A delta of an option is a measure reflects the change in its value in response to a unit change in the price of its underlying. For a European call option on a non-dividend-paying stock, delta is given by:
Δ long call = N(d1)
where: N(d1) is the cumulative probability function for a standardized normal distribution (the probability that the option price will be less than d1).
For a short position in a European call option, delta is calculated as:
Δ short call = – N(d1)
A long position in a European call option can be delta-hedged by maintaining a short position of N(d1) shares for each long option. Likewise, a short position can be delta-hedged by maintaining a long position of N(d1) shares for each short option.
For a European put option on a non-dividend-paying stock, delta is given by:
Δ long put = N(d1) – 1
The negative delta implies that a long position in a put option need to be hedged with a long position in the underlying, and vice versa (a short position in a put should be hedged with a short position in the underlying).
For more, see: delta of a European stock option- an example.
