Valuation Perspectives and Decompositions for Variable Annuities with GMWB riders

The guaranteed minimum withdrawal benefit (GMWB) rider, as an add on to a variable annuity (VA), guarantees the return of premiums in the form of peri- odic withdrawals while allowing policyholders to participate fully in any market gains. GMWB riders represent an embedded option on the account value with a fee structure that is different from typical financial derivatives. We consider fair pricing of the GMWB rider from a financial economic perspective. Particular focus is placed on the distinct perspectives of the insurer and policyholder and the unifying relationship. We extend a decomposition of the VA contract into components that reflect term-certain payments and embedded derivatives to the case where the policyholder has the option to surrender, or lapse, the contract early.Comment: 18 pages, proof of Lemma A.1 expanded for clarit

Pricing and Hedging GMWB Riders in a Binomial Framework

The guaranteed minimum withdrawal benefit (GMWB) rider guarantees the return of premiums in the form of periodic withdrawals while allowing policyholders to participate fully in any market gains. The product has evolved into a lifetime version (GLWB) and is a vital component of the variable annuity marketplace, representing asset values of $294B as of September 2011. GMWB riders represent an embedded option on the account value with a fee structure that is different from typical financial derivatives. We present an in-depth study into pricing and hedging the GMWB rider from a financial economic perspective. Our main contributions are twofold. We construct a binomial asset pricing model for GMWBs under optimal policyholder behaviour which results in explicitly formulated perfect hedging strategies in a binomial world. The numerical toolbox for pricing GMWBs in a Black-Scholes world is expanded to include binomial methods. To motivate our work, we begin with a review of the continuous model and a comprehensive synthesis of results from the literature. Throughout, particular focus is placed on the unique perspectives of the insurer and policyholder and the unifying relationship. We also present an approximation algorithm 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. Finally, we explore the effect of deterministic mortality on pricing GMWBs, and run mortality simulations to obtain hedging results which support the diversification principle