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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 strategiesfunded using only periodic fee income. We consider the separate perspectives ofthe insurer and policyholder and introduce a unifying relationship.Decompositions of the VA and GMWB contract into term-certain payments andoptions representing the guarantee and early surrender features are extended tothe binomial framework. We incorporate an approximation algorithm for Asianoptions that significantly improves efficiency of the binomial model whileretaining accuracy. Several numerical examples are provided which illustrateboth the accuracy and the tractability of the binomial model. We extend thebinomial model to include policy holder mortality and death benefits. Pricing,hedging, and the decompositions of the contract are extended to incorporatemortality risk. We prove limiting results for the hedging strategies anddemonstrate mortality risk diversification. Numerical examples are providedwhich illustrate the effectiveness of hedging and the diversification ofmortality risk under capacity constraints with finite pools.

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