人口老龄化背景下长寿风险管理方法的探讨

伴随着长寿风险的累积,养老保障型产品提供者管理长寿风险的压力逐步凸显,本文主要对比分析了不同长寿风险管理方法,并通过研究Swiss Re死亡率证券和EIB/BNP长寿债券的设计,分析了各类养老基金通过资本市场实现长寿风险转移与对冲管理的可能方式。     

长寿债券的运行机制与定价模型

通过分析长寿债券的市场发展以及连续型和触发型两类长寿债券的运行机制,采用风险中性定价方法推导出当死亡率服从双指数跳跃(DEJD)分布时,长寿债券的定价解析式,研究发现,无论从理论还是实践看,设计并发行触发型长寿债券是一种应对长寿风险更为明智的选择。     

我国养老保险公司的长寿风险证券化——基于百分位分层定价法

长寿风险证券化可以把长寿风险转移到资本市场,有效管理养老保险公司的长寿风险。本文主要研究利息率与死亡率挂钩的逆生存债券,研究内容分为死亡率预测与债券定价两个部分。由于投资者对风险的偏好不同,本文利用百分位分层定价法对逆生存债券进行定价。数值分析展示了债券价格随利率变化的情况,共分四个层次,不同的分层对应不同的价格和风险,投资者可以根据自身的风险偏好选择不同的分层债券。最后就养老保险公司在长寿风险证券化方面存在的问题给出相关建议。     

基于风险立方方法的长寿风险债券定价研究

面对世界范围内长寿风险越来越严峻的趋势,长寿风险管理成为全世界面临的共同难题。近年来死亡率风险证券化引起人们的广泛关注,长寿债券作为死亡率风险证券化中最常用的一种方法,可以有效地将长寿风险转移至资本市场。本文通过对国外经典死亡率债券的比较,在离散型死亡率模型假设条件下,设计一支可调整上触碰点的触发型长寿债券,运用带永久跳跃的APC模型和风险立方方法对长寿债券进行定价。实证结果显示风险溢价的结果比较稳定,设置不同的初始上触碰点,风险溢价差异较大。     

我国随机死亡率的长寿风险建模和衍生品定价

长寿风险近年来对各国保险业、养老金体系、社会保障体系造成大规模影响,成为保险和风险管理学术界关注和研究的重点。采用国际前沿的研究方法,系统深入地采用中国数据研究这一问题。在Lee-Carter模型的基础上,通过双指数跳跃扩散模型对Lee-Carter模型中的时间序列因子进行拟合,较好地刻画了中国人口死亡率的长寿跳跃和死亡跳跃;引用Swiss Re死亡债券度量长寿风险的市场价格,预估未来中国人口死亡率,并得出了寿险衍生品Q型远期的中国定价。     

基于双因素Wang转换方法的长寿风险债券定价研究

在比较国外经典债券设计的基础上,基于离散型死亡率模型假设,设计一种可调整上触碰点的触发型长寿债券,运用带永久跳跃的APC模型和双因素Wang转换定价方法对长寿债券进行定价,实证结果表明:在不同的参数组合下的风险溢价均处在一个合理的范围,由于模型参数多、可用死亡率数据年限短,风险溢价的结果对无风险利率等参数敏感性较高.     

长寿风险证券化的理论研究动态

国际寿险业在资本市场上尝试进行长寿风险证券化的同时,学术界也不断在探索长寿风险资本市场的创新性解决方案,并已取得了丰硕的理论成果。本文阐述了关于连续型和触发型长寿债券的设计机制及其定价模型的研究成果;分析了长寿互换的设计机制和定价模型的研究进展;梳理了其他长寿风险金融衍生工具的设计机制和定价模型的研究动态。     

死亡率分解模型及其在长寿分级基金构建中的应用

论文提出了一种有别于传统死亡率模型的新的长寿风险度量模型,叫做死亡率分解模型。基于该模型,论文对美国的死亡率数据进行了分析和对比,同时对中国的死亡率进行了两个角度的分析,并给出了相对更有说服力的结果。同时,论文借助模型的分解结果,提出构建多层次的长寿风险基金,用以应对中国社会日益严重的养老问题。     

