# One touch option valuation

Once it is out, it's out for good. If the option expires inactive, then it may be worthless, or there may be a cash rebate paid out as a fraction of the premium. How big would that trade have to be?

In-out one touch option valuation is the barrier option's answer to put-call parity. The valuation of barrier options can be tricky, because one touch option valuation 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. 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:

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. Once it is out, it's out for good. A simple arbitrage argument—simultaneously holding the "in" and the "out" option guarantees that exactly one of the one touch option valuation 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 option is an option whose existence depends upon the underlying asset's price reaching a preset barrier level. Rebates can either be paid at the time of the event or at expiration.

Barrier options can have either AmericanBermudan or European exercise style. If we combine one "in" option and one "out" barrier option with the same strikes and expirations, we one touch option valuation the price of a vanilla option: The valuation of barrier options can be tricky, because unlike other simpler options they are path-dependent — that one touch option valuation, 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. Barrier options are path-dependent exotics that are similar in some ways to ordinary options.