What is Delta?
Delta is an options Greek that measures the rate of change of an option's price relative to a $1 move in the underlying asset. For calls, delta ranges from 0 to 1. For puts, delta ranges from -1 to 0. Delta tells you how much your option position will gain or lose for small moves in the underlying.
Understanding Delta Values
A call option with 0.50 delta gains $0.50 for every $1 increase in the underlying and loses $0.50 for each $1 decrease. A put option with -0.40 delta loses $0.40 for every $1 increase and gains $0.40 for each $1 decrease.
Deep in-the-money calls have deltas approaching 1, meaning they move nearly dollar-for-dollar with the underlying. Far out-of-the-money calls have deltas near 0. At-the-money options typically have deltas around 0.50.
Delta as Probability Proxy
Delta is often interpreted as an approximate probability that the option will expire in-the-money. A 0.30 delta call has roughly a 30% chance of being profitable at expiration. This interpretation is an approximation but useful for intuition.
Delta and Position Sizing
Delta allows different options positions to be compared in terms of equivalent underlying exposure. If you own 10 calls with 0.50 delta each, your position has 500 total delta, equivalent to owning 500 units of the underlying from a price movement perspective.
Delta Hedging
Delta neutral strategies involve offsetting option delta with underlying positions. If you sell a call with 0.60 delta, you can buy 0.60 units of the underlying to hedge. The combined position has zero delta and is not affected by small price movements.
Delta hedging removes directional risk, isolating other factors like volatility and time decay.
Delta Changes
Delta is not constant. It changes as the underlying price moves, and this rate of change is measured by gamma. At-the-money options have the highest gamma, meaning their delta changes most rapidly with price movements.