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Variable annuities: A unifying valuation approach

Listed author(s):
  • Bacinello, Anna Rita
  • Millossovich, Pietro
  • Olivieri, Annamaria
  • Pitacco, Ermanno

Life annuities and pension products usually involve a number of guarantees, such as minimum accumulation rates, minimum annual payments or a minimum total payout. Packaging different types of guarantees is the feature of so-called variable annuities. Basically, these products are unit-linked investment policies providing a post-retirement income. The guarantees, commonly referred to as GMxBs (namely, Guaranteed Minimum Benefits of type ‘x’), include minimum benefits both in the case of death and survival. In this paper we propose a unifying framework for the valuation of variable annuities under quite general model assumptions. We compute and compare contract values and fair fee rates under ‘static’ and ‘mixed’ valuation approaches, via ordinary and least squares Monte Carlo methods, respectively.

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File URL: http://www.sciencedirect.com/science/article/pii/S0167668711000618
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Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 49 (2011)
Issue (Month): 3 ()
Pages: 285-297

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Handle: RePEc:eee:insuma:v:49:y:2011:i:3:p:285-297
DOI: 10.1016/j.insmatheco.2011.05.003
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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  1. 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.
  2. Ledlie, M. C. & Corry, D. P. & Finkelstein, G. S. & Ritchie, A. J. & Su, K. & Wilson, D. C. E., 2008. "Variable Annuities," British Actuarial Journal, Cambridge University Press, vol. 14(02), pages 327-389, July.
  3. Milevsky, Moshe A. & Salisbury, Thomas S., 2006. "Financial valuation of guaranteed minimum withdrawal benefits," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 21-38, February.
  4. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
  5. Jeffrey R. Brown & James M. Poterba, 2006. "Household Ownership of Variable Annuities," NBER Chapters,in: Tax Policy and the Economy, Volume 20, pages 163-191 National Bureau of Economic Research, Inc.
  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. Anna Rita Bacinello & Enrico Biffis & Pietro Millossovich, 2010. "Regression-based algorithms for life insurance contracts with surrender guarantees," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 1077-1090.
  8. 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.
  9. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
  10. Bauer, Daniel & Kling, Alexander & Russ, Jochen, 2008. "A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 38(02), pages 621-651, November.
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