No modem is going to be able to make your external IP static, that is something your ISP has to setup.
Usually in New Zealand ISP's charge you $10+ per month just to make your IP static.
You can use www.noip.com, it basically assigns one ip address for example ' blair.noip.org' and on start up assigns your current router ip to noip address. Best to look at youtube tutorials on how to set them up.