Variable annuities with complex surrender features are nowadays increasingly popular for managing longevity risks. The study of their accurate pricing and sensitivity analysis is one of the main actuarial research topics. This paper studies the valuation problem of variable annuity contracts with guaranteed minimum maturity benefits on a set of predetermined discrete tenor dates under regime-switching Lévy models. Extending from existing vanilla payoffs, we consider the guaranteed minimum maturity benefits with lookback and geometric average features. We customise the dynamic programming principle to solve the corresponding optimal stopping problem, relying on some semi-analytical valuation formulae resulting from an acute Fourier cosine series expansion. Finally, numerical illustrations are provided to show the accuracy and efficiency of the proposed method. We also demonstrate the use of our proposed method in a range of sensitivity analysis exercises, which shed light on the pricing and risk management of complex variable annuity products.

具有复杂退保特征的可变年金如今越来越受欢迎，用于管理长寿风险。对其准确定价和敏感性分析的研究是精算学的主要研究课题之一。本文研究了在制度转换 Lévy 模型下，在一组预定的离散期限内保证最低到期收益的可变年金合同的估值问题。从现有的普通收益扩展，我们考虑具有回顾和几何平均特征的保证最小成熟度收益。我们自定义动态规划原理来解决相应的最优停止问题，依赖于锐傅里叶余弦级数展开产生的一些半解析估值公式。最后，提供了数值说明以显示所提出方法的准确性和效率。我们还在一系列敏感性分析练习中展示了我们提出的方法的使用，这些练习阐明了复杂可变年金产品的定价和风险管理。