The post below is a classic by Joe Greenley. If you follow steps 1-4 you should have a non-raveling end to your bungee. The end works a little like the end of a shoe string and can be used for the same purpose. It can be used to push the end of the bungee through a hole in the deck which is too tight for the bungee to normally fit through. Then, by stretching the bungee, you can move it to the required position, leaving a nearly water-tight and good looking through hull bungee attachment.

I will also add the post to the Kayak Wiki as this question comes up every so often.

Rick