Cross-border integration requires the removal of entry barriers, the convergence of legal, supervisory and fiscal conditions underlying financial markets, the harmonisation of financial standards and the creation of common payment, clearing and settlement systems. To a certain extent, the geographical dimension of financial market integration is brought about by institutional integration.
The idea of helicopter money has also been discussed in academic circles: the ECB could give euro area citizens a one-off gift of € in order to boost the economy. You rightly say in academic circles … but how is this money then distributed. Should everybody get the same amount of money, rich and poor?