  The subject of the present article is the study of correlations between large
insurance companies and their contribution to systemic risk in the insurance
sector. Our main goal is to analyze the conditional structure of the
correlation on the European insurance market and to compare systemic risk in
different regimes of this market. These regimes are identified by monitoring
the weekly rates of returns of eight of the largest insurers (five from Europe
and the biggest insurers from the USA, Canada and China) during the period
January 2005 to December 2018. To this aim we use statistical clustering
methods for time units (weeks) to which we assigned the conditional variances
obtained from the estimated copula-DCC-GARCH model. The advantage of such an
approach is that there is no need to assume a priori a number of market
regimes, since this number has been identified by means of clustering quality
validation. In each of the identified market regimes we determined the commonly
now used CoVaR systemic risk measure. From the performed analysis we conclude
that all the considered insurance companies are positively correlated and this
correlation is stronger in times of turbulences on global markets which shows
an increased exposure of the European insurance sector to systemic risk during
crisis. Moreover, in times of turbulences on global markets the value level of
the CoVaR systemic risk index is much higher than in "normal conditions".
