# Eachway Tunnel

The eachway tunnel (aka corridor, rangebet or ranger) is a volatility trade, as is the standard tunnel option, but with the eachway tunnel there are a further two strikes providing three different settlements levels, not counting the ‘dead heats’.

There are similarities with selling the conventional straddle but with the eachway tunnel, since the payoff doesn’t consist of two 45º lines but instead offers a staggered payoff, it enables the payoffs to be adjusted, so that in the following example the payoff consists of 100:40:0 as opposed to 100:50:0.

Eachway Tunnel Greeks | Below Lowest Strike | Between 1st & 2nd Strikes | Between Centre Strikes | Between 3rd & 4th Strikes | Above Highest Strike |
---|---|---|---|---|---|

Delta | +ve | +ve | +ve -ve | -ve | -ve |

Gamma | +ve | -ve +ve | -ve | +ve -ve | +ve |

Theta | -ve | +ve -ve | +ve | -ve +ve | -ve |

Vega | +ve | -ve +ve | +ve -ve +ve | +ve -ve | +ve |

## Eachway Tunnel Expiry Values

The example offered in Figure 1 is the Hang Seng 19,250/19,750/20,250/20,750 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.

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

Figure 2 illustrates the price profiles over time with 22% implied volatility.

The 25-day (blue) eachway tunnel has a price that travels from 18.83 and 20.43 at the outer ranges (18,900 and 21,100) of the HSI range to just 29.72 with the underlying at 20,000; this reflects low eachway tunnel delta and gamma. The 1-day (red) to expiry 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 greater risk for the trader and market-maker when the underlying is close to the two inner strikes.

The 1-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 counterparts and has clear attractions for both traders and clearing houses.

With the underlying at the edges of the graph, i.e. at 18,900 and 21,100, with 3 days to expiry the strategy is worth about 7.83 and 9.32 and may be considered a directional play. For example, if the underlying rallied from 18,900 to 19250 where the eachway tunnel is worth about 25.37 a 224% return could be achieved, just a 350 tick move. This return would be 1,177% if the underlying was between the two central strikes at expire, a rise of between 850 and 1,350.

## Eachway Tunnel and Implied Volatility

The graph below offers each way tunnel price profiles over a range of different implied volatilities for the above Hang Seng Index example. Here a wide (and unrealistic) range of implied volatilities are used to illustrate the effect of implied volatility on the price of the strategy.

At a high implied volatility the underlying is forecast to oscillate along the HSI price range which, in turn, offers very little chance of an accurate forecast as to where it might be at the expiry of the strategy. As volatility falls to 6% (red) the head-and-shoulders profile is gradually assumed. At 20,000 a seller of volatility at 30%, i.e. a buyer of the strategy, would make a profit of 11.28 if it fell to 22%.

## Evaluating the Eachway Tunnel

The EW tunnel is formed from 4 binary call options and is calculated by:

EW Tunnel = 100 x (0.4 x Binary Call(K_{1}) + 0.6 x Binary Call(K_{2})

– 0.6 x Binary Call(K_{3}) – 0.4 x Binary Call(K_{4}))

where K_{1} is the lowest strike and K_{4} is the highest.

As with the eachway call and eachway put the returns are not cast in stone but the first two and last two settlement prices must each add up to 1, e.g. 0.4 and 0.6 as above, or 0.25 and 0.75, 0.2 and 0.8 etc..