# Down and In Binary Put Options (K>B)

## Down-and-in binary put 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.

Down-and-in binary put options involve a knock-in that has the barrier lower than the underlying price and, on hitting the barrier, convert into binary put options.

i. Of interest are down-and-in binary put options where the barrier is lower than the strike and for the below examples Wheat futures are used.

ii. What are of no interest at all are down-and-in binary put options where the barrier is above the strike since the knock-in price profile exactly follows that of the binary option it would convert into.

Figure 1 shows wheat down and in binary put options with 2, 4 and 25 days to expiry and 35% implied volatility. The strike price is 640 and the barrier is set at 620. The solid lines describe the 640 binary put options whereas the dashed lines are the 620 knock-in profiles.

At the strike the difference between the 2-day and 4-day knock-ins is roughly the same as the difference between the 4-day and 25-day knock-ins. Nevertheless, the 2-day and 4-day knock-ins are a considerably cheaper alternative to the binary option itself being respectively 34.72 and 15.62 cheaper, whereas the green solid and dashed lines of the 25 day profiles are just 1.53 apart.

An example of the potential of this strategy is if there was a significant support level between the barrier and the strike. If the support level was midway between the barrier and the strike then buying the knock-in offers a cheap entry into the speculative position that the support level will be breached, and once breached and the barrier triggered, the support level now forms a solid resistance level.

Figure 2 illustrates the same down and in binary put options but over a range of implied volatilities, the time to expiry fixed at 2 days.

The lower the implied volatility the higher the price disparity between the binary put and the down-and-in profile with this disparity progressively taking place at a lower wheat price until it reaches the maximum difference of 100.

**Evaluating the Knock-In**

The down-and-in binary put profile (green) is calculated by subtracting the down-and-in binary call options price (orange) from the one-touch put price (red) which, at the barrier, is the same as the binary put option (black).

**Down and In Binary Put = One-Touch Put(B) ― Down and In Binary Call**