Up-and-In Binary Call Options (K<B)
Up-and-in binary call options are not the most useful of speculative instruments but nevertheless they provide a cheap alternative to gaining speculative exposure to markets, in common with all knock-ins.
Up-and-in binary call options involve a knock-in that has the barrier higher than the underlying price and, on hitting the barrier, convert into binary call options.
i. Of interest are up-and-in binary call options where the barrier is higher than the strike and for the below examples the Forex pair of US dollars and Russian roubles are used.
ii. What are of no interest at all are up-and-in binary call options where the barrier is below the strike since the knock-in price profile exactly follows that of the binary option it would convert into.
Figure 1 shows US dollar/Russian rouble up-and-in binary call options with 2, 10 and 50 days to expiry and 10% implied volatility. The strike price is 29.50 and the barrier is set at 30.50. The solid lines describe the 29.50 binary call options whereas the dashed lines are the 30.50 knock-in profiles.
The 2-days knock-in profile (dashed black) travels up to meet the 2-day binary call (black) at a price of 100 which means that the knock-in has a profile similar to that of a one touch call. The 10-days (red) and 50-days (green) profiles offer shallower knock-ins and less gearing. Nevertheless, the 2-day and 10-day knock-ins are a considerably cheaper alternative to the binary option itself.
An example of the potential of this strategy is if there was a significant resistance level between the strike and the barrier. If the resistance level was midway between the strike and the barrier then buying the knock-in offers a cheap entry into the speculative position that the resistance level will be breached, and once breached and the barrier triggered, the resistance level now forms a solid support level.
Fig.1 – USD/RUB Up-and-In Binary Call Option w.r.t. Time to Expiry
Figure 2 illustrates the same up-and-in binary call options but over a range of implied volatilities, the time to expiry fixed at 25 days.
The lower the implied volatility the higher the price disparity between the binary call and the up-and-in profile with this disparity progressively taking place at a higher USD/RUB price until it reaches the maximum difference of 100.
Evaluating the Knock-In
Up-and-in binary call options profile (black) is calculated by subtracting the up-and-in binary put price (blue) from the one-touch call price (green) which, at the barrier, is the same as the binary call option.
Up-and-In Binary Call Options = One-Touch Call(B) ― Up-and-In Binary Put