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 up front. We drive the pricing results by the Black and Schoels model (1973) using 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.

由于可变年金产品的复杂性，我们依靠数值分辨率来公平定价保证最低提款利益 (GMWB) 附加险。该保单在人寿保险合同中称为嵌入式看跌期权，使合同所有者可以在固定期限内提取固定金额。我们假设预先支付一笔保费。我们通过 Black 和 Schoels 模型 (1973) 使用蒙特卡洛模拟来驱动定价结果，以在与合同设计和概念、投保人特征和失效行为以及不同市场参数相关的特定假设下近似公平费用。更值得注意的是，我们的算法允许执行敏感性分析，以寻求不同参数对 Solvency II推荐的策略价值的影响规律性。我们发现 GMWB 公平费用对合同输入的任何突然变化都非常敏感和敏感。