Pricing and Hedging GMWB Riders in a Binomial Framework

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 similar to those presented in Hyndman and Wenger (Insurance Math. Econom. 55:283-290, 2014) 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 model.