A barrier option is an option whose existence depends on the underlying touching a set level. A knock-in only comes alive if the barrier is reached. A knock-out is cancelled if it is. Barriers make options cheaper than their vanilla equivalent and are the building blocks of most structured products.
How it works
There are four basic types: down-and-in, down-and-out, up-and-in and up-and-out, each on a call or a put. The barrier can be monitored continuously, daily on closes or only at maturity. Some knock-outs pay a rebate when they are cancelled. Without rebate, in-out parity holds: knock-in + knock-out = vanilla, for the same strike, barrier and expiry. This identity is a quick check on any price. Near the barrier, the value of a knock-out can collapse to zero on a small move, so delta and gamma become very large and can change sign.
Example
Hypothetical one-year puts struck at 100 with the underlying at 100. The vanilla put costs 8.00. A down-and-in put with a barrier at 80 costs 5.80. By parity, the down-and-out put with the same barrier is worth 8.00 − 5.80 = 2.20. If the underlying touches 80, the knock-out is cancelled and the knock-in becomes a vanilla put.
On the desk
The hedger cannot always trade at the barrier price in a gap. Desks therefore shift the barrier slightly in their pricing to cover hedging costs, and they watch open barrier levels across the market, which can attract or repel spot.
Educational definition. Worked examples are hypothetical. Not an offer or a recommendation.