Any person at any time may produce their own currency, one can even do so on the back of a paper napkin, ripped beer coaster or whatever. This is NOT a banking privilege, it is within the lawful ability of anyone capable of engaging in commerce.
It is called a 'negotiable instrument' ... it gives the holder rights to a sum of money. Notice that I say 'holder' ... this is what distinguishes it from a non-negotiable instrument, the fact that you don't need to redeem it from source, you can pass it to another who then becomes the 'holder in due course' and thus obtains the rights conferred.
The conferable rights over a sum of money (or, indeed, other asset) are themselves 'value'
Do banks do this ? Yes, all the time! ... one of the simplest examples are cheques drawn against the bank, which are considered 'as good as cash'. Usually they will be drawn out to the order of the person you wish to pay ... but can equally be drawn out to bearer. The only reasons they resist making out to bearer is :
- Out of some piffling concern over your security (blah)
- Because the bank (and the Taxman) likes to know all things
But you can write your own at 'any time' on 'any thing' ... See the apocryphal, yet deliciously entertaining, tale of the 'negotiable cow'