On the valuation of the initiation option in a GLWB variable annuity

In this paper we focus on the initiation option featured in many Guaranteed Lifelong Withdrawal Benefit variable annuity contracts, granting their owner the right to decide the age at which lifetime withdrawals should begin. Such contracts have been successfully analysed using a PDE approach. The latter method is elegant, but becomes less viable when the valuation model is more involved and other guarantees are considered. As an alternative, we exploit the Least Squares Monte Carlo approach and model the interaction of the initiation option with lapses and other riders.