Delta

  Delta measures how rapidly the value of an option moves in relation to the underlying value. It is the change in an option's price divided by the change in the price of the underlying instrument. An option whose price changes by $1 for every $2 change in the price of the underlying has a delta of 0.5. At-the-money options have delta's near 0.5. The delta rises toward 1.0 for options that are deep-in-the-money, and approaches 0 for deep-out-of-the-money options The hedge ratio is determined by the delta.

  The expected change in the option premium for one unit change in the price of the underlying instrument, i.e. the first derivative.