Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-12T19:47:55.015Z Has data issue: false hasContentIssue false
  • English
  • Français

Are Flexible Premium Variable Annuities Under-Priced?

Published online by Cambridge University Press:  09 August 2013

Yichun Chi  and
X. Sheldon Lin
Yichun Chi
Affiliation:
China Institute for Actuarial Science, Central University of Finance and Economics, Beijing, China100081, E-Mail: [email protected]
X. Sheldon Lin
Affiliation:
Department of Statistics, University of Toronto, 100 St. George Street, Toronto Ontario, CanadaM5S 3G3, E-Mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A variable annuity (VA) is a deferred annuity that allows an annuitant to invest his/her contributions into a range of mutual funds. A separate account termed as sub-account is set up for the investment. Unlike a mutual fund, a VA offers a guaranteed minimum death benefit or GMDB and often offers a guaranteed minimum living benefit or GMLB during the accumulation phase of the VA contract. Almost all the research to date has focused on single premium variable annuities (SPVAs), i.e. it is assumed that an annuitant makes a single lump-sum contribution at the time of issue. In this paper, we study flexible premium variable annuities (FPVAs) that allow contributions during the accumulation phase. We derive a valuation formula for guarantees embedded in FPVAs and show that the delta hedging strategy for an FPVA is substantially different from that for an SPVA. The numerical examples illustrate that the cost in the form of mortality and expense (M&E) fee for an FPVA in many situations is significantly higher than the cost for a similar SPVA. This finding suggests that the current pricing practice by most VA providers that charges the same M&E fee for both should be re-examined.

Keywords

Variable AnnuityFlexible PremiumGMDBGMLBArithmetic Asian OptionMortality and Expense Fee
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 42 , Issue 2 , November 2012 , pp. 559 - 574
Copyright
Copyright © International Actuarial Association 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bauer, D., Kling, A. and Russ, J. (2008) A universal pricing framework for guaranteed minimum benefits in variable annuities. Astin Bulletin 38(2), 621–651.Google Scholar
Broadie, M., Glasserman, P. and Kou, S. (1999) Connecting discrete and continuous path-dependent options. Finance and Stochastics 3(1), 55–82.Google Scholar
Chen, Z., Vetzal, K. and Forsyth, P.A. (2008) The effect of modelling parameters on the value of GMWB guarantees. Insurance: Mathematics and Economics 43(1), 165–173.Google Scholar
Coleman, T.F, Li, Y. and Patron, M.-C. (2006) Hedging guarantees in variable annuities under both equity and interest rate risks. Insurance: Mathematics and Economics 38(2), 215–228.Google Scholar
Dai, M., Kwok, Y.K. and Zong, J.P. (2008) Guaranteed minimum withdrawal benefit in variable annuities. Mathematical Finance 18(4), 595–611.Google Scholar
Geman, H. and Yor, M. (1993) Bessel processes, Asian options, and perpetuities. Mathematical Finance 3(4), 349–375.CrossRefGoogle Scholar
Hürlimann, W. (2010) Analytical pricing of the unit-linked endowment with guarantees and periodic premiums. Astin Bulletin 40(2), 631–653.Google Scholar
Insured Retirement Institute (IRI) (2011) 2011 IRI Fact Book: A Guide to Information, Trends, and Data in the Retirement Income Industry.Google Scholar
Lin, X.S., Tan, K.S. and Yang, H. (2009) Pricing annuity guarantees under a regime-switch model. North American Actuarial Journal 13(3), 316–338.CrossRefGoogle Scholar
New York Life 2011. Facts about the New York Life flexible premium variable annuity. www.newyorklife.com/newyorklife.com/General/FileLink/ Google Scholar
Nielsen, J.A. and Sandmann, K. (2002) The fair premium of an equity-linked life and pension insurance. In: Sandmann, K., Schönbucher, P. (Eds), Advances in Finance and Stochastics: Essays in Honor of Dieter Sondermann. Springer, Heidelberg.Google Scholar
Milevsky, M.A. and Salisbury, T.S. (2006) Financial valuation of guaranteed minimum withdrawal benefits. Insurance: Mathematics and Economics 38(1), 21–38.Google Scholar
Rogers, L.C.G. and Shi, Z. (1995) The value of an Asian option. Journal of Applied Probability 32(4), 1077–1088.CrossRefGoogle Scholar
Schrager, D.F. and Pelsser, A.A.J. (2004) Pricing rate of return guarantees in regular premium unit linked insurance. Insurance: Mathematics and Economics 35(2), 369–398.Google Scholar
Shaked, M. and Shanthikumar, J.G. (2007) Stochastic Orders. Springer, New York.Google Scholar
Thompson, G. (1999) Fast narrow bounds on the value of Asain options. Working paper, Centre for Financial Research, University of Cambridge.Google Scholar
Vecer, J. (2002) Unified Asian pricing. Risk, June, 113–116.Google Scholar
Yor, M. (2001) Exponential Functionals of Brownian Motion and Related Processes. Springer.Google Scholar