A barrier option is a type of financial option where the option to exercise depends on the underlying crossing or reaching a given barrier level. Barrier options are always cheaper than a similar option without barrier. Barrier options were created to provide the insurance value of an option without charging as much premium.
Types
Barrier options are path-dependent exotics that are similar in some ways to ordinary options. There are put and call, as well as European and American varieties. But they become activated or, on the contrary, null and void only if the underlying reaches a predetermined level (barrier).
The four main types of barrier options are:
- Up-and-out: spot price starts below the barrier level and has to move up for the option to be knocked out.
- Down-and-out: spot price starts above the barrier level and has to move down for the option to become null and void.
- Up-and-in: spot price starts below the barrier level and has to move up for the option to become activated.
- Down-and-in: spot price starts above the barrier level and has to move down for the option to become activated.
Valuation
The simplest way to value barrier options is using a static replicating portfolio of vanilla options, so chosen so as to mimic the value of the barrier at expiry and at selected discrete points in time along the barrier. This approach was pioneered by Peter Carr and gives closed form prices and replication strategies for all types of barrier options.
EVENT
A barrier event occurs when the underlying crosses the barrier level. While it seems straightforward to define a barrier event as “underlying trades at or above a given level,” in reality it’s not so simple. What if the underlying only trades at the level for a single trade? How big would that trade have to be? Would it have to be on an exchange or could it be between private parties? When barrier options were first introduced to options markets, many banks had legal trouble resulting from a mismatched understanding with their counterparties regarding exactly what constituted a barrier event.