We swapped equivalent amounts of currency. It's not like we have no collateral.
Exactly right. That’s why it doesn’t show up as a liability - in fact, it shows up on the Fed’s balance sheet as “Other Federal Reserve Assets” or some such.
Since this is a swap between central banks, there is (supposedly) no counterparty risk.
I forgot to mention that the outgoing swap to the ECB (or other bank) shows up as as liability.
The net:net effect is that the balance sheet hasn’t changed. It just got moved around.