This post ist published by Hamish Raw of https://hamishraw.com/
Double no touch binary options consist of two strikes/barriers, one below the current underlying price and the other above the current underlying price. If at any time prior to and including expiry the underlying trades at or through either strike/barrier then the strategy immediately ‘loses’ and is settled at zero. If at expiry neither of the strikes/barriers has been traded at or through then the strategy settles at 100.
In terms of taking a view on volatility, double no touch binary options are probably the most efficient of all instruments including conventional straddles and strangles. If the trader wants to sell volatility, which in the conventional sense would require selling at-the-money straddles or strangles, the trader would need to buy, not sell, double no touch binary options. This is very much a sudden death approach to trading, but at the same time a very lucrative approach to shorting volatility assuming strikes are not touched.
The above graph shows the routes to expiry for 210/240 coffee double no-touch binary options . With 100 days to expiry the profile is almost flat and never exceeds a price of 6.14. In other words, with 100 days to go to expiry and a volatility of 20% the odds of the underlying remaining within the 210 to 240 corridor without ever touching either strike is just 6.14%. As time passes the profiles starts to rise and fill in the rectangle bounded by the double no touch binary options prices of 0 and 100 and the strike prices.
Understanding the profile of double no-touch binary options is of immense importance to those buyers of time decay because the most profitable no-touch trades on a daily basis would be positions which are of varying degrees in-the-money. For example, with 100 days to go it doesn’t really matter where the underlying is in relation to the strikes as the buyer will not make a profit over one day. With 25 days and 8 days to go you’d want to be buying double no-touch binary options if the price of coffee is at or very near 225. With 8 days to go you’d want to buy this double no touch if the underlying was off centre where the greatest time decay exists. An analysis of time decay and the most profitable underlying price levels at which to purchase double no touch binary options is in the section Double No Touch Theta.
The price profiles of double no-touch binary options are greatly impacted by implied volatility, i.e. double no touch vega is high. It follows that the greater the volatility of the underlying the greater the chance of one of the strikes being hit, hence the lower the price of the double no touch.
Figure 2 offers price profiles of double no touch binary options over a range of implied volatilities. In the 20-day example at 50% volatility the double no-touch is almost worthless implying there’s no chance of the underlying avoiding hitting one of the strikes. As volatility falls to 10% the double no-touch gains value. At 5% the double no-touch has fair value of 100 over the range of coffee prices from 222 to 228. Clearly when volatility is high the greatest gains from selling volatility, i.e. buying double no touch binary options, is when the price of coffee is midway between the strikes. As implied volatility falls the greatest gains have moved away from the midpoint of the strikes and has moved towards the strikes. Trading vega is covered in more detail at Double No Touch Vega.
Double no touch binary options are a challenge conceptually but as with financial instruments in general the more complex they are the better chance of making money from them. To that end the conventional premium seller should take a good look at buying double no touch binary options as they provide many opportunities for taking advantage of time decay.
Evaluating Double No Touch Binary Options
If the fair value of tunnels can be calculated by subtracting the lower strike binary put plus the upper strike binary call option from 100, can Double No Touch binary options, the no touch equivalent of the tunnel, be calculated in the same manner by aggregating the one-touch put and one-touch call and subtracting the result from 100? Conditional probability says “No”.
Figure 3 offers two double no touch binary options using a Fourier series calculation, and one using the above ‘Tunnel’ method.
What is immediately apparent is that the tunnel method creates a double no touch fair value that can be negative, thereby immediately eliminating it as a viable evaluation. This is basically because at the lower strike the upper strike one-touch call may have some value and while at the upper strike the lower strike one touch put may also have value. Therefore at either strike, where the actual value of double no touch binary options should be 0, they are in fact negative.
The correct method to use is the Fourier Series and the website intmath offers a clear and concise appreciation of Fourier’s methodology.