Using Neural Networks to Price and Hedge Variable Annuity Guarantees," Risks, MDPI, vol. 7(1), pages 1-19, December.
    2. Guojun Gan, 2018. "Valuation of Large Variable Annuity Portfolios Using Linear Models with Interactions," Risks, MDPI, vol. 6(3), pages 1-19, July.
    3. Guojun Gan & Emiliano A. Valdez, 2018. "Nested Stochastic Valuation of Large Variable Annuity Portfolios: Monte Carlo Simulation and Synthetic Datasets," Data, MDPI, vol. 3(3), pages 1-21, September.
    4. Thorsten Moenig, 2021. "Efficient valuation of variable annuity portfolios with dynamic programming," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(4), pages 1023-1055, December.
    5. 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.

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