Delta

Delta is the first-order partial derivative of an option's price with respect to the underlying's price. It measures how many dollars the option will gain (or lose) for a $1 move in the underlying.

Calls have delta between 0 and 1; puts between −1 and 0. Deep-in-the-money options approach |1|, deep out-of-the-money options approach 0.

Practical uses:

• Approximate the share-equivalence of an option position.
• Build delta-neutral hedges when running a market-neutral book.
• Estimate, very roughly, the probability the option finishes ITM (delta of 0.30 ≈ 30% ITM probability under Black-Scholes assumptions).