There are no such "banks" but some projects have been lending bitcoin in exchange of altcoins as collateral like the ones OSS has posted in their post. But please use them with caution. You are giving your money to an anonymous organization and thus you are at risk. Still people use them regularly.

Alternatively you can go the "lending" section of this forum and check out the lenders threads there. Many well reputed users are lending out their money to borrowers willing to provide a valid collateral. This is called P2P lending and at least you can trust the uses here because of their long history of reputed trades or use a reputable escrow of this forum.