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A barrier option is an option whose valuation formula for window barrier options trading depends upon the underlying asset's price reaching a preset barrier level. Barrier options are path-dependent exotics that are similar in some ways to ordinary options.
You can call or put in AmericanBermudanor European exercise style. But they become activated or extinguished only if the underlying reaches a predetermined level the barrier.
If valuation formula for window barrier options trading option expires inactive, then it may be worthless, or there may be a cash rebate paid out as a fraction of the premium.
Once it is out, it's out for good. Also note that once it's in, it's in for good. In-out parity is the barrier option's answer to put-call parity. If we combine one "in" option and one "out" barrier option with the same strikes and expirations, we get the price of a vanilla option: A simple arbitrage argument—simultaneously holding the "in" and the "out" option guarantees that exactly one of the two will pay off identically to a standard European option while the other will be worthless.
The argument only works for European options without rebate. A barrier event occurs when the underlying crosses the barrier valuation formula for window barrier options trading.
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 valuation formula for window barrier options trading 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.
Barrier options are sometimes accompanied by a rebatewhich is a payoff to the option holder in case of a barrier event. Rebates can either be paid at the time of the event or at expiration. Barrier options can have either AmericanBermudan or European exercise style. The valuation of barrier options can be tricky, because unlike other simpler options they are path-dependent — that is, the value of the option at any time depends not just on the underlying at that point, but also on the path taken by the underlying since, if it has crossed the barrier, a barrier event has occurred.
Although the classical Black—Scholes approach does not directly apply, several more complex methods can be used:. From Wikipedia, the free encyclopedia.