Barrier options are path-dependent options, that are either initiated (knocked in) or eliminated (knocked out) upon reaching a certain barrier level.
Barriers are classed as "up" or "down", depending upon their position relative to the spot prices at the start of the Option. A standard barrier option has only one barrier which can be "up" or "down". A double barrier option has both an "up" and "down" barrier.
Barriers are either "in" or "out". A barrier is considered touched when the spot price of the underlying asset equals or crosses the barrier value. Once an "in" barrier is touched the option is "knocked in", and will pay out in the same way as a vanilla option. If an "out" barrier is touched then the option is "knocked out" and has no value.
In cases where the option expires and an "in" barrier has not been touched, or an "out" barrier has been touched then the Barrier Option may pay a rebate to the holder.
Look-barrier options, first introduced by Bermin (1996), can be regarded as a combination of a barrier option and a forward starting fixed strike lookback option. The look-barrier option's barrier starts at the option's starting date and exists until the barrier end date. If the barrier is not triggered during this period, the fixed strike lookback option will be initiated at the barrier end date.
A soft-barrier option (also known as a Step Option) is similar to a standard barrier option, except that the barrier is no longer a single level. Instead it is a soft range between an upper level and a lower level. Soft-barrier options are knocked in or out proportionally.
Resolution has seven functions for pricing barrier options.