Standard American barrier options are one of the most frequently traded exotic FX derivative contracts. American barrier options have a vanilla payoff at expiry plus they also have a single American-style barrier. There are two main variations: Regular barrier options have the American barrier positioned out-of-the-money compared to the option payoff and reverse barrier options have the American barrier positioned in-the-money compared to the option payoff. As described in Chapter 20, American barriers are monitored continuously against the spot level in the market.
A regular American knock-out (KO) call option structure is shown in Exhibit 24.1. Note that the barrier is positioned out-of-the-money.
Consider a CCY1 call knock-out barrier option with the barrier positioned so far below the strike that there is zero chance of spot hitting the barrier and then ending up back in-the-money at expiry. The pricing and risks of this knock-out option will be identical to the equivalent vanilla option:
As Exhibit 24.2 shows, even with a barrier (1.2000) much closer to the strike (1.3000), ...