Semicoherent Multipopulation Mortality Modeling: The Impact on Longevity Risk Securitization

Abstract

Multipopulation mortality models play an important role in longevity risk transfers involving more than one population. Most of the existing multipopulation mortality models are built on the hypothesis of coherence, which assumes that there always exists a force that brings the mortality differential between any two populations back to a constant long-term equilibrium level. This hypothesis prevents diverging long-term forecasts, which do not seem to be biologically reasonable. However, the coherence assumption may be perceived by market participants as too strong and is in fact not always supported by empirical observations. In this article, we introduce a new concept called "semicoherence," which is less stringent in the sense that it permits the mortality trajectories of two related populations to diverge, as long as the divergence does not exceed a specific tolerance corridor, beyond which mean reversion will come into effect. We further propose to produce semicoherent mortality forecasts by using a vector threshold autoregression. The proposed modeling approach is illustrated with mortality data from U.S. and English and Welsh male populations, and is applied to several pricing and hedging scenarios.

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

“…This is how the error correction term forces the two time series to revert to the long-term equilibrium. Li et al (2016) found threshold behavior when modeling multi-population mortality by VAR model, i.e., the time series data follow different VAR models depending on the value of a threshold variable. Since VECM is a special case of VAR model, we are interested in whether threshold effect also presents in VECM and how to incorporate the threshold effect by the threshold VECM (TVEM) model.…”

“…Other examples of coherent models include the two-population model proposed by Cairns et al (2011), the gravity model by Dowd et al (2011), and the application of vector error correction model (VECM) by Zhou et al (2014). Li et al (2016) criticized that the hypothesis of coherence for being too strong and not always appropriate. A coherent multi-population mortality model may understate the range of possible mortality differentials between two populations.…”

“…A coherent multi-population mortality model may understate the range of possible mortality differentials between two populations. To address this problem, Li et al (2016) proposed the concept of semicoherence, which is incorporated into mortality forecasts by using a three-regime threshold vector autoregression model. In the middle regime, where the mortality differential between populations does not exceed a specific tolerance corridor, the mortality trajectories of two related populations are allowed to diverge.…”

“…The existence of cointegration relation has been confirmed among the mortalities of selected countries. The threshold behavior of the VAR model observed by Li et al (2016) suggests that a fixed relation may be inappropriate for certain countries. However, no existing literature on mortality modeling has yet considered the possibility of changing cointegration relations over time.…”

“…Therefore, it is essential to incorporate such changes in the multi-population mortality models. Although the threshold VAR used in Li et al (2016) can accommodate changes in the VAR relation, it does not take cointegration or long-term equilibrium into account. In this paper, we improve on the threshold of Li et al (2016) by considering threshold VECM (TVECM) proposed by Hansen and Seo (2002), which incorporates both threshold effect and cointegration relation.…”