You most likely use a CEA mode. These include overscan borders, so the framebuffer resolution is smaller than the native resolution of the screen.
There's no way around setting the correct video mode manually if your monitor prefers such a mode. You may simply want to force a 1920x1080 DMT mode with HDMI audio. This can be done by setting
in /boot/config.txt. See this page for a list of video modes (and other options). There are some alternatives, including creating an alternative edid file for your monitor, but the solution above is most simple.
Some older TV sets don't like DMT modes. You have to go with a CEA mode then and adjust the overscan border. You can do this by tweaking the
in /boot/config.txt. Negative values are allowed.