A universal pricing framework for guaranteed minimum benefits in variable annuities. (English) Zbl 1274.91399

Summary: 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.


91G20 Derivative securities (option pricing, hedging, etc.)
91G60 Numerical methods (including Monte Carlo methods)
Full Text: DOI


[1] DOI: 10.1111/j.1539-6975.2006.00165.x
[2] European Insurance 22 (2005)
[3] DOI: 10.2307/251521
[4] Brownian Motion and Stochastic Calculus (1991) · Zbl 0734.60060
[5] European Life Insurance 28 (2004)
[6] Options, Futures and other Derivatives · Zbl 1087.91025
[7] Working Paper (2007)
[8] DOI: 10.2307/252238
[9] Series: Stochastic Modelling and Applied Probability 53 (2003)
[10] Insurance: Mathematics and Economics 39 pp 193– (2006)
[11] Risk-Neutral Valuation – Pricing and Hedging of Finanicial Derivatives (2004)
[12] Scandinavian Actuarial Journal 1 pp 26– (1994)
[13] Business Studies 11 pp 31– (1972)
[14] Annuistar Plus Annuity Prospectus 2 (2005)
[15] DOI: 10.1007/s007800100041 · Zbl 0983.62076
[16] DOI: 10.1016/0304-405X(77)90015-0
[17] Presentation at the Morgan Stanley New Analyst Day (2006)
[18] Insurance: Mathematics and Economics 38 pp 21– (2006)
[19] Working Paper York University and The Fields Institute (2002)
[20] The Journal of Risk and Insurance 68 pp 91– (2001)
[21] Insurance: Mathematics and Economics 33 pp 595– (2004)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.