Down and Out Binary Call Options K ≤ B
Down and out binary call options K ≤ B is a fairly trivial strategy but is illustrated to draw a comparison to the one-touch put. When the strike is below the barrier the strike is rendered irrelevant.
Down and out binary call options K ≤ B (with strike below the barrier) is fundamentally a short position in a one-touch put with strike the same as the knockout barrier.
Down and Out Binary Call Options K ≤ B ≏ 100 – One Touch Put (K=B)
Figure 1 shows the profiles over time where there is a uniform increase in fair value as time to expiry decreases determining positive down and out binary call theta.
Figure 2 provides fair value profiles over a range of implied volatilities and here the fair value increases as implied volatility falls indicating negative down and out binary call vega throughout.
Both Figs. 1 & 2 show upward-sloping profiles indicating positive down and out binary call delta throughout indicating that this strategy is a directional play.
The decreasing gradient of the slope of the profiles indicates negative down and out binary call gamma throughout, that gamma clearly being most negative in the 0.1-day to expiry profile.