# One Touch Put Options

One touch put options are basic barrier options where the barrier is below the asset price.

One touch put options are plain barrier options where the underlying has to trade at or below the strike price for the strategy to immediately settle at 100. So, in the example of Figure 1 copper has to move to 205 or lower for the one touch put to be triggered and settle at 100 with immediate liquidation of the position.

One touch put options are American options as opposed to the European version of Binary Put Options. In options terminology a European option can only be exercised at expiry while the American option can be exercised at any time up to and including expiry. Since there is absolutely no point in waiting until expiry to exercise a one touch put then it is generally settled immediately.

One-Touch Put Option GreeksOut-of-the-MoneyIn-the-Money
Delta-veN/A
Gamma+ve N/A
Theta-veN/A
Vega+veN/A

### Unambiguous One-Touch Put Options

Unlike the European binary put option one-touch put options have no ambiguous area where the underlying settles exactly on the strike. In one touch terms this immediately defines the winning bet so that there is no ‘dead heat’ possibility, the option has just two settlement prices, 0 or 100. The expiry price profile is the same as Figure 1 of the Binary Put Option page but without the ‘dead heat’ settlement at 50.

This characteristic means that with the same strike, implied volatility and time to expiry one-touch put options will be twice the price of the European binary put option. Why? At the strike one touch put options will be worth 100, while the binary put option will be worth 50. At any time prior to expiry there would be the possibility of locking in a profit by buying the binary put option twice and selling the one-touch put once if the binary put options was offered at less than 50% of the one touch put, and vice versa,

Unfortunately financial markets are never quite so easy to take money from since at the strike one-touch put options disappear having settled at 100, leaving the risk of having a binary put option to ‘leg’ out of. Furthermore, there is additional risk if the position is short two binary put options and long one one-touch put if the underlying price barrels down through the strike with no chance of the short binary put options being closed out at 50, e.g. on ‘the open’ the underlying price might gap down through the strike and hence any ‘arbitrage profits’ turn into losses.

### One Touch Put Options Over Time

Fig.1 – Copper One-Touch Put Options w.r.t. Time to Expiry

Figure 1 shows the one-touch put over time for copper. Although the 25-day profile has a fairly mild gradient reflecting a low delta, the profile with just 0.2 days to expiry reveals extremely high gearing; in fact this option and the one-touch call have probably the highest gearing of any financial instrument.

### One Touch Put Options and Implied Volatility

Figure 2 details the effect of different implied volatilities on one touch puts.

Fig.2 – Copper One-Touch Put Options w.r.t. Implied Volatility

Yet again the profiles are fairly standard with the lower implied volatilities representing a lower probability of the strike being reached.

With both illustrations it is evident that the risk reversal cannot take place where theta and vega change sign. For this reason one-touch put options would be a far more efficient method of trading time decay and implied volatility although selling theta and volatility means immediate loss should the strike be hit. Therefore the seller of one-touch put options who wishes to take in time decay or wishes to short implied volatility needs to be fairly confident that the underlying price is unlikely to fall to the strike.

From a practical standpoint, if the CME offered these one-touch put options there is likely to be considerable demand from the over-the-counter brigade who are pricing up and trading copper barrier options for their clients. These barrier options may consist of knock-ins and knock-outs which are very popular in the OTC market so liquid one-touch put options and one-touch call options would be a very simple method of hedging away the position prior to the barrier being triggered.

### One Touch Put Options Formula

$\textup{One-Touch&space;Put}=\left&space;(&space;\frac{K}{S}&space;\right&space;)^{\frac{2r}{\sigma&space;^{2}}}N\left&space;(&space;-d_{3}&space;\right&space;)+\frac{S}{K}N\left&space;(&space;-d_{1}&space;\right&space;)$

where:

$d_{1}=\frac{ln\left&space;(&space;\frac{S}{K}&space;\right&space;)+\left&space;(&space;r-D+\frac{\sigma&space;^{2}}{2}&space;\right&space;)t}{\sigma&space;\sqrt{t}}$

$d_{3}=\frac{ln\left&space;(&space;\frac{S}{K}&space;\right&space;)-\left&space;(&space;r+\frac{\sigma&space;^{2}}{2}&space;\right&space;)t}{\sigma&space;\sqrt{t}}$

and:

$\textup{S}=\textup{price&space;of&space;the&space;underlying}$

$\textup{K}=\textup{strike&space;price}$

$\textup{r}=\textup{risk&space;free&space;rate&space;of&space;interest}$

$\textup{D}=\textup{continuous&space;dividend&space;yield&space;of&space;underlying}$

$\textup{t}=\textup{time&space;in&space;years&space;to&space;expiry}$

$\sigma&space;=\textup{annualised&space;standard&space;deviation&space;of&space;asset&space;returns}$

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