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

死亡率建模、长寿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, ChiLiang
• 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: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=567635
• 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，解决生命的确保以及整个社会至关重要。死亡率是塑造一个国家的人口结构的重要因素，进而影响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，因为收入和福利取决于死亡率。死亡率也是确定人寿保险和年金产品的保费和储量的关键因素之一。因此，死亡率的建模是一个非常重要的问题。有证据表明，在过去几十年中，人类死亡率逐渐提高。未能适当衡量死亡率的下降趋势将低估年金和铅笔产品的保费和储量，然后将年金和铅笔提供商暴露于财务困境的风险中。由于长期准确预测死亡率非常困难，因此年金和铅笔提供商需要通过采用一些策略和/或购买适当的死亡率与死亡率的证券来对冲寿命风险。与金融研究人员广泛创建并在金融市场中翻译的基于利息的证券不同，与死亡率相关的证券很少发行和翻译。面对死亡率改善现象，年金和铅笔提供商现在需要更多的死亡率连接证券作为对冲寿命风险的工具。拟议的研究计划涉及死亡率的建模，寿命和死亡率风险的对冲以及与死亡率相关证券的定价。在项目中，我打算关注以下三个主要目标：•为了建模死亡率，我想提出关系模型（死亡率建模的关系模型将一个死亡率序列与另一个死亡率连接到另一个关系的关系）及其在样本中拟合的死亡率和样本外死亡率的变化；模型中还将涉及一些重要特征，包括队列效应，跳跃成分，常见的冲击，依赖性，随机过程和时间序列。 •为了对冲死亡率和寿命风险，我将把我先前建议的死亡率持续时间和凸状态应用于三种或更多保险产品的投资组合，并将其用于其他一些与死亡率相关的证券；关于重量产生对冲死亡率和寿命风险的最佳性能的最佳问题也将详细研究。 •为基于众所周知的Lee-Carter模型或提议的关系模型定价现有的死亡率连接证券，将考虑第一个目标中的特征以反映一种或多种不同情况；将提出从现有基于利息的衍生品启发的新的死亡率证券，即使涉及先进的金融数学，也将在很大程度上研究其定价。关系模型及其变化是建模死亡率和对冲死亡率/寿命风险的全新方法。它们易于实施，在死亡率拟合/预测方面具有良好的性能，并且由于其简单性和有效性以及两个死亡率序列之间的关系而提供许多潜在的应用。该研究计划的完成将有助于生活，社会保障和退休福利提供者，相关行业减少了由死亡/寿命风险造成的财务困扰的可能性。我希望对死亡率研究领域做出重大贡献。