长寿风险的稳健对冲与稳健管理技术研究进展

本文总结了长寿风险的稳健对冲与稳健管理技术的最新研究成果,特别概述了人口寿命与死亡率的预测方法和长寿风险对冲工具的发展近况和长寿风险定价方法,详细分析了长寿风险对冲过程中不稳健性的来源和长寿风险稳健性对冲技术的最新研究进展。最后,通过对长寿风险稳健对冲与稳健管理技术的最新研究进展进行综述和评析,期望为后续长寿风险的稳健对冲与稳健管理技术的研究提供文献和理论基础。     

长寿风险对基本医疗保险统筹基金的冲击效应研究——基于VaR与CVaR模型的综合测算

借鉴金融风险管理中VaR和CVaR模型对尾部风险的测量思路,通过构建有限数据Lee-Carter死亡率预测模型,测算了人口的长寿风险及其对基本医疗保险统筹基金的冲击效应,结果表明:2015-2060年基本医疗保险参保人群将面临巨大的长寿风险,极端情况下长寿风险将给统筹基金收支结余超预期下降造成不容忽视的尾部损失;推迟退休年龄、提高生育率、调整个人账户和报销比例、提高职工缴费工资和控制住院费用增长均可以在一定程度上缓解长寿风险的冲击.建议明确政府在基本医疗保险长寿风险管理中的主导作用,构建医疗、养老和长期护理保险的三险联动保障机制.     

两因子随机死亡率状态空间模型及长寿风险测度

引入状态空间模型对传统两因子CBD模型拟合阶段和预测阶段进行联合建模,并基于卡尔曼滤波方法对模型参数进行估计。进一步考虑到死亡率数据的小样本特征,结合Bootstrap仿真技术和生存年金组合折现模型对长寿风险进行测度。利用1996~2011年数据展开实证研究,结果表明:结合模型解释能力、参数估计结果和误差项正态分布检验结果,两因子状态空间模型要优于传统CBD模型;年金组合规模的扩大可以消除微观长寿风险,但不能消除宏观长寿风险和参数风险;宏观长寿风险占据着不可分散风险的主导地位。     

Lifetime asset allocation with idiosyncratic and systematic mortality risks

This paper considers a lifetime asset allocation problem with both idiosyncratic and systematic mortality risks. The novelty of the paper is to integrate stochastic mortality, stochastic interest rate and stochastic income into a unified framework. An investor, who is a wage earner receiving a stochastic income, can invest in a financial market, consume part of his wealth and purchase life insurance or annuity so as to maximize the expected utility from consumption, terminal wealth and bequest. The problem is solved via the dynamic programming principle and the Hamilton–Jacobi–Bellman equation. Analytical solutions to the problem are derived, and numerical examples are provided to illustrate our results. It is shown that idiosyncratic mortality risk has significant impacts on the investor’s investment, consumption, life insurance/annuity purchase and bequest decisions regardless of the length of the decision-making horizon. The systematic mortality risk is largely alleviated by trading the longevity bond. However, its impacts on consumption, purchase of life insurance/annuity and bequest as well as the value function are still pronounced, when the decision-making horizon is sufficiently long.     

Cohort and value-based multi-country longevity risk management

ABSTRACT

Multi-country risk management of longevity risk provides new opportunities to hedge mortality and interest rate risks in guaranteed lifetime income streams. This requires consideration of both interest rate and mortality risks in multiple countries. For this purpose, we develop value-based longevity indexes for multiple cohorts in two different countries that take into account the major sources of risks impacting life insurance portfolios, mortality and interest rates. To construct the indexes we propose a cohort-based affine model for multi-country mortality and use an arbitrage-free multi-country Nelson–Siegel model for the dynamics of interest rates. Index-based longevity hedging strategies have the advantages of efficiency, liquidity and lower cost but introduce basis risk. Graphical risk metrics are a way to effectively capture the relationship between an insurer's portfolio and hedging strategies. We illustrate the effectiveness of using a value-based index for longevity risk management between two countries using graphical basis risk metrics. To show the impact of both interest rate and mortality risk we use Australia and the UK as domestic and foreign countries, and, to show the impact of mortality only, we use the male populations of the Netherlands and France with common interest rates and basis risk arising only from differences in mortality risks.     

