The third pin in your cord is the ground. Running an additional ground wire would be redundant.
*Most* monitors don't use a three prong cord, so it's generally stated to ground the monitor frame.
If a cab is already wired with a ground strap for the monitor, and I install a monitor with a 3-prong cord, I usually hook up the ground strap too. A little bit of extra safety never hurts. If you have a three prong monitor cord and no ground strap in the cab, I wouldn't bother installing one.
Regards,
D