Extreme,

First just checking -- 'fades' usually refer to the entire image (video or still) gradually disappearing as the frame become blank black. As you say 'all round the sides' I presume you want what might be more properly called a vignette. One way of doing this is to create a graded mask in any painting program and put it on a track under (higher number) your clip. 

Then select it and apply something from  'Effects' >> 'Video effects' >> "chroma key'. On the image below I'd use 'White ' which make the white part transparent so you can see through that part the to your clip.

A better mask mask would have a reasonable area of pure white and the transition to black just around the edges.

Regards,

Carl