This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract. 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 policyholder's withdrawal behaviours 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.
Permanent
In this paper we describe and compare different numerical schemes for\ud
the valuation of unit-linked contracts with and without surrender option. We implement\ud
two different algorithms based on the Least Squares Monte Carlo method\ud
(LSMC), an algorithm based on the Partial Differential Equation Approach (PDE)\ud
and another based on Binomial Trees. We introduce a unifying way to define and\ud
solve the valuation problem in order to include the case of contracts with premiums\ud
paid continuously over time, along with that of single premium contracts, usually\ud
considered in the literature. Finally, we analyse the impact on the fair premiums of\ud
the main parameters of the model
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