Euribor's annual lending rate rose to 0.35% (see chart below). The last time first-round banks lent to each other at this rate was in late 2014, before the ECB launched its massive QE program.
So it appears that in July we will indeed see the ECB raise the rate from its current negative values of minus 0.5%. The regulator will have to start tightening financial conditions with the Eurozone economy slowing sharply. Inflation close to 8% is forcing the ECB to raise the rate. Let's see where this leads.
Yields on Greek and Italian government debt are already approaching critical levels. I wonder what the ECB will do if yields continue to rise. On the one hand we need to fight inflation, but on the other hand we can't allow a sovereign default by Greece or Italy. It is not quite clear how these two problems can be solved simultaneously.