Pricing Guaranteed Minimum Withdrawal Benefits: a PDE Approach

In this paper, a financial engineering method is developed for pricing guaranteed minimum withdrawal benefits which are extremely popular in variable annuities markets. The embedded options of the contract which provide money-back guarantees and market guarantees on invested principal regardless of market performance are separated. By analyzing the periodic cash-flows of the policy and using the Feynman-Kac formula, a new pricing model which is characterized by a simple two-dimensional partial differential equation (PDE) is presented. Then the effect of the key parameter on the policy value and the fair insurance charge are also obtained by combining the finite difference approach with search method. Finally, the numerical results show that the pricing method is efficient and in accord with the current model.