Binary Touch Options - two sides of the same coin

In our previous article we introduced Binary Touch Options through One-Touch (OT) and No-Touch (NT). We will now show the links between the two through their payouts, and show that they are in fact two sides of the same coin.

One-Touch options pay out a notional amount if a certain trigger level is hit within the life of the option. No-Touch options pay out a notional amount if a certain trigger level is not hit within the life of the option. What happens then, if we were to buy both a One-Touch and No-touch option with same notional amounts, trigger levels, and expiries?  We would in fact receive the payout no matter what!

Let’s look at an example: We assume that EURUSD is trading at 1.4300. We buy both a One-touch and No-touch with EUR 1,000 notional each, two week maturity and a trigger level of 1.4100. The payoff, if 1.4100 trades, is EUR 1,000 from the One-Touch whilst the No-Touch becomes worthless.  On the other hand, if 1.4100 never trades within the two weeks, the NT pays out EUR 1,000 whilst the One-Touch expiries worthless. The payoffs in the two situations can then be summarized in the table below:



We notice that we get a EUR 1,000 payout no matter what.  We can thus conclude that the price of the portfolio containing both the One-Touch and the No-Touch should be equal to the notional amount of the individual touch option. This can be written as:

Notional Amount  =  Premium OT  +  Premium NT  (*  See note)

Rearranging, we see that the premium of the No-Touch can be expressed from the price of the One-Touch:

Premium NT  =  Notional Amount  –  Premium OT

What does this mean for the relationship between buying a One-Touch and shorting a No-Touch?  Carrying on with the previous example:  The price of the One-Touch is 40 percent and the price of the No-Touch is thus 60 percent  (* see note).  Let us compare buying EUR 1,000 notional of the One-Touch and shorting the equivalent of the No-Touch.

When going long the One-Touch we pay the premium at the beginning, here EUR 400 (40% * 1,000).  When shorting the No-Touch we receive the premium of EUR 600 (60% * 1,000).  Now if spot trades at the trigger of 1.4100 then the One-Touch pays out the notional of EUR 1,000 put together with the paid premium the return is EUR 600. In the case of the short No-Touch it becomes worthless and the premium received is thus secured. The profit is also EUR 600. If the spot never trades at 1.4100 the One-Touch expiries worthless so the paid premium of EUR 400 is lost. In the case of the short No-Touch the notional of EUR 1,000 will have to be paid to the buyer, put together with the premium received this also leads to a loss of EUR 400. The cases are illustrated in the table below:



The final payoff is the same for the long One-Touch and the short No-Touch, however the occurrence of the payments and payoffs are distributed differently. What we can say is that the two positions are two sides of the same coin. Therefore, a long One-Touch position is practically the same as being short the No-Touch with the same trigger and maturity.  Likewise being short the One-Touch is practically the same as being long the No-Touch.

In terms of ultimate profit and loss the positions are the same.  They only differ through the cash flow timeline. 

Saxo Bank recently introduced Binary Touch Options for 6 of the most liquid currency pairs (EURUSD, GBPUSD, USDJPY, EURJPY, EURGBP and AUDUSD). They can be traded from the Saxo Bank Option Board in the “Prices and Trades” menu of the SaxoTrader trading platform.

For more information and examples please visit the BTO section on www.saxobank.com.

(*)  Please note that for this example and article and for the sake of simplicity, we are ignoring the effects of interest rate and carry on the cash flows. We are also working on mid-market assumptions, where there is no bid-ask spread.