I tried to export PHAsset Video by UIActivityViewController in iOS.
It worked fine when PHAsset was image. The problem was when PHAsset
You shouldn't attach the AVURLAsset itself, instead you should specify its URL of the AVURLAsset as the activityItems.
So, use avAsset.URL should work, avAsset is an instance object of type AVURLAsset.
Edit
let theAsset = avAsset as AVURLAsset
let videoURL = theAsset.URL
var activityVC = UIActivityViewController(activityItems: [videoURL], applicationActivities: nil)