Delta

Delta measures how much an option price changes for every $1 move in the underlying asset. It is the most intuitive of the Greeks and the first one every options trader needs to master.

Practical Interpretation

A call with a delta of 0.50 gains roughly $0.50 for every $1 the stock rises. A put with a delta of −0.40 loses $0.40 for every $1 the stock rises. Delta also serves as a rough approximation of the probability that the option expires in the money — useful as a shorthand, though it is not the exact probability.

Delta and Moneyness

At the money: delta ≈ ±0.50 — maximum uncertainty about whether the option finishes in or out of the money.
Deep in the money: delta approaches ±1.00 — the option behaves almost like the underlying itself.
Deep out of the money: delta approaches 0 — very little sensitivity to price.

Delta as a Hedge Ratio

Market makers use delta to hedge their books. If you sell 10 call contracts with a delta of 0.50, you need to buy 500 shares (10 × 100 × 0.50) to be delta neutral. That hedge has to be adjusted continuously as delta itself changes — which is precisely what gamma measures.

What Moves Delta

Time matters: as expiration approaches, in-the-money deltas converge toward ±1 and out-of-the-money deltas toward 0. Implied volatility matters too — higher IV expands the deltas of out-of-the-money options and compresses those of in-the-money options, because a wider distribution makes distant strikes more reachable.