If you are with Nvidia, some graphic cards can enable Performance Boosters in the Control panel, it helps me siphon out the crap stuff even when I don't need it. If not you should really find out what card you have and the size of your video ram. I'm no expert but there is a way to get good performance on your game, by optimizing it via the Steam launcher. I used to play DayZ a lot and everyone I knew got terrible performance for the game, but they figured out a way via Steam to optimize your start-up settings so it uses up a dedicated amount of your Ram, without the changing sporadically and causing leakage like this. This may look like an extreme way to fix your game, and I don't even know if it works with Call of Duty. Anyway, if you're desperate this could work.
Go to your Steam and right-click your Black Ops III in the Library,
Go into your Game's Properties and find the "Set Launch Options" option and a box will pop up.
These are the things you can type in that I found when trying to optimize DayZ:
Do what you can. If it doesn't work, well, at least you tried something. For me with a lot of games it helps in the long run.
Hope this helped mate.