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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, [email protected]
Alexander Kling
Affiliation:
Institut für Finanz- und Aktuarwissenschaften, Helmholtzstraβe 22, 89081 Ulm, Germany, Tel.: +49 (731) 5031242, Fax: +49 (731) 5031239, [email protected]
Jochen Russ
Affiliation:
Institut für Finanz- und Aktuarwissenschaften, Helmholtzstraβe 22, 89081 Ulm, Germany, Tel.: +49 (731) 5031233, Fax: +49 (731) 5031239, [email protected]
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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

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