英文标题：
《Variable Annuity with GMWB: surrender or not, that is the question》
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作者：
Xiaolin Luo and Pavel Shevchenko
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最新提交年份：
2015
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英文摘要：
Under the optimal withdrawal strategy of a policyholder, the pricing of variable annuities with Guaranteed Minimum Withdrawal Benefit (GMWB) is an optimal stochastic control problem. The surrender feature available in marketed products allows termination of the contract before maturity, making it also an optimal stopping problem. Although the surrender feature is quite common in variable annuity contracts, there appears to be no published analysis and results for this feature in GMWB under optimal policyholder behaviour - results found in the literature so far are consistent with the absence of such a feature. Also, it is of practical interest to see how the much simpler bang-bang strategy, although not optimal for GMWB, compares with optimal GMWB strategy with surrender option. In this paper we extend our recently developed algorithm (Luo and Shevchenko 2015a) to include surrender option in GMWB and compare prices under different policyholder strategies: optimal, static and bang-bang. Results indicate that following a simple but sub-optimal bang-bang strategy does not lead to significant reduction in the price or equivalently in the fee, in comparison with the optimal strategy. We observed that the extra value added by the surrender option could add very significant value to the GMWB contract. We also performed calculations for static withdrawal with surrender option, which is the same as bang-bang minus the \"no-withdrawal\" choice. We find that the fee for such contract is only less than 1% smaller when compared to the case of bang-bang strategy, meaning that th \"no-withdrawal\" option adds little value to the contract.
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中文摘要：
在投保人的最优退出策略下，保证最小退出收益的可变年金（GMWB）的定价是一个最优随机控制问题。已上市产品中的退保功能允许在到期前终止合同，这也是一个最佳停止问题。尽管退保特征在可变年金合同中非常常见，但在最优保单持有人行为下，GMWB中似乎没有关于这一特征的公开分析和结果——到目前为止，文献中发现的结果与缺乏这一特征的情况一致。此外，看看简单得多的bang-bang策略（虽然对GMWB来说不是最优的）与带有放弃选项的最优GMWB策略相比，这也是一个实际的兴趣所在。在本文中，我们扩展了我们最近开发的算法（Luo和Shevchenko 2015a），将退保期权纳入GMWB，并比较了不同投保人策略下的价格：最优、静态和bang-bang。结果表明，与最优策略相比，遵循简单但次优的bang-bang策略不会导致价格显著降低或费用相当。我们观察到，退保期权增加的额外价值可以为GMWB合同增加非常重要的价值。我们还计算了带放弃选项的静态撤回，这与bang-bang减去“不撤回”选项相同。我们发现，与bang bang strategy相比，此类合同的费用仅减少不到1%，这意味着“不撤资”选项对合同的价值几乎没有增加。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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