In this paper, we review and discuss some challenges in insuring flood risk in Europe on the national level, including high correlation of damages. Making use of recent advances in extreme value theory, we, furthermore, model flood risk with heavy-tailed distributions and their truncated counterparts and apply the discussed techniques to an inflation- and building-value-adjusted annual data set of flood losses in Europe. The analysis leads to Value-at-Risk estimates for individual countries and for Europe as a whole, allowing to quantify the diversification potential for flood risk in Europe. Finally, we identify optimal risk pooling possibilities in case a joint insurance strategy on the European level cannot be realized and quantify the resulting inefficiency in terms of additional necessary solvency capital. Thus, the results also contribute to the ongoing discussion on how public risk transfer mechanisms can supplement missing private insurance coverage.