Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy
Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy
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DOI：
10.1016/j.econmod.2010.09.016
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发表时间：
2011
影响因子：
4.7
通讯作者：
Quansheng Gao;Ting He;Chi Zhang
中科院分区：
文献类型：
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作者：
Quansheng Gao;Ting He;Chi Zhang
本文通过分位数套期保值来研究随机利率经济下的股票寿险合同，目的是寻找初始预算约束下成功套期保值的最优概率。现有的大多数研究都集中在通过分位数对冲或在随机利率框架下对与股票挂钩的人寿保险合同进行估值。然而，少数银行同时考虑了这两种技术，这使得对与股票挂钩的寿险合同进行估值变得更加困难。本文采用经典的HJM模型对利率期限结构进行建模，该模型将随机利率经济嵌入到一个包含任意数量附加风险资产的经济中。利用计量变更方法，给出了确定性收益合约、纯股权挂钩终身合约、带担保的股权挂钩终身合约、带最低担保的股权挂钩终身合约和有上限收益的股权挂钩终身合约四种产品公允价值的明确公式。我们发现显式公式主要由正态分布函数和二维正态分布函数组成。我们还利用利率、股票价格和中国的生命表数据来考察生存概率的敏感性。
In this paper we examine equity-linked life insurance contracts in a stochastic interest rate economy via quantile hedging whose purpose is to look for the optimal probability of a successful hedge under initial budget constraint. Most of the existing studies have focused on valuing equity-linked life insurance contracts by quantile hedging or in a framework of stochastic interest rates. However, a few have taken into account simultaneously the two techniques, which make valuing equity-linked life insurance contracts more difficult. We model the term structure of interest rates by classical HJM model that imbeds stochastic interest rate economy into one containing an arbitrary number of additional risky assets. By means of the change of measure approach, we give explicit formulas for the fair values of the following four products: deterministic payoff contract, pure equity-linked life contract, equity-linked life contract with guarantee, equity-linked life contract with minimum guarantees and capped benefits. We find that the explicit formulas are mainly composed of normal distribution functions and two-dimensional normal distribution functions. We also investigate sensibility of the survival probability using data of interest rates, stock prices and life table from China.