Modeling Multi-Country Mortality Dependence by a Vine Copula
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Modeling Multi-Country Mortality Dependence by a Vine Copula

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Multi-country mortality dependence attracts the attention of insurers owning life insurance or annuity businesses across countries. When implementing a sophisticated enterprise risk management (ERM) program, it is crucial to model the structure of such dependence accurately, even though capital regulations, such as Solvency II and ICS, do not mandate a focus on geographical diversification.
Elliptic and Archimedean copulas are often used as a tool of risk aggregation in advanced ERM. However, they cannot always flexibly capture complex tail dependence, especially under certain stressed situations.
This study proposes modeling multi-country mortality dependence by a vine copula, which provides greater flexibility and efficiently characterizes the dependence structure. We demonstrate the usefulness of a vine copula using actual data. First, we use a Lee-Carter model to estimate the mortality rates of 13 countries (12 European countries and Australia). Subsequently, we use a vine copula to model the dependence among the time-varying mortality improvement parameters of each country.
Consequently, we obtain a dependence structure resembling the actual geographical relationships, which is intuitively understandable. We also demonstrate that the vine copula is superior on some measures to other benchmark copulas. Finally, we conduct a simulation in a stressed environment and reveal that benchmark copulas underestimate the tail dependence of concentrated exposure. This study contributes to developing internal models for capital regulation.

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