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

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.

Coherent extrapolation of mortality rates at old ages applied to long term care

“…Li proposed a method based on the Lee-Carter model to forecast the mortality of a group of populations by allowing each population to have its own age pattern and level but have a common trend. Later, Zhou et al (2019) and Li et al (2017) approached this problem of coherent mortality forecasting with the concept of semicoherence. The idea is to fix a weaker assumption on the coherence between the mortality laws by allowing the mortality trajectories of two populations to diverge, as long as the difference between the two mortality laws does not exceed what they called a tolerance corridor.…”

Disentangling Trend Risk and Basis Risk with Functional Time Series

“…Notably, under the gravity model, the population with a bigger size is the main driving force while the population with a smaller size is orbiting the other population, similar to being attracted by gravity. Zhou et al (2014Zhou et al ( , 2019) considered a multi-population model where the underlying period effects from different populations are assumed to follow the vector auto-regressive (VAR) model and the vector error correction (VECM) model. Furthermore, Chen et al (2015) used a factor copula approach to capture mortality dependence among different populations.…”