Down-and-In One-Touch Call
Down-and-in one-touch calls, like down-and-in calls, are as useful as the positioning of the barrier. Yet again this strategy is perfect for the chartist who wants to take a position based on a support level being touched, holding and bouncing back up to a particular level.
On offer in this section are examples using the US 10 Yr Treasury Note future. In the first illustration (Fig.1) the example is of down-and-in one-touch calls with barrier at 129.08 and strike at 130.00. The knock-in profile (black) shows the Notes must fall to touch the barrier at 129.08 at which point the strategy transforms into a one-touch call option (red) with strike at 130.00. If the Notes do not touch the barrier by expiry the strategy settles at zero.
The knock-in and the one-touch call profiles intersect at the barrier. If the barrier is pitched at a major level of support it provides a compelling instrument for chartists to back their view that the level will hold and the underlying bounce off it. In this instance the chartist is invited to speculate on whether the Notes will bounce ¾ point to hit the strike at 130.00.
Down-and-In One-Touch Call w.r.t. Time
Figure 2 shows down-and-in one-touch calls with 2, 4 and 10 days to expiry and 10% implied volatility. Even with just two days to expiry the knock-in at the strike is worth 11.78 offering a return of nearly 750% should the Notes fall and bounce ¾ point in 2-days. As the time to expiry increases to 4 days and 10 days at the Notes level of 130.00 the knock-in increases in value to 26.8 and 48.2 decreasing the returns to 273% and 107% respectively. In effect the 10-day profile is suggesting that it is just short of Evens-money probability that the Notes will travel down to 129.08 and subsequently trade back up at 130.00 in the next 10-days.
The attraction of this strategy to the chartist who believes that the Notes 129.08 level is a critical support level is the return on offer when the time to expiry is running down. With 10 days to expiry a 107% return might seem a good bet itself since at 10% volatility a daily price range of a point is hardly pushing things.
Down-and-In One-Touch Call w.r.t. Implied Volatility
Figure 3 illustrates the same down-and-in one-touch calls but over a range of implied volatilities, the time to expiry fixed at 2 days. An out-of-the-money one-touch call nearly always1 has positive vega meaning that an increase in volatility increases the value of the one-touch call which in turn demands an increase in value of the knock-in which has to intercept the one-touch at the barrier; the barrier also has a greater chance of being touched with higher volatility. This can be contrasted with the down-and-out one-touch call where a higher volatility increases the chance of the one-touch call being knocked-out and settling at zero.
The advantages to the chartist are:
- Back the support level with a minimum risk strategy. Often support levels are pivotal points from which the underlying may move from aggressively in either direction. A chartist who is buying futures at the underlying could be wearing a significant loss in a very short period of time if the support level is targeted and comes under sustained and heavy selling.
- Alternatively, should the support level hold and bounce aggressively from it then buying at the barrier may be almost impossible. This strategy alleviates the need to climb on board a rapidly rising market as the buyer of the knock-in has automatically received a long position in the market via his converted call.
- The market does not need to be monitored by the naked buyer of the strategy.
The above points outline the disadvantages of this bet to the market-maker:
- On triggering the barrier a market-maker short this strategy needs to buy double the short underlying position being held already as a hedge in the falling market. If the market bounces aggressively then buying back the hedge and buying more for the naked short one-touch call position could be extremely difficult.
- But the silver lining to this particular cloud is if the underlying gaps down through the barrier on the open one morning. The position is now a short one-touch call which is getting cheaper; furthermore the market-maker is still short the hedge from above the barrier. So not all doom and gloom for the market-maker.
All-in-all, if a big ‘hedgie’ starts buying the above knock-in then it might be a reasonable bet that the hedge fund will be doing its utmost to take the Notes down to the support with a large buy order at the support level.
The knock-in component of the down-and-in call resembles a one-touch put with the pay-off adjusted so that instead of a winning price of 100, the one-touch price at the barrier equates to the call premium. It is not so. The knock-in is graphically displayed in Figure 4 alongside the one-touch put with barrier/strike at 129.08 and there is a clear disparity.
The knock-in evaluation is generally based on a ‘heat reflection’ theory(!), which mathematically, is totally beyond me, but should any punter/financial engineer wish to contribute please comment below.
In the Knock-Out section where K<B then the profile is simple: since the strike is below the barrier then should the underlying not touch the barrier it will settle at 100, else 0. This is nothing less than 100 less than the one-touch put yet this option would be priced as the binary call less the knock-in, so there is a clear discrepancy. More under down-and-out binary call options.
1 As implied volatility increases the vega falls to zero and should the implied volatility increase beyond this point the vega will turn negative as the strike constrains the option value to 100. Increasing implied volatility subsequently has a disproportionate effect on the value of the one-touch call as the probability of the underlying falling further outweighs the impact of the underlying hitting the strike.