檢測跨國死亡率之因果關係及長期均衡以發展死亡連結證券為例

Detecting Causality and Long-Run Equilibrium Relationships of Mortality Rates across Countries for Developing Mortality-Linked Securities

建構多國死亡率指數對設計死亡率連結證券是相當重要的，本文探討跨國死亡率關聯性，主要著重於因果及長期均衡關係。為能克服死亡率資料期間較短之問題，本研究採用追蹤共整數的方法代替傳統共整數的方式來檢測跨國死亡率之關聯性，並以瑞士再保所發行的死亡率債券為跨國死亡率關聯性之研究範例，該債券死亡率指數連結法國、英格蘭、義大利、美國及瑞士五個國家。依據HMD資料庫以資料期間1950至2009進行分析，本研究發現這些國家死亡率，存在共整合效果且存在雙向短期因果關係及長期均衡，然而，此一現象並無法藉由傳統共整合方法來發現。了解不同國家死亡綠之關聯性，可幫助資本市場發展出有避險效率的死亡率連結證券。

The construction of a multi-country mortality index is essential for designing a mortality- linked security in the “Life Market”. This paper investigates the relationships of mortality rates across countries. Particularly, we focus on the causality and long-run equilibrium relationships. To overcome the problem of the short time spans of mortality data sets, we adopt a panel co-integration approach instead of a traditional co-integration approach. Using the mortality index underlying the Swiss mortality bond, we detect the relationship of mortality rates in France, England, the United States, Italy, and Switzerland based on the Human Mortality Database from 1950 to 2009 as an example. We find the mortality rates in these countries exhibit co-integration effects, with a bi-directional short-run causality and long-run equilibrium relationships. However, such effects are not detected by a traditional co-integration approach. Understanding the relationships of mortality rates across countries can help in development of an effective capital market solution.