Starting an exchange is a significant amount of work, and doing it yourself with no budget will take a good amount of time and effort. Just getting it to work properly is difficult enough, but then you'll have to secure it from an onslaught of hackers and helpdesk tickets.

Assuming you want to proceed, I've actually looked into this myself and spent a good amount of time trying to do just that. The best open source exchange I've found is Peatio, however, you will definitely need to work with the code to make it work. I found there were bugs that needed ironing out and any custom features had to be hand coded. It does look pretty slick though and is 95% of what you need for free.

Good luck in your venture.