Optimal Surrender Policy for Variable Annuity Guarantees

32 Pages Posted: 11 Nov 2013 Last revised: 31 Jan 2014

See all articles by Carole Bernard

Carole Bernard

Grenoble Ecole de Management; Vrije Universiteit Brussel (VUB)

Anne MacKay

University of Waterloo

Max Muehlbeyer

Ulm University

Date Written: January 20, 2014


This paper proposes a technique to derive the optimal surrender strategy for a variable annuity (VA) as a function of the underlying fund value. This approach is based on splitting the value of the VA into a European part and an early exercise premium following the work of Kim and Yu (1996) and Carr, Jarrow and Myneni (1992). The technique is first applied to the simplest VA with GMAB (path-independent benefits) and is then shown to be possibly generalized to the case when benefits are path-dependent. Fees are paid continuously as a fixed percentage of the fund value. Our approach is useful to investigate the impact of path-dependent benefits on surrender incentives.

Keywords: Variable annuities, Optimal surrender, GMMB, GMSB

JEL Classification: G13, G22

Suggested Citation

Bernard, Carole and MacKay, Anne and Muehlbeyer, Max, Optimal Surrender Policy for Variable Annuity Guarantees (January 20, 2014). Available at SSRN: https://ssrn.com/abstract=2352572 or http://dx.doi.org/10.2139/ssrn.2352572

Carole Bernard

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, 1050

Anne MacKay (Contact Author)

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1

Max Muehlbeyer

Ulm University ( email )

Albert-Einstein-Alee 11
Ulm, D-89081