What is Delta?
How much an option price moves for a $1 move in the underlying — the directional exposure number.
Definition
Delta (Δ) is the first derivative of option price with respect to the underlying. A delta of 0.45 means the option gains ~$0.45 for every $1 the underlying rises. Calls have positive delta (0 to +1); puts have negative delta (0 to -1). At-the-money options have delta ≈ ±0.5; deep ITM ≈ ±1; deep OTM ≈ 0.
Why it matters for trading
- Delta is the position size translator. A trader holding 10 calls with delta 0.45 has the directional exposure of 450 underlying shares — even though the notional capital deployed is a fraction of that.
- Dealer aggregate delta is what drives gamma hedging flow. When SPX rises, dealer delta goes more positive; they sell underlying to neutralise — that creates the GEX-driven mean-reversion in positive-gamma regimes.
- Delta probability proxy: a 0.30 delta is informally "30% chance of finishing in-the-money". Useful for sizing wing trades but breaks down near event vol.