I've worked in three different banks and was able to bring my laptop (not connected to the bank network of course), use my headphones to cut the open space noise and listen to anything I want.

As in your bank, proxy was very restrictive, a lot of the web wasn't reachable, but with my laptop when I had free time between projects or issues I could use them for something interesting, and management/security was OK with that.

Seems like hell, just get out of there if you can and have the chance to. In the meantime try to ask for other tasks, or try to refactor some code, there's always room for improvement somewhere, and it's better than looking at the clock for hours a day.

Good luck!