含组合型GMWB条款的变额年金定价
Pricing of Variable Annuities with Combined Guaranteed Minimum Withdrawal Benefit
摘要: 带有最低保障条款的变额年金是目前存在的商业年金中对养老金系统的最好补充。本文通过对现有最低保障类条款的结合，构造了在严重通货膨胀的当下更适合市场环境的组合型条款。本文在最低提款保障上添加了最低到期保障以及可随时退保的选择权，在无套利假设的前提下使用现金流法通过研究保险公司的可能性损失，在随机死亡率、随机利率、理性退保等假设下给出了公平费率的定价公式。运用蒙特卡洛法对保险公司的潜在损失和公平费率进行了模拟计算和敏感性分析，同时讨论了添加可提前退保权益对保险公司可能面对风险的影响。数值仿真结果说明了本文定价模型的稳定性和高效性。
Abstract:
Variable annuities with minimum guaranteed benefits are the best supplements to pension system among the current commercial annuities. This study builds a new guaranteed rider to fit the severe inflation by integrating the previous guaranteed minimum benefits. This paper adds the surrender option and the guaranteed minimum maturity benefit to the guaranteed minimum withdrawal benefit, as well as using the numéraire approach to price the fair premium by studying the potential loss of insurance company under the no-arbitrage hypothesis, with stochastic mortality and interest rate assumptions. Use Monte Carlo method to simulate and sensitivity analyze the potential loss of insurance company and fair rate and discuss the risk that insurance company may face with surrender option. The numerical results are consistent and efficient.
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