Delta

Delta is the most widely used option Greek. It measures how much an option's price is expected to change when the underlying moves by $1. A call with a delta of 0.40 should gain about $0.40 if the stock rises $1. Delta also tells you how many shares an option position behaves like, how many shares you need to hedge it and, roughly, the chance that the option will finish in the money.

Delta for calls and puts#

Calls have positive delta because they gain when the underlying rises; puts have negative delta because they gain when it falls. For the same strike and expiry, call delta minus put delta is about 1, a consequence of Put-Call Parity.

Traders often quote delta as a whole number per contract: a 0.40 delta call is "40 delta" and behaves like 40 shares per 100 share contract.

Three ways to read delta#

1. Price sensitivity#

2. Share equivalent and hedge ratio#

Delta tells you how many shares your position is like.

position delta = option delta × 100 × number of contracts

Ten 0.38 delta calls behave like 380 shares. To hedge them, a trader could short 380 shares, making the position delta neutral. See Delta Hedging.

3. Rough probability#

Delta is often used as a quick estimate of the chance an option finishes in the money. A 0.20 delta call is treated as roughly a 20% chance. This is an approximation; models give a separate figure for the risk neutral probability, which is slightly different, especially for long dated or high volatility options. Option sellers often choose strikes by delta for this reason.

What changes delta#

Near expiry, delta becomes very sensitive: an at the money option can swing from 0.2 to 0.8 on a small move. See Option Expiration Dates.

Using delta in strategy choice#

Delta in portfolios#

Adding up delta across all positions gives a portfolio's net directional exposure. Market makers and volatility traders aim to keep net delta close to zero so that their profits come from volatility and time, not direction. See Managing Portfolio Greeks.

Common mistakes#

• Treating delta as fixed. It changes with price, time and volatility.
• Confusing contract delta with share count without the 100 multiplier.
• Relying on delta as an exact probability.

Frequently asked questions#

What is delta in options?#

The expected change in an option's price for a $1 change in the underlying, from 0 to 1 for calls and from minus 1 to 0 for puts.

What does a delta of 0.50 mean?#

The option gains about $0.50 for each $1 rise in the underlying, behaves like 50 shares per contract and is roughly at the money.

Is delta the probability of expiring in the money?#

It is a common rough guide, but not exact. Pricing models give a separate risk neutral probability that is usually close but not identical.

Next, learn how delta itself changes in Gamma.