I have two monitors model iiyama pl2792q with the same problem: They have a black border at top, left and right, but not at bottom.
With the underscan/overscan option I can only make the content smaller (it is already at 0% overscan). Described in this answer: https://superuser.com/a/232082
I changed the resolution from 1920x1080 to 1920x1200 - no solution.
Graphics card: AMD Radeon HD 6700 Series
Is it possible, that this black border is a hardware problem?