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, 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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=588850
• 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.

对死亡率的变化对社会福利计划至关重要。在设计人寿保险和环境产品的保费和储量时，死亡率是适当地衡量死亡率下降的情况下，低估了溢价和养老金产品的保费和储备遇难者。 拟议的研究计划对死亡率建模，长寿和死亡率的套餐有联系，我打算关注以下三个主要目标： •对于与另一个关系的死亡率CE建模），是样本中拟合和样本外死亡率的变化，预测了一些重要特征，包括thort效果，跳跃成分，常见的冲击，依赖于模型。 •分别将研究详细研究死亡率和寿命风险保险产品和其他寿命的风险； •根据众所周知的Lee-Charter模型的定价，将考虑反映一个或多个各种场所的特征；和定价事件，高级金融数学在很大程度上涉及。 关系模型是崭新的死亡率和对冲死亡率/长寿风险，以实施良好的死亡率，并提供许多有效的应用程序，并加上两个死亡率序列之间的关系。社会保障和退休拟合提供者，并减少了死亡率/寿命风险引起的财务困扰的可能性。