Mortality regimes and longevity risk in a life annuity portfolio

This paper explores the presence of changes of trends or jumps in French mortality from 1947 to 2007, and assesses their implications on the longevity risk management of a life annuity portfolio. We accomplish this by extending the Poisson log-bilinear regression developed by Brouhns et al. (2002) with a regime-switching model. Estimation results show that French mortality is characterized by two distinct regimes. One refers to a strong uncertainty state, which corresponds to the longevity conditions observed during the decade following World War II. The second regime is related to the low volatility of longevity improvements observed during the last 30 years. We use these results to analyze the impact of mortality regimes on the longevity risk management of a life annuity portfolio. Simulation results suggest that the changes of trends in the mortality process have some implications for longevity risk management.     

A Two-Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration

In this article, we consider the evolution of the post‐age‐60 mortality curve in the United Kingdom and its impact on the pricing of the risk associated with aggregate mortality improvements over time: so‐called longevity risk. We introduce a two‐factor stochastic model for the development of this curve through time. The first factor affects mortality‐rate dynamics at all ages in the same way, whereas the second factor affects mortality‐rate dynamics at higher ages much more than at lower ages. The article then examines the pricing of longevity bonds with different terms to maturity referenced to different cohorts. We find that longevity risk over relatively short time horizons is very low, but at horizons in excess of ten years it begins to pick up very rapidly. A key component of the article is the proposal and development of a method for calculating the market risk‐adjusted price of a longevity bond. The proposed adjustment includes not just an allowance for the underlying stochastic mortality, but also makes an allowance for parameter risk. We utilize the pricing information contained in the November 2004 European Investment Bank longevity bond to make inferences about the likely market prices of the risks in the model. Based on these, we investigate how future issues might be priced to ensure an absence of arbitrage between bonds with different characteristics.     

The fair value of guaranteed annuity options

We discuss the fair valuation of Guaranteed Annuity Options, i.e. options providing the right to convert deferred survival benefits into annuities at fixed conversion rates. The use of doubly stochastic stopping times and of affine processes provides great computational and analytical tractability, while enabling to set up a very general valuation framework. For example, the valuation of options on traditional, unit-linked or indexed annuities is encompassed. Moreover, security and reference fund prices may feature stochastic volatility or discontinuous dynamics. The longevity risk is also taken into account, by letting the evolution of mortality present stochastic dynamics subject not only to random fluctuations but also to systematic deviations.     

A partial internal model for longevity risk

This paper proposes a simple partial internal model for longevity risk within the Solvency 2 framework. The model is closely linked to the mechanisms associated with the so-called Danish longevity benchmark, where the underlying mortality intensity and the trend is estimated yearly based on mortality experience from the Danish life and pension insurance sector, and on current data from the entire Danish population. Within this model, we derive an estimate for the 99.5% percentile for longevity risk, which differs from the longevity stress of 20% from the standard model. The new stress explicitly reflects the risk associated with unexpected changes in the underlying population mortality intensity on a one-year horizon and with a 99.5% confidence level. In addition, the model contains a component, which quantifies the unsystematic longevity risk associated with a given insurance portfolio. This last component depends on the size of the specific portfolio.     

Lee-Carter模型在中国城市人口死亡率预测中的应用与改进

由死亡率下降带来的长寿风险给社会、政治以及经济带来了新的挑战。为了更加准确地对长寿风险进行评估和管理,需要对未来死亡率趋势进行预测。本文针对我国死亡率数据样本量小以及数据存在缺失的实际情况,对Lee-Carter模型进行了改进,通过一个双随机过程对Lee-Carter模型中的时间项进行建模。在模型中考虑了样本量不足对预测结果造成的影响,使得改进后的Lee-Carter模型更加适合目前中国的人口死亡率预测。