In this paper we present a dynamic programming algorithm for pricing variable annuities
with Guaranteed Minimum Withdrawal Benefits (GMWB) under a general Lévy processes
framework. The GMWB gives the policyholder the right to make periodical withdrawals
from her policy account even when the value of this account is exhausted. Typically, the
total amount guaranteed for withdrawals coincides with her initial investment, providing
then a protection against downside market risk. At each withdrawal date, the policyholder
has to decide whether, and how much, to withdraw, or to surrender the contract. We
show how different levels of rationality in the policyholder’s withdrawal behaviour can be modelled. We perform a sensitivity analysis comparing the numerical results obtained for
different contractual and market parameters, policyholder behaviours, and different types
of Lévy processes.
