Analytic valuation of guaranteed lifetime withdrawal benefits with a modified ratchet

Guaranteed Lifetime Withdrawal Benefits (GLWBs) are an increasingly popular add-on to Variable Annuities, offering a guaranteed stream of payments for the remainder of the policyholder's life. GLWBs have typically been priced using numerical methods such as finite difference schemes or Monte Carlo simulations; obtaining accurate and precise solutions using these methods can be very computationally expensive. In this paper, we extend an existing method for analytic pricing of these policies to a more general fee structure. We introduce a novel variation on the commonly offered ratchet rider that more directly addresses policyholder motivation around lapse-and-reentry behaviour. We then modify our pricing method to accommodate this new rider and compare it to the existing annual ratchet with respect to a policyholder's incentive to lapse such a policy.