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A Universal Pricing Framework for Guaranteed Minimum Benefits in Variable Annuities 1

Published online by Cambridge University Press:  17 April 2015

Daniel Bauer ,
Alexander Kling  and
Jochen Russ
Daniel Bauer
Affiliation:
Department of Risk Management and Insurance Georgia State University, 35 Broad Street, Atlanta, GA 30303, USA, Tel.: +1 (404) 4137490, Fax: +1 (404) 4137499, DBauer@gsu.edu
Alexander Kling
Affiliation:
Institut für Finanz- und Aktuarwissenschaften, Helmholtzstraβe 22, 89081 Ulm, Germany, Tel.: +49 (731) 5031242, Fax: +49 (731) 5031239, A.Kling@ifa-ulm.de
Jochen Russ
Affiliation:
Institut für Finanz- und Aktuarwissenschaften, Helmholtzstraβe 22, 89081 Ulm, Germany, Tel.: +49 (731) 5031233, Fax: +49 (731) 5031239, J.Russ@ifa-ulm.de
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Abstract

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Variable Annuities with embedded guarantees are very popular in the US market. There exists a great variety of products with both, guaranteed minimum death benefits (GMDB) and guaranteed minimum living benefits (GMLB). Although several approaches for pricing some of the corresponding guarantees have been proposed in the academic literature, there is no general framework in which the existing variety of such guarantees can be priced consistently. The present paper fills this gap by introducing a model, which permits a consistent and extensive analysis of all types of guarantees currently offered within Variable Annuity contracts. Besides a valuation assuming that the policyholder follows a given strategy with respect to surrender and withdrawals, we are able to price the contract under optimal policyholder behavior. Using both, Monte-Carlo methods and a generalization of a finite mesh discretization approach, we find that some guarantees are overpriced, whereas others, e.g. guaranteed annuities within guaranteed minimum income benefits (GMIB), are offered significantly below their risk-neutral value.

Keywords

Variable Annuityguaranteed minimum benefitsrisk-neutral valuation
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 38 , Issue 2 , November 2008 , pp. 621 - 651
Copyright
Copyright © ASTIN Bulletin 2008

Footnotes

1

The authors thank Hans-Joachim Zwiesler for useful insights and comments.

2

Corresponding author.

References

7. References

Aase, K.K. and Persson, S.A. (1994) Pricing of Unit-Linked Insurance Policies. Scandinavian Actuarial Journal 1, 26–52.CrossRefGoogle Scholar
Bingham, N.H. and Kiesel, R. (2004) Risk-Neutral Valuation – Pricing and Hedging of Finanicial Derivatives. Springer Verlag, Berlin.Google Scholar
Dahl, M. and Møller, T. (2006) Valuation and hedging life insurance liabilities with systematic mortality risk. Insurance: Mathematics and Economics 39, 193–217.Google Scholar
Glasserman, P. (2003) Monte Carlo Methods in Financial Engineering . Series: Stochastic Modelling and Applied Probability, Vol. 53. Springer Verlag, Berlin.Google Scholar
Greene, M.R. (1973) A Note on Loading Charges for Variable Annuities. Journal of Risk and Insurance 40, 473–478.CrossRefGoogle Scholar
Holz, D., Kling, A. and Ruß, J. (2007) Guaranteed Minimum Withdrawal Benefits for Life – An Analysis of Lifelong Withdrawal Guarantees. Working Paper, Ulm University.Google Scholar
Hull, J.C. (1997) Options, Futures and other Derivatives. Prentice-Hall International, London.Google Scholar
Jpmorgan (2004) Variable Annuity Guarantees – Increased Volatility Risk. European Life Insurance, 28. April 2004.Google Scholar
Karatzas, I. and Shreve, S.E. (1991) Brownian Motion and Stochastic Calculus. Springer, Berlin, 1991.Google Scholar
Ledlie, M.C., Corry, D.P., Finkelstein, G.J., Ritchie, A.J., Su, K. and Wilson, D.C.E. (2008) Variable Annuities. Working Paper Presented to the Faculty of Actuaries, 17/03/2008 and the Institute of Actuaries, 31/03/2008.CrossRefGoogle Scholar
Brothers, Lehman (2005) Variable Annuity Living Benefit Guarantees: Over Complex, Over Popular and Over Here? European Insurance, 22. April 2005.Google Scholar
Milevsky, M. and Posner, S.E. (2001) The Titanic Option: Valuation of the Guaranteed Minimum Death Benefit in Variable Annuities and Mutual Funds. The Journal of Risk and Insurance 68, 91–126.Google Scholar
Milevsky, M. and Salisbury, T.S. (2002) The Real Option to Lapse and the Valuation of Death-Protected Investments. Working Paper York University and The Fields Institute, Toronto.Google Scholar
Milevsky, M. and Salisbury, T.S. (2006) Financial valuation of guaranteed minimum withdrawal benefits. Insurance: Mathematics and Economics 38, 21–38.Google Scholar
Mueller, H. (2006) Life Insurance and Annuities – Current Issues and Trends. Presentation at the Morgan Stanley New Analyst Day, New York, NY, January 12, 2006.Google Scholar
Myers, S.C. (1977) Determinants of Corporate Borrowing. Journal of Financial Economics 5, 147–175.CrossRefGoogle Scholar
Møller, T. (2001) Risk-minimizing hedging strategies for insurance payment processes. Finance and Stochastics 5, 419–446.Google Scholar
Pioneer, (2005) Annuistar Plus Annuity Prospectus, 2. Mai 2005.Google Scholar
Rentz, R.A. Jr. (1972) Variable Annuities… Useful but Unknown. Business Studies 11, 31–42.Google Scholar
Sloane, W.R. (1970) Life Insurers, Variable Annuities and Mutual Funds: A Critical Study. The Journal of Risk and Insurance 37, 87–104.CrossRefGoogle Scholar
Tanskanen, A. and Lukkarinen, J. (2004) Fair Valuation of Path-Dependent Participating Life Insurance Contracts. Insurance: Mathematics and Economics 33, 595–609.Google Scholar
Ulm, E.R. (2006) The Effect of the Real Option to Transfer on the Value of Guaranteed Minimum Death Benefits. The Journal of Risk and Insurance 73, 43–69.CrossRefGoogle Scholar