Barrier Option

From WilmottWiki

A barrier option is like any other type of option, but it is subject to barrier conditions on some observed value - usually the market price of the underlying. Such conditions are whether the barrier is an upper or lower barrier, the level of the barrier and what happens when the observed value goes above (or below) the barrier. An example could be an up-and-out call on WTI (oil) set at $100. This means that option behaves like a normal call, but if WTI exceeds $100 at any point during the lifetime of the option then the option knocks-out, i.e. it becomes worthless.

Further examples of barriers are:

• up-and-in - the derivative only has value if the observed value goes above the barrier
• down-and-out - the derivative only has value if the observed value stays above the barrier
• down-and-in - the derivative only has value if the observed value drops below the barrier

Exotic barrier options can involve many barriers.

Pricing barriers present some special challenges - for example greek calculations when the underlying is very close to the barrier tend to be unstable.