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Risks 2019, 7(1), 14; https://doi.org/10.3390/risks7010014

Changes of Relation in Multi-Population Mortality Dependence: An Application of Threshold VECM

1
Department of Economics, University of Melbourne, Parkville, VIC 3010, Australia
2
Manulife-Sinochem, Shanghai 200121, China
3
Department of Mathematics, Towson University, Towson, MD 21252, USA
*
Author to whom correspondence should be addressed.
Received: 7 January 2019 / Revised: 26 January 2019 / Accepted: 28 January 2019 / Published: 1 February 2019
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Abstract

Standardized longevity risk transfers often involve modeling mortality rates of multiple populations. Some researchers have found that mortality indexes of selected countries are cointegrated, meaning that a linear relationship exists between the indexes. Vector error correction model (VECM) was used to incorporate this relation, thereby forcing the mortality rates of multiple populations to revert to a long-run equilibrium. However, the long-run equilibrium may change over time. It is crucial to incorporate these changes such that mortality dependence is adequately modeled. In this paper, we develop a framework to examine the presence of equilibrium changes and to incorporate these changes into the mortality model. In particular, we focus on equilibrium changes caused by threshold effect, the phenomenon that mortality indexes alternate between different VECMs depending on the value of a threshold variable. Our framework comprises two steps. In the first step, a statistical test is performed to examine the presence of threshold effect in the VECM for multiple mortality indexes. In the second step, threshold vector error correction model (TVECM) is fitted to the mortality indexes and model adequacy is evaluated. We illustrate this framework with the mortality data of England and Wales (EW) and Canadian populations. We further apply the TVECM to forecast future mortalities and price an illustrative longevity bond with multivariate Wang transform. Our numerical results show that TVECM predicted much faster mortality improvement for EW and Canada than single-regime VECM and thus the incorporation of threshold effect significant increases longevity bond price. View Full-Text
Keywords: multi-population mortality; vector error correction; longevity risk; longevity bond; Wang transform multi-population mortality; vector error correction; longevity risk; longevity bond; Wang transform
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Zhou, R.; Xing, G.; Ji, M. Changes of Relation in Multi-Population Mortality Dependence: An Application of Threshold VECM. Risks 2019, 7, 14.

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