Delta estimates how much an option's price is expected to change for a $1 move in the underlying stock. It's the most commonly referenced of the options Greeks because it directly answers a question every options trader asks: "if the stock moves, how much does my option move?"
Delta, Defined
A call option with a Delta of 0.50 would be expected to gain about $0.50 in value for every $1 the stock rises (and lose about $0.50 for every $1 it falls). A put option with a Delta of -0.50 moves the opposite way — it gains value as the stock falls.
Delta's Range
Call Deltas range from 0 to 1 (or 0 to 100 in some platforms' notation). Put Deltas range from 0 to -1. An option deep in the money trades with a Delta approaching 1 (or -1) — it moves almost dollar-for-dollar with the stock. An option far out of the money has a Delta near 0 — it barely reacts to small stock moves at all.
Delta as a Probability Estimate
Many traders informally use Delta as a rough estimate of the probability an option expires in the money — a 0.30 Delta call is loosely read as "roughly a 30% chance of expiring in the money." This is an approximation traders find useful, not a mathematically precise probability, and it shouldn't be treated as a guarantee.
A stock trades at $100. A $105 call has a Delta of 0.35. If the stock rises to $103 (a $3 move), the call's price would be expected to rise by roughly $3 × 0.35 = $1.05, all else being equal. In practice, Gamma (how Delta itself changes) means this is an approximation, especially for larger moves.
How Delta Changes
Delta isn't fixed — it shifts as the stock price moves closer to or further from the strike, and it shifts as expiration approaches (an at-the-money option's Delta tends to move toward the extremes faster the closer it gets to expiration). This rate of change is itself measured by Gamma — see the Greeks overview for how Gamma and Delta relate.
See Delta in Action
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