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EFFICIENT DYNAMIC HEDGING FOR LARGE VARIABLE ANNUITY PORTFOLIOS WITH MULTIPLE UNDERLYING ASSETS
ASTIN Bulletin: The Journal of the IAA ( IF 1.9 ) Pub Date : 2020-08-11 , DOI: 10.1017/asb.2020.26
X. Sheldon Lin , Shuai Yang

A variable annuity (VA) is an equity-linked annuity that provides investment guarantees to its policyholder and its contributions are normally invested in multiple underlying assets (e.g., mutual funds), which exposes VA liability to significant market risks. Hedging the market risks is therefore crucial in risk managing a VA portfolio as the VA guarantees are long-dated liabilities that may span decades. In order to hedge the VA liability, the issuing insurance company would need to construct a hedging portfolio consisting of the underlying assets whose positions are often determined by the liability Greeks such as partial dollar Deltas. Usually, these quantities are calculated via nested simulation approach. For insurance companies that manage large VA portfolios (e.g., 100k+ policies), calculating those quantities is extremely time-consuming or even prohibitive due to the complexity of the guarantee payoffs and the stochastic-on-stochastic nature of the nested simulation algorithm. In this paper, we extend the surrogate model-assisted nest simulation approach in Lin and Yang [(2020) Insurance: Mathematics and Economics, 91, 85–103] to efficiently calculate the total VA liability and the partial dollar Deltas for large VA portfolios with multiple underlying assets. In our proposed algorithm, the nested simulation is run using small sets of selected representative policies and representative outer loops. As a result, the computing time is substantially reduced. The computational advantage of the proposed algorithm and the importance of dynamic hedging are further illustrated through a profit and loss (P&L) analysis for a large synthetic VA portfolio. Moreover, the robustness of the performance of the proposed algorithm is tested with multiple simulation runs. Numerical results show that the proposed algorithm is able to accurately approximate different quantities of interest and the performance is robust with respect to different sets of parameter inputs. Finally, we show how our approach could be extended to potentially incorporate stochastic interest rates and estimate other Greeks such as Rho.



中文翻译:

具有多个底层资产的大型可变年金投资组合的有效动态对冲

可变年金(VA)是与股票挂钩的年金,可为保单持有人提供投资担保,其年金通常投资在多个基础资产(例如共同基金)中,这使VA负债面临重大市场风险。因此,对冲市场风险对风险管理投资组合的风险管理至关重要,因为风险管理担保是可能长达数十年的长期负债。为了对冲VA负债,发行保险公司将需要构建由基础资产组成的对冲投资组合,这些资产的头寸通常由负债希腊人确定,例如部分美元三角洲。通常,这些数量是通过嵌套模拟方法计算的。对于管理大量虚拟资产投资组合(例如,超过10万份保单)的保险公司,由于保证收益的复杂性以及嵌套模拟算法的随机随机性,计算这些数量非常耗时甚至禁止。在本文中,我们在Lin和Yang [(2020)保险:数学和经济学91(85-103),以有效地计算具有多个基础资产的大型VA投资组合的总VA负债和部分美元Delta。在我们提出的算法中,嵌套模拟是使用少量选定的代表性策略和代表性外部循环运行的。结果,大大减少了计算时间。通过大型合成VA产品组合的损益分析,进一步说明了该算法的计算优势和动态套期保值的重要性。此外,通过多次仿真运行测试了所提出算法性能的鲁棒性。数值结果表明,所提出的算法能够精确地估计不同的感兴趣量,并且对于不同的参数输入集,其性能是鲁棒的。最后,

更新日期:2020-09-22
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