Barrier options can be priced in either of the pricing pages.
A barrier option is a European style vanilla option that is activated (knocked in) or terminated (knocked out) under conditions specified in the option's contract. The conditions are defined in terms of one or two barriers that may be touched:
If they are European, only on the expiry date of the option.
If they are American, at any time during the lifetime of the option.
If there is a payout, it is that of the underlying vanilla option.
Why use barrier options?
You would use a barrier because of both the following reasons combined:
It is inevitable cheaper than its equivalent vanilla counterparty. This is because it has a risk of being knocked out, or of not being knocked in. By a similar logic, a double knockout option is cheaper than a single knockout option because it has two knockout barriers and thus double the risk of being knocked out.
You have a particular take on the spot's movement that makes the risk of the added barriers worthwhile.
Types of barrier options
You can create the following barrier options: