含有多种最低利益保证的变额年金定价

Pricing Variable Annuities Embedding Various Guaranteed Minimum Benefits

摘要:

我国人口老龄化速度加快, 具有抗通胀、养老和投资功能的变额年金产品引起了人们的关注. 对同时含有多种最低利益保证的变额年金定价进行研究. 首先在跳扩散模型下, 提出了柳树法定价变额年金的数值方法. 同时考虑了返回初值型、Rollup 型和Ratchet型的最低利益保证. 本文方法可以很容易推广到其他的随机过程, 并且柳树构建过程和定价过程相互独立, 在不同的风险资产价格过程下定价, 无需额外的工作量, 具有较高的通用性. 相比于现有的方法, 降低了计算维度, 减少了计算时间. 最后通过数值试验, 与蒙特卡洛法进行对比, 说明了本文方法的准确性、高效性.

Abstract:

With the acceleration of population aging in China, the variable annuities have drawn a lot of attentions due to its anti-inflation, pension and investment functions. This paper studies the valuation of variable annuities embedding various guaranteed minimum benefits. We propose a willow tree method for pricing variable annuities under the jump-diffusion model in three guarantee types, including return of premium, Roll-up and Ratchet types. Our tree structure can be easily extended to other stochastic models. The willow tree construction and pricing procedure are independent of each other. Thus, for different stochastic models, it does not need extra work and has better applicability. Finally, numerical experiments demonstrate the accuracy and high efficiency of the proposed method compared with Monte Carlo method.