The discussion about a fiscal stabilisation capacity as a way of providing more fiscal integration in the euro area has strengthened in the aftermath of the European sovereign debt crisis. Among the instruments that can be used for temporary macroeconomic stabilisation in the presence of both asymmetric and area-wide shocks, a euro area unemployment insurance scheme has attracted increased attention. We build a two-region DSGE model with supply, demand and labour market frictions and introduce in it an area-wide unemployment insurance scheme that is entitled to borrow in financial markets. The model is calibrated to the euro area core and periphery data. For a country-specific negative demand shock hitting the periphery, we find the scheme to reduce the drop in Periphery output by about one fifth and the drop in union output by about a third. The scheme is effective when some households are cut from financial markets, and even more so when the national government also loses market access.