The GMWB guarantee embedded in Life Insurance Contracts: Fair Value Pricing Problem

Due to the complexity of the variable annuities products, we rely on numerical resolution to fairly price the guaranteed minimum withdrawal benefit (GMWB) rider. This policy, known as an embedded put option in the life insurance contracts, gives the contract owner the possibility to withdraw a fixed amount for a fixed period. We assume a single premium payment upfront. We use a Monte Carlo simulation to approximate the fair fees under specific assumptions related to the contract design and conception, the policyholder characteristics and lapse behavior, and different market parameters. More notably, our algorithm allows to perform a sensitivity analysis to seek the impact of different parameters on the value of the policy as recommended by the Solvency II regularities. We find that the GMWB fair fees are intensively sensitive and responsive to any sudden change in the contract inputs.