英文标题：
《GMWB Riders in a Binomial Framework - Pricing, Hedging, and
Diversification of Mortality Risk》
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作者：
Cody B. Hyndman and Menachem Wenger
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最新提交年份：
2016
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英文摘要：
We construct a binomial model for a guaranteed minimum withdrawal benefit (GMWB) rider to a variable annuity (VA) under optimal policyholder behaviour. The binomial model results in explicitly formulated perfect hedging strategies funded using only periodic fee income. We consider the separate perspectives of the insurer and policyholder and introduce a unifying relationship. Decompositions of the VA and GMWB contract into term-certain payments and options representing the guarantee and early surrender features are extended to the binomial framework. We incorporate an approximation algorithm for Asian options that significantly improves efficiency of the binomial model while retaining accuracy. Several numerical examples are provided which illustrate both the accuracy and the tractability of the binomial model. We extend the binomial model to include policy holder mortality and death benefits. Pricing, hedging, and the decompositions of the contract are extended to incorporate mortality risk. We prove limiting results for the hedging strategies and demonstrate mortality risk diversification. Numerical examples are provided which illustrate the effectiveness of hedging and the diversification of mortality risk under capacity constraints with finite pools.
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中文摘要：
在最优投保人行为下，我们构建了可变年金（VA）的最低保障提取福利（GMWB）附加项的二项模型。二项模型的结果是明确制定了完美的对冲策略，只使用定期费用收入。我们考虑保险人和投保人的不同观点，并引入一种统一的关系。将VA和GMWB合同分解为代表担保和提前退保特征的特定付款和期权，并扩展到二项式框架。我们为亚式期权引入了一种近似算法，该算法在保持精度的同时显著提高了二项式模型的效率。文中给出了几个数值例子，说明了二项式模型的精度和可处理性。我们扩展了二项式模型，将投保人死亡率和死亡抚恤金包括在内。定价、套期保值和合同的分解被扩展到包含死亡风险。我们证明了风险分散和限制风险的策略。文中给出了一些数值例子，说明了在容量有限的情况下，对冲的有效性和死亡率风险的多样化。
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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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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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