Sometime later this month you can expect AMD's new "Crimson Edition" driver but in the meantime the company offers Catalyst 15.11 beta, which you can download over here. This new release has optimizations for the new Call of Duty game as well as a bunch of bug fixes.
Call of Duty : Black Ops III - includes quality and performance optimizations
 The Oculus runtime may crash on launch
 The Intel graphics is flagged in an error state in the Device Manager in systems with switchable graphics
 An error may be experienced when installing the latest graphics driver package on some AMD Radeon™ R9 380 series products
 The secondary graphics adapter is missing in the Device Manager and the AMD Catalyst™ Control Center after installation of the driver
 A TDR error is experienced when launching Star Wars™: Battlefront while a You Tube video plays in the background
 An extended black screen may be experienced during bootup under Windows® 10 between the Windows® Logo and the Windows® login prompt
 Ashes of the Singularity™ may crash on some AMD 300 series GPUs
 Ashes of the Singularity™ may fail to launch on some GPUs with 2GB Video Memory.
 Call of Duty : Black Ops III - Flickering may be observed when running the game in DirectX® 11 mode and with AMD Crossfire™ enabled
 Batman™: Arkham Knight - An application crash may be experienced at some game locations
 A black screen may be experienced on booting Windows® 10 on some systems with switchable graphics - with AMD Radeon™ HD5000 series graphics cards, when connected to an HDMI monitor
 Elite: Dangerous - poor performance may be experienced in SuperCruise mode