英文标题：
《The implied longevity curve: How long does the market think you are
  going to live?》
---
作者：
Moshe A. Milevsky, Thomas S. Salisbury, Alexander Chigodaev
---
最新提交年份：
2018
---
英文摘要：
  We use life annuity prices to extract information about human longevity using a framework that links the term structure of mortality and interest rates. We invert the model and perform nonlinear least squares to obtain implied longevity forecasts. Methodologically, we assume a Cox-Ingersoll-Ross (CIR) model for the underlying yield curve, and for mortality, a Gompertz-Makeham (GM) law that varies with the year of annuity purchase. Our main result is that over the last decade markets implied an improvement in longevity of of 6-7 weeks per year for males and 1-3 weeks for females. In the year 2004 market prices implied a $40.1\\%$ probability of survival to the age 90 for a 75-year old male ($51.2\\%$ for a female) annuitant. By the year 2013 the implied survival probability had increased to $46.1\\%$ (and $53.1\\%$). The corresponding implied life expectancy has increased (at the age of 75) from 13.09 years for males (15.08 years for females) to 14.28 years (and 15.61 years.) Although these values are implied directly from markets, they are consistent with demographic projections. Similar to implied volatility in option pricing, we believe that our implied survival probabilities (ISP) and implied life expectancy (ILE) are relevant for the financial management of assets post-retirement and very important for the optimal timing and allocation to annuities; procrastinators are swimming against an uncertain but rather strong longevity trend.
---
中文摘要：
我们使用寿命年金价格，通过将死亡率和利率的期限结构联系起来的框架，提取有关人类寿命的信息。我们反转模型并执行非线性最小二乘法以获得隐含的寿命预测。在方法上，我们假设潜在收益率曲线为Cox-Ingersoll-Ross（CIR）模型，死亡率为Gompertz-Makeham（GM）定律，该定律随年金购买年份而变化。我们的主要结果是，在过去十年中，市场表明男性的寿命每年提高6-7周，女性的寿命每年提高1-3周。2004年，市场价格意味着75岁男性年金受益人活到90岁的概率为40.1美元（女性为51.2美元）。到2013年，隐含生存概率已增至46.1\\%%$（和53.1\\%%$）。相应的隐含预期寿命（75岁时）已从男性的13.09岁（女性的15.08岁）增加到14.28岁（和15.61岁）虽然这些价值直接来自市场，但它们与人口预测一致。与期权定价中的隐含波动性类似，我们认为我们的隐含生存概率（ISP）和隐含预期寿命（ILE）与退休后资产的财务管理相关，对于最佳时机和年金分配非常重要；拖延者正在对抗一种不确定但相当强劲的长寿趋势。
---
分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
--

---
PDF下载：
-->