Delta
Also called: delta, option delta, hedge ratio.
Formula
Approximate premium change = Delta x Change in the underlying.
How it is read
Delta answers the question people actually ask when an index rises and their option does not. How much of the move was this strike ever going to pick up? It is also read as a rough sense of how likely the option is to finish with intrinsic value. And it is used to express a position's exposure in units of the underlying rather than in contracts. Delta is not fixed. It rises as an option moves toward the money and falls as it moves away. The rate of that change is gamma.
What it does not tell you
Delta is a first-order approximation, valid for a small move. Over a large move the delta itself has changed, so the estimate drifts. It also describes only the underlying's effect on the premium. It says nothing about the premium a position loses to time or to a fall in implied volatility. A delta near 0.5 is sometimes described as a 50% probability of finishing in the money. That is a rough correspondence produced by the pricing model, not a measured frequency.
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Related concepts
Delta: Why the Index Moved and the Option Barely Did
Delta is the fraction of the underlying's move that an option's premium picks up. An at-the-money option has a delta near 0.5. A 100-point move in the index then moves its premium by roughly 50 points. A far out-of-the-money option can have a delta of 0.1 or less, so the same 100 points moves it about 10. Being right about direction is not enough. The strike decides how much of that being right is paid out.
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