# Up-and-Out Binary Call Option

## The up-and-out binary call option has a barrier (B) above the underlying at which, if touched or traded above, the bet is knocked out, plus a strike (K) below the barrier.

(N.B. The Up-and-out binary call option where the barrier is less than the strike is trivial since the strategy can never ‘win’ and therefore is always worth zero.)

The following illustration shows the Hang Seng up-and-out binary call option with the barrier at 22,500 and strike at 22,000 and a range of days running from 25 down to 0.5. This strategy has similar characteristics to the out-of-the-money tunnel with the higher strike being a short one-touch and the lower strike being a binary call.

Figure 2 shows the same strategy but over a range of implied volatilities.

This strategy is in effect the same as a long binary call with a short one-touch call so that this strategy may be of interest if the speculator fancies the market up but is confident that a level of resistance above the strike but just below the barrier will hold. Dependent on implied volatility, time to expiry and distance between the strike and the barrier this strategy could offer a cheaper point of entry than, for example, the tunnel with strikes K and B. This advantage could quite possibly be eroded if the market-makers consider that as an exotic option it justifies opening the spread up.

In summary, not a ‘killer’ strategy with broad practical use.

#### Formula

where:

where:

and: