#### Delta Hedge

To offset the delta of an option or other non-linear trade, usually with a linear derivatives position

Detail

If we buy a simple call option, or sell a simple put option, then we may or may not have a long position when the delivery date of the (potentially exercised) contract is made

In reality the option will either get exercised or not - let's say the option is for the delivery of 1,000 MT of coal in January 2016 at ARA (Amsterdam Rotterdam Antwerp location) - we will either have a position of 1,000 MT at that time, or not

On any particular day the option will have a calculable delta, which roughly translates into a probability of the option being exercised:

An option with a delta of 0.01 has a 1% chance of being exercised

An option with a delta of 0.5 has about a 50% chance of being exercised

Traders generally hedge the exposure of the option (which is the delta times the volume), so if the delta is 0.5 they will hedge 500 MT of coal

In general as the option exercise time approaches the delta of the option will swing quite rapidly toward 0 or 1 (or -1) so that the hedge swings toward 1,000 Mt or 0 MT

If you're wondering why an option with a delta of 0.5 (meaning the value of each MT changes by €0.5 for each change in €1 per MT in the value of coal) has a 50% chance of being exercised then think the other way round - if the option was certain to be exercised then its value would change by €1 per MT per change of €1 per MT in the price of coal, so its delta would be one - the delta is effectively the probability of being exercised