The underlying price could be considered the ribbon on a rope that two tug-of-war teams are pulling on, once the team to the right pulls the ribbon to the upper strike the buyer wins, should the team to the left pull the ribbon to the lower strike (barrier) then the seller wins.
Tug-of-War options were traded on the floor of LIFFE between bund options market-makers.
On LIFFE, ironically, the bet was not traded after the bet was initially established. The bet involved a lower and upper strike equidistantly below and above the current futures price. So, if the bund was trading at 100.00 and a ‘local’ shouted out “90’s before 10’s, £1,000” then they are stating that they wish to bet £1,000 that the bund will fall to 99.90 before it rises to 100.10. If another trader accepts the trade then that trader is saying the bund will touch 100.10 before 99.90. If neither level was touched the bet was null and void.
When the bet was struck the levels are both 10 ticks from the underlying giving both traders a 50:50 chance of success, so the implied price of the trade is 50. If neither level is touched then no matter what the price, the bet is annulled, i.e. settles at 50.
The above illustration shows the Oil Tug-of-War with strikes of $100 and $108. As the time to expiry decreases the price profile tends to the black profile, then subsequently the expiry profile which is a horizontal line at 50 from the barrier to the strike.
The 25 day profile is a straight line travelling from the barrier with zero price to the strike with priced 100. In effect the Tug-of-War with enough time to expiry becomes a ‘limit-up/limit-down’ future. A series of Tug-of-War’s with strikes midway between tick prices, e.g. 99.995/100.005, 100.005/100.015, 100.015/100.025 etc. when aggregated provides a ‘limit-up/limit-down’ future without the time to expiry condition.
Below is the same Tug-of-War but with implied volatility as the variable and five days to expiry. Yet again the straight line is apparent this time with high implied volatility.
The Tug-of-War offers a good return for ‘bottom-pickers’ at the $101.00 level. With implied volatility at 15% the Tug-of-War is worth 21.32 which is the maximum loss should Oil fall to $100. If the Gold price avoids the $100 price the minimum the bet will settle at is 50, a 500% return on fair value.
Of all the binary instruments detailed on this site the Tug-of-War is undoubtedly the most convoluted to calculate yet the most simple to understand and trade.
Tug of War = [100/108 Down-and-Out One-Touch Call
100/108 Up-and-Out One-Touch Put]
In options parlance, tug-of-war options are a combo that generates a price from -100 to +100. By adding 100 the price range changes to 0 to +200, which then need to be divided by 2 to return the range from 0 to 100.