You're a bit confused here. AntiVirus's are just security programs usually with the assumption of a realtime scanner for computer protection, what they do depends on the AV and the version of the AV you get. Some have paid and free versions that limit functionality from realtime scanning to firewalls. Some have firewalls, other's don't.
For online banking, I don't think they really protect you as much as just monitoring the traffic to and from your comuter ports. Really almost always for online banking security, it's just common sense. I don't use my WiFi for online banking, I use my own home network ethernet, and I don't use chrome for that either. It's usually Firefox.
You still need to protect yourself from phising sites, and attempts, which are most common through email. Some AV's can make you aware of it, as well as your email client, but too many people rely soulfully upon the AV itself like it's some kind of superhero. Which is not the case.
No matter what you do, there's still potential of viruses and intruders, regardless of what AV you have installed.