Answer here depends on what you're hosting and doing for the bank but generally...assuming you do not require complex integrations into BBG or proprietary tools you should be able to host off-prem. We fought hard for it and eventually got through and our clients greatly appreciate it (we can update very quickly). The key here is selling through the front office instead of the back-office. The golden rule of selling software to a bank is that clients value making a dollar more than they value saving a dollar so do your best to position your solution around that and target the front office. They'll ram it through the system if it indeed is true. PS: happy to chat further "offline/hn". Email me (in profile)
EDIT: Assuming your service is SpiderOak, from my experience/perspective this would be a very hard sell to a bank. They have (albeit inferior) solutions for this and will not trust a third party to do it easily. I wouldnt even know how to go about selling it given you would have to go through the COO and vendor department. We offer a "similar" service in that we host virtual data rooms that contain tons of proprietary / confidential data. The difference is we do it in the context of a transaction (a front-office P&L event) which makes it a much easier sell. It's also not permanent.
Oh and for the sake of completeness: I'm not in any way affiliated with SpiderOak, though I suppose some of my post history mentions SO quite often as I'm a rather heavy user of their services.
EDIT: Assuming your service is SpiderOak, from my experience/perspective this would be a very hard sell to a bank. They have (albeit inferior) solutions for this and will not trust a third party to do it easily. I wouldnt even know how to go about selling it given you would have to go through the COO and vendor department. We offer a "similar" service in that we host virtual data rooms that contain tons of proprietary / confidential data. The difference is we do it in the context of a transaction (a front-office P&L event) which makes it a much easier sell. It's also not permanent.