it all just lives in a bunch of csv files on a few people’s PCs and every night a 62 year old man copy pastes it together and checks everything and then uploads it to some old mainframe. he is the only one who knows how to do that job.
The old man has an ancient PC choking on dust under his desk that runs a QWS3270 terminal that updates the mainframe directly. If it's a big bank, the bank owns the mainframe. If it's a small bank, a vendor (probably Fiserv) does.
Source: I've consulted for a lot of banks.