Variable annuities have become popular retirement and investment vehicles due to their attractive guarantee features. Nonetheless, managing the financial risks associated with the guarantees poses great challenges for insurers. One challenge is risk quantification, which involves frequent valuation of the guarantees. Insurers rely on the use of Monte Carlo simulation for valuation as the guarantees are too complicated to be valued by closed-form formulas. However, Monte Carlo simulation is computationally intensive. In this paper, we empirically explore the use of tree-based models for constructing metamodels for the valuation of the guarantees. In particular, we consider traditional regression trees, tree ensembles, and trees based on unbiased recursive partitioning. We compare the performance of tree-based models to that of existing models such as ordinary kriging and generalised beta of the second kind (GB2) regression. Our results show that tree-based models are efficient in producing accurate predictions and the gradient boosting method is considered the most superior in terms of prediction accuracy.

中文翻译：

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可变年金估值的基于树的模型：参数调整和实证分析

可变年金因其有吸引力的保证功能而成为流行的退休和投资工具。尽管如此，管理与担保相关的财务风险给保险公司带来了巨大挑战。一项挑战是风险量化，其中涉及对担保的频繁估值。保险公司依赖使用蒙特卡罗模拟进行估值，因为担保过于复杂，无法通过封闭式公式进行估值。然而，蒙特卡罗模拟是计算密集型的。在本文中，我们经验性地探索了使用基于树的模型来构建用于担保估值的元模型。特别是，我们考虑了传统的回归树、树集合和基于无偏递归分区的树。我们将基于树的模型的性能与现有模型的性能进行比较，例如普通克里金法和第二类 (GB2) 回归的广义 beta。我们的结果表明，基于树的模型在产生准确的预测方面是有效的，并且梯度提升方法被认为在预测精度方面是最优越的。