Delta

Delta is one of the infamous Greeks of Modern Portfolio Theory.

It is the most straightforward of the Greeks, however, being the partial derivative of an option (future, or whatever) with respect to the underlying (here, stock price):

\[ \delta=\frac{\partial f(S,...)}{\partial S} \]

As a (partial) derivative, delta indicates how much the option moves when the underlying moves.

For instance, an option with a delta of +0.3 moves 30 percent of the underlying in the same direction. If the underlying moves up 20 percent, the option moves up 6 percent; if the underlying moves down 20 percent, the option moves down 6 percent.

Conversely, options with negative deltas move opposite to the direction of the underlying: They move down when the underlying moves up and up when the underlying moves down.

Because of this neat little trick, options with negative deltas form the basis of hedging.