Imposing a tax on the big four banks in exchange for the implicit support lenders receive from taxpayers would raise almost $15 billion for the public coffers over the next few years, according to new costings of a Greens policy.

The Greens have seized on Reserve Bank analysis released this week, which found the major banks receive a benefit worth up to $3.7 billion from the assumption they would be bailed out in a crisis.

A 2015 RBA internal paper, released under Freedom of Information laws, estimated the major banks benefited by between $1.9 billion and $3.7 billion because the assumption of taxpayer support gives them cheaper funding than otherwise.

On Thursday, Greens treasury spokesman, lower house MP Adam Bandt, released new costings from the Parliamentary Budget Office, arguing that a levy was the right response to banks being "too big to fail".