GMWB Riders in a Binomial Framework - Pricing, Hedging, and Diversification of Mortality Risk

41 Pages Posted: 31 Oct 2014 Last revised: 7 Jul 2016

See all articles by Cody Blaine Hyndman

Cody Blaine Hyndman

Concordia University, Quebec - Department of Mathematics and Statistics

Menachem Wenger

Concordia University, Quebec - Department of Mathematics & Statistics

Date Written: July 6, 2016

Abstract

We construct a binomial model for a guaranteed minimum withdrawal benefit (GMWB) rider to a variable annuity (VA) under optimal policyholder behaviour. The binomial model results in explicitly formulated perfect hedging strategies funded using only periodic fee income. We consider the separate perspectives of the insurer and policyholder and introduce a unifying relationship. Decompositions of the VA and GMWB contract into term-certain payments and options representing the guarantee and early surrender features are extended to the binomial framework. We incorporate an approximation algorithm for Asian options that significantly improves efficiency of the binomial model while retaining accuracy. Several numerical examples are provided which illustrate both the accuracy and the tractability of the binomial model. We extend the binomial model to include policy holder mortality and death benefits. Pricing, hedging, and the decompositions of the contract are extended to incorporate mortality risk. We prove limiting results for the hedging strategies and demonstrate mortality risk diversification. Numerical examples are provided which illustrate the effectiveness of hedging and the diversification of mortality risk under capacity constraints with finite pools.

Keywords: variable annuity, GMWB, optimal stopping, hedging, binomial models, mortality

JEL Classification: G22, G12, G13, C61, C63

Suggested Citation

Hyndman, Cody Blaine and Wenger, Menachem, GMWB Riders in a Binomial Framework - Pricing, Hedging, and Diversification of Mortality Risk (July 6, 2016). Available at SSRN: https://ssrn.com/abstract=2516369 or http://dx.doi.org/10.2139/ssrn.2516369

Cody Blaine Hyndman (Contact Author)

Concordia University, Quebec - Department of Mathematics and Statistics ( email )

Concordia University
1455 boulevard de Maisonneuve Ouest
Montreal, Quebec H3G 1M8
Canada
514-848-2424 (Phone)

Menachem Wenger

Concordia University, Quebec - Department of Mathematics & Statistics ( email )

Canada

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