# Tunnel Options

### Tunnel Options at Expiry

Tunnels options settle at 100 if, at expiry, the underlying is between the strikes or at zero if outside the strikes at. If the asset settles on the strike (a draw) then the option settles at 50.

The tunnel buyer is similar to a conventional straddle seller in that they are both speculating that the underlying will be between the two strikes at expiry. The difference between these strategies is that the straddle has sidelines at an angle of 45°. In contrast the tunnel, at the strikes, has vertical sides dropping from 100 to zero as depicted by Figure 1.

The Tunnel is calculated as:

Tunnel Option    =    Binary Call(K1) – Binary Call(K2)

where K1 is the lower strike and K2 the upper strike of the binary call options.

In Figure 1 the settlement price is zero outside the strikes and 100 inside. Should the underlying settle exactly on either strike then adopting the ‘dead heat’ rule would create a settlement price of 50. Calculating the value of the tunnel option is akin to evaluating a conventional call spread, i.e. subtract the value of the upper strike binary call option from the value of the lower strike binary call option.

### Tunnel Options and Time to Expiry

Between the strikes at the asset price of 100.00 as time passes the tunnel is worth more. This indicates that at 100.00 the tunnel has positive tunnel option theta.

In the illustration of Figure 2 the middle point between the strikes is at 100. If the 101.00 binary call is worth 25 one might reasonably expect that the 99.00 binary put to also be worth somewhere close to 25. Hence the 99.00 binary call would be worth 75. The tunnel would then be valued as:

99.00/101.00 Tunnel             =          99.00 binary call – 101.00 binary call

=          75 – 25

=          50

For the 99.00 binary put to have the same as the 101.00 binary call would require:

1. Interest rates are zero so no cost of carry
2. The implied volatility of the 99.00 binary put is the same as the 101.00 binary call
3. Same time to expiry, and
4. A Normal bell-shaped distribution applies OR a lognormal distribution with very short time to expiry and/or very low implied volatility.

### Tunnel Options and Volatility

The tunnel is clearly a volatility play if bought or sold with the underlying price within the two strikes. Figure 3 illustrates the 99.00/101.00 tunnel over a range of implied volatilities.

A buyer of the tunnel option may believe that the implied volatility is too high as, for example, a series of national holidays are coming up with traders thoughts diverted away from trading and more on their sun tan lotion. If, on the other hand, the speculator believes the market will become more volatile a sale of the tunnel would be appropriate.

Example: the trader who believes that an asset price may become less volatile might consider that the probability of the asset price being over 101.00 at expiry only 15%, i.e. the binary call should be worth 10 ticks less than the current 25 price tag. This would suggest that the 99.00 binary put should worth around 15  also, leading to the 99.00 binary call being worth 85. This would imply a tunnel price of 70 (85 – 15) which in itself is implying that there is a 70% chance of the underlying being between the strikes as opposed to the current 50% market forecast.

### Tunnels as a Directional Play

If the tunnel was out-of-the-money when bought, i.e. the asset price was below the lower strike or above the upper strike, then the trade is a directional play as the buyer is speculating that the underlying is going to move towards the strikes.

1. If, with the underlying at 100.00 a trader fancies the market up then they could buy the 101.00 binary call for 25.
2. Should the trader be correct and the market rises to 101.00 then the trader might sell his binary call at 50 and close out for a 25 profit.
3. Alternatively he may hang on and wait for the underlying to rise to 102.00 where he may sell the 103.00 binary call for 25.
4. At this point the trader has bought the 101.00/103.00 tunnel for zero.
5. If instead of 4. the trader hung on for the underlying to trade 103.00 then the 103.00 call could be sold for 50, meaning that the trader has now banked a profit of 25 along with owning the 101.00/103.00 tunnel for nothing. In effect the trader has paid -25 for the tunnel which has to settle between 0 and 100.

‘Legging’ into structured positions, such as the tunnel option, could become an important part of the everyday strategy of the binary trader.

The strategies with two strikes are the tunnel option and the eachway call and eachway put and these strategies offer the best potential for legging into winning, no loss scenario positions.

By: Hamish Raw

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