A flexible tree for evaluating guaranteed minimum withdrawal benefits under deferred life annuity contracts with various provisions

Valuing guaranteed minimum withdrawal benefit (GMWB) has attracted significant attention from both the academic field and real world financial markets. However, some popular provisions of GMWB contracts, like the deferred life annuity structure, rollup interest rate guarantees, and surrender options are hard to be evaluated analytically and are rarely addressed in the academic literature. This paper proposes a flexible tree model that can accurately evaluate the values and the fair insurance fees of GMWBs. The flexibility of our tree allows us to faithfully implement the aforementioned provisions without introducing significant numerical pricing errors. The mortality risk can also be easily incorporated into our pricing model. Our numerical results verify the robustness of our tree and demonstrate how the aforementioned provisions and the mortality risk significantly influence the values and the fair insurance fees of GMWBs.