Modeling of mortality rates, hedging of longevity and mortality risks, and pricing of mortality-linked securities

死亡率建模、寿命和死亡风险对冲以及死亡相关证券的定价

• 批准号: RGPIN-2014-06168
• 负责人: Tsai, CaryChiLiang
• 金额: $ 0.8万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=612071
• 关键词: Modeling; mortality; rates; hedging; longevity

Modeling the changes/dynamics of mortality rates is critical to the social benefit programs, solvency of life insurers, and the society as a whole. Mortality is a significant factor in shaping the population structure of a country that in turn affects the growth prospects of many industries. Retirement programs and long-term care systems need to consider the dynamics of mortality rates as well since incomes and benefit outgoes depend on mortality. Mortality is also one of the key factors in determining the premiums and reserves of life insurance and annuity products. Therefore, modeling of mortality is a very important issue. Evidence shows that human mortality rates improve gradually over the past decades. A failure to appropriately measure the downward trends in mortality rates would underestimate the premiums and reserves for annuity and pension products and then expose annuity and pension providers to the risks of financial distress. Since forecasting mortality rates accurately for a long period is extremely difficult, annuity and pension providers need to hedge the longevity risk by adopting some strategies and/or buying appropriate mortality-linked securities. Unlike interest-based securities which are widely created by financial researchers and traded in financial markets, mortality-linked securities have been rarely issued and traded. Facing the phenomenon of mortality improvement, annuity and pension providers now are in need of more mortality-linked securities as instruments for hedging longevity risk. The proposed research program pertains to modeling of mortality rates, hedging of longevity and mortality risks, and pricing of mortality-linked securities. In the project, I intend to focus on the following three main objectives: • For modeling of mortality, I would like to propose relational models (a relational model in modeling of mortality rates connects one mortality sequence to the other with some relationship) and its variations for in-sample mortality fitting and out-of-sample mortality forecasting; some important features including the cohort effect, a jump component, a common shock, dependency, stochastic processes and time series will also be involved in the models. • For hedging of mortality and longevity risks, I will apply my previously proposed mortality durations and convexities to a portfolio of three or more insurance products and to some other mortality-linked securities; the optimal problems regarding the weights producing the best performance of hedging mortality and longevity risks, respectively, will also be studied in details. • For pricing of existing mortality-linked securities based on the well-known Lee-Carter model or the proposed relational models, the features in the first objective will be considered to reflect one or more of various situations; new mortality-linked securities inspired from existing interest-based derivative ones will be proposed, and their pricing even though advanced financial mathematics is involved will be investigated to a great extent. The relational models and their variations are brand-new approaches to modeling mortality rates and hedging mortality/longevity risks. They are easy to implement, have good performance in mortality fitting/forecasting, and offer many potential applications due to their simplicity and effectiveness plus a relationship between two mortality sequences. The completion of this research program will help life insurers, social security and retirement benefit providers, and relevant industries reduce the possibilities of financial distress caused by mortality/longevity risks. I expect to make significant contributions to the field of mortality study.

对死亡率的变化/动态进行建模对于社会福利计划、寿险公司的偿付能力以及整个社会至关重要。死亡率是影响一国人口结构的一个重要因素，而人口结构又影响到许多行业的增长前景。退休计划和长期护理系统也需要考虑死亡率的动态变化，因为收入和福利支出取决于死亡率。死亡率也是决定寿险和年金产品保费和准备金的关键因素之一。因此，死亡率的建模是一个非常重要的问题。有证据表明，人类死亡率在过去几十年中逐渐下降。如果不能适当衡量死亡率的下降趋势，就会低估年金和养老金产品的保费和准备金，从而使年金和养老金提供者面临财务困境的风险。由于长期准确预测死亡率是极其困难的，年金和养老金提供者需要通过采取一些策略和/或购买适当的死亡率挂钩证券来对冲长寿风险。与由金融研究人员广泛创建并在金融市场上交易的基于利息的证券不同，与死亡率挂钩的证券很少发行和交易。面对死亡率改善的现象，年金和退休金提供者现在需要更多的死亡率挂钩证券作为对冲长寿风险的工具。 拟议的研究计划涉及死亡率的建模，对冲寿命和死亡率风险，以及死亡率挂钩证券的定价。在该项目中，我打算重点关注以下三个主要目标： ·对于死亡率建模，我想提出关系模型（死亡率建模中的关系模型将一个死亡率序列与另一个死亡率序列以某种关系连接起来）及其变化，用于样本内死亡率拟合和样本外死亡率预测;一些重要的特征，包括队列效应，跳跃成分，共同冲击，依赖性，随机过程和时间序列也将包括在模型中。 ·对于死亡率和寿命风险的对冲，我将把我以前提出的死亡率持续期和凸性应用于三个或更多保险产品的投资组合以及其他一些与死亡率相关的证券;关于分别产生对冲死亡率和寿命风险的最佳性能的权重的最优问题也将被详细研究。 ·对于基于著名的Lee-Carter模型或所提出的关系模型的现有死亡率关联证券的定价，第一目标中的特征将被认为反映了各种情况中的一种或多种;将提出从现有的基于利息的衍生品中启发的新的死亡率关联证券，并且即使涉及高级金融数学，也将在很大程度上研究其定价。 关系模型及其变体是建模死亡率和对冲死亡率/寿命风险的全新方法。它们易于实现，在死亡率拟合/预测方面具有良好的性能，并且由于它们的简单性和有效性以及两个死亡率序列之间的关系而提供了许多潜在的应用。这项研究计划的完成将有助于人寿保险公司、社会保障和退休福利提供者以及相关行业减少死亡/长寿风险造成财务困境的可能性。我希望能对死亡率研究领域做出重大贡献。