# An Introduction to Tunnel Options

Tunnel options, a.k.a. corridor options or rangebets, are all-or-nothing binary options that settle at 100 if the underlying is between the strikes at expiry, or at zero if outside the strikes at expiry.

Tunnel Options GreeksBelow Lower StrikeBetween StrikesAbove Upper Strike
Delta+ve+ve -ve-ve
Gamma+ve-ve+ve
Theta-ve+ve-ve
Vega+ve -ve-ve-ve +ve

## Tunnel Options

Tunnel options are a long binary call option and a short binary call option, the long having a lower strike than the short. The tunnel options buyer is similar to a conventional condor buyer in that they are both speculating that the underlying will be between the two strikes at expiry. The difference between the two strategies is that the condor has an extra two strikes outside the inner two strikes so that the expiry settlement price profile slopes down from the inner two strikes to the outer two strikes, in effect a long call spread with a short call spread above it. In contrast tunnel options have the strikes dropping from the two strikes vertically to zero as depicted by Figure 1.

Fig.1 – Soybean 1150/1250 Binary Tunnel Options Settlement Price at Expiry

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.

## Pricing Tunnel Options

Calculating the value of tunnel options is akin to a conventional call spread, i.e. subtract the value of the upper strike call option from the value of the lower strike call option.

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

where the first term and second terms are the binary call options with strikes K1 and K2 respectively.

## Tunnel Options Over Time

In the Soybean illustration of Figure 2 the middle point between the strikes is at 1200.

Fig.2 – Soybeans 1150/1250 Tunnel Options Fair Value w.r.t. Time to Expiry

If the 1250 binary call is worth 25 one might reasonably expect that the 1150 binary put to also be worth somewhere close to 25, hence the 1150 binary call will be worth 75. The binary tunnel option would then be valued as:

Soybeans 1150/1250 Tunnel Option          =          1150 binary call – 1250 binary call

=          75 – 25

=          50

For the 1150 binary put to be the same as the 1250 binary call would require:

1. Interest rates are zero so no cost of carry
2. The implied volatility of the 1150 binary put is the same as the 1250 binary call
3. That a normal bell-shaped distribution applies.

## Tunnel Options and Implied Volatility

Tunnel options are clearly a volatility play if tunnel options are bought or sold with the underlying price already within the two strikes. Figure 3 illustrates the soybean 1150/1250 binary  tunnel option over a range of implied volatilities.

Fig.3 – Soybeans 1150/1250 Tunnel Option Price w.r.t. Implied Volatility

A buyer of tunnel options 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 tunnel options would be appropriate.

Example: the trader who believes that the soybeans market may become less volatile might consider that the probability of the soybeans price being over 1250 at expiry only 15%, i.e. the binary call should be worth 10 ticks less than at present. This would suggest that the 1150 binary put should be only worth 15, leading to the 1150 binary call being worth 85. This would imply a tunnel options price of 70 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.

If the tunnel option was out-of-the-money when bought then the trade is a directional play as the buyer is speculating that the underlying is going to move towards the strikes.

## ‘Legging’ In To Tunnel Options

If, with the underlying at 1200 a trader fancies the market up then they could buy the 1250 binary call for 25. Should the trader be correct and the market rises to 1250 then the trader might sell his binary call at 50 and close out for a 25 profit. Alternatively he may hang on and wait for the underlying to rise to 1300 where he may sell the 1350 binary call for 25. At this point the trader has bought the Soybean 1250/1350 tunnel option for zero. Should the trader instead hang on for the underlying to trade 1350 then the 1350 binary call could be sold for 50, meaning that the trader has now banked a profit of 25 along with owning the 1250/1350 binary tunnel option for nothing. In effect the trader has paid -25 for the binary tunnel option which has to settle between 0 and 100.

‘Legging’ into structured positions, such as the tunnel, could become an important part of the everyday strategy of the binary trader. The strategies with two strikes are the tunnel and eachway binary call and eachway binary put and these strategies offer the best potential for legging into winning, no loss scenario positions.

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