Adam Clarke on Genesis 42:15

By the life of Pharaoh - חי פרעה chey Pharaoh, Pharaoh liveth. As if he had said, As surely as the king of Egypt lives, so surely shall ye not go hence unless your brother come hither. Here therefore is no oath; it is just what they themselves make it in their report to their father, Gen 43:3 : the man did solemnly protest unto us; and our translators should not have put it in the form of an oath, especially as the original not only will bear another version, but is absolutely repugnant to this in our sense of the word.