The fastest telephoto lens is the Sigma 200-500mm f/2.8 APO EX DG. It has a maximum aperture of f/2.8, which allows for a fast shutter speed and low light photography. However, this lens is also quite large and heavy, and also quite expensive. Other fast telephoto lens options are the Canon EF 300mm f/2.8L IS II USM and the Nikon AF-S Nikkor 300mm f/2.8G ED VR II.