Extremes for a general contagion risk measure

Contagion of risk among banks or insurers is an important contributing factor to the financial crisis of 2007–2009, amplifying shocks into systemic events, of which concepts appeared in the existing literature to evaluate the expected downside risk of a financial or insurance institution under some extreme scenarios. The limit behavior of a general contagion risk measure is investigated in this paper, with the help of general notions of Extreme Value Theory (EVT). Undoubtedly, the extremes of margins and the strength of dependence amongst the system components have a major impact on our asymptotic approximations. Numerical studies are provided to illustrate our theoretical findings. In the context of interest, the EVT approach has an immediate implication for determining the systemic importance under the modern prudent regulatory frameworks.