The OP is not trying to start a hosting company. He is simple trying to run a site from his router if it is possible, "just to do it".
Possible, yes indeed, but very, very complicated in so many ways. Updates, security patches, dynamic/changing ip numbers, security measures, the fact that most internet connections are made to download and not to upload would eventually cause your ISP to complain about your upstream traffic. So many variables to take into concern, it's just simpler to pay $5 a month to Godaddy or HostGator or 24hservers.com to host it for you and get rid of all the headaches. Good idea in theroy but in reality, not a chance in hell!