Correlation, tail dependence and diversification

Abstract

In this contribution we analyze the interplay between correlation, tail dependence and diversification between risks which has a great impact on the calculation of the Solvency Capital Requirement under the Solvency II directive. The analysis shows that the prevailing assumption of an economic relationship between diversification and correlation or stochastic dependence is misleading under the risk measure VaR (Value at Risk) used under Solvency II and can lead to an underestimation of the necessary economic capital.