# Up and In Binary Call Options

# Up and In Binary Call Options definition and price profile

This post is published by Hamish Raw of https://hamishraw.com/

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 hardly of 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.

## Up and In Binary Call Options (K<B)

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.

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. Figure 3 illustrates the price disparity between 25-day binary calls and up and in binary call options where the peak of the maximum disparity slides to the right before falling back to zero at 30.50. Should the maximum disparity be considered the ideal time to enter the up-and-in then Figure 3 provides the optimal entry points: Figure 3 also provides something else in the price profiles of the up-and-out binary call where K<B.

Figure 4 provides the profiles of the same price disparity as Figure 3 but with respect to time to expiry. The less time there is to expiry the greater the disparity is but whether this is a worthwhile strategy to follow without other determining rules must be doubtful. Yet there have been more bizarre methods to determine entering trades……….!

## 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**

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