Interest rate is one of the main risks for the liability of the variable annuity (VA) due to its long maturity. However, most existing studies on the risk measures of the VA assume a constant interest rate. In this paper, we propose an efficient two-dimensional willow tree method to compute the liability distribution of the VA with the joint dynamics of the mutual fund and interest rate. The risk measures can then be computed by the backward induction on the tree structure. We also analyze the sensitivity and impact on the risk measures with regard to the market model parameters, contract attributes, and monetary policy changes. It illustrates that the liability of the VA is determined by the long-term interest rate whose increment leads to a decrease in the liability. The positive correlation between the interest rate and mutual fund generates a fat-tailed liability distribution. Moreover, the monetary policy change has a bigger impact on the long-term VAs than the short-term contracts.

利率是可变年金（VA）到期期限的主要风险之一。但是，现有的大多数关于VA风险度量的研究都假设利率不变。本文提出了一种有效的二维柳树方法，通过共同基金和利率的共同动态来计算虚拟资产的负债分布。然后可以通过对树结构的反向归纳来计算风险度量。我们还将分析有关市场模型参数，合同属性和货币政策变化的敏感性以及对风险衡量的影响。它说明了VA的负债由长期利率确定，长期利率的增加导致负债的减少。利率与共同基金之间的正相关关系产生了一个冗长的负债分布。此外，货币政策的变化对长期风险价值的影响要大于短期合同。