European Binary Options | Eachway Tunnel Delta | Eachway Tunnel Gamma | Eachway Tunnel Theta | Eachway Tunnel Vega |

The eachway tunnel is a volatility trade, as are standard tunnels. The eachway tunnel has a further two strikes providing three different settlements levels, not counting the ‘dead heats’.

### Eachway Tunnel Valuation

The Eachway Tunnel is calculated as:

Eachway Tunnel = R_{1} x Binary Call(K_{1}) + R_{2} x Binary Call(K_{2}) – R_{2} x Binary Call(K_{3}) – R_{1} x Binary Call(K_{4})

where:

K_{1} is the lowest strike, K_{2} the next highest strike, K_{3} the next highest strike while K_{4} is the highest strike, and

R_{1} + R_{2} = 1 and R_{2} ≥ R_{1}, and

K_{2} – K_{1} = K_{4} – K_{3}

### Eachway Tunnel at Expiry

The examples offered in Figures 1a & 1b are the 98.50/99.50/100.50/101.50 eachway tunnel which settles at zero outside the outer two strikes, between the inner two strikes the strategy settles at 100, while between the inner strikes and outer strikes the settlement price is 40 (Figure 1a) and 25 (Figure 1b).

The eachway tunnel provides a second place for the buyer who believes the underlying will be between the two inner strikes but gets it slightly wrong.

### Eachway Tunnel Over Time

Figures 2a & 2b provide the eachway tunnel price profiles over a range of days to expiry, 5% volatility, and different settlement values of 40 and 25.

The 25-day (blue) eachway tunnel of Figure 2a has a value that travels from 18.76 and 19.33 at the outer levels (97.80 and 102.20) of the range to just 26.43 with the underlying at 100.00; this reflects low eachway tunnel delta and gamma. The 0.5-day to expiry (red) profile is still smooth and still has not adopted the ‘head and shoulders’ expiry settlement shape. With 0.1 days to expiry (black) the ‘head and shoulders’ profile is now pronounced with greatest risk for the trader and market-maker when the underlying is close to the two inner strikes.

The 0.5-day and longer eachway tunnel price has profiles akin to short conventional straddle price profiles but without the unlimited downside risk. This strategy has the ability to compete with its conventional options counterparts and has clear attractions for both traders and clearing houses.

Figures 2a & 2b where the underlying asset prices are at the edges of the graph, i.e. at 97.80 and 102.20, the eachway tunnel can also offer a directional play. With 2 days to expiry Figure 2b shows the strategy is worth about 4.90 and 5.30 at 97.80 and 102.20 respectively. If the underlying rallied from 97.80 or fell from 102.20 to 100.00, where the eachway tunnel is worth about 61.48, returns of 1,155% and 1,057% could be achieved. These returns would be 1,941% and 1,781% if the underlying was between the two central strikes at expire although a moves of this magnitude would undoubtedly lead to higher volatility therefore a lower value at 100.00

### Eachway Tunnel and Volatility

The underlying asset has now risen in a day to 100.00 from 97.80. If the volatility remained the same at 10% then the profitability of the purchase of this 2-day eachway tunnel is fairly evident from Figures 2a and 2b.

But when the ratio is 0.25.100 as in Figure 2b the rise in volatility from 10% to 14% sees the profit fall by as much as the green profile at 100.00 to the yellow profile where the eachway tunnel is worth only 49.10, a fall of 61.48 – 49.10 = 12.38.

At the underlying of 100.00 and volatility of just 2.0% and two days to expiry the 0.25.100 eachway straddle has already reached the maximum value of 100.00. Selling the eachway straddle on the bid is now a long volatility play as the trader now needs the asset price to move below 99.50 or above 100.50.

The limited loss nature of this binary option volatility play means that the position has similar features to a conventional iron butterfly or condor.

By: Hamish Raw