Delta is the option's price change per $1 move in the stock: calls run 0 to +1, puts 0 to -1. It doubles as the position's stock-equivalent exposure, a rough probability of finishing in the money, and the hedge ratio market makers trade against.
Delta is the first of the option Greeks and the one most screens are built on. It measures how much an option's price changes when the stock moves $1, and because that sensitivity rises as an option moves into the money, it also works as a rough gauge of how likely the option is to finish there.
| Option | Call delta | Put delta |
|---|---|---|
| Deep in the money | Near +1.00 | Near -1.00 |
| At the money | About +0.50 | About -0.50 |
| Out of the money | +0.10 to +0.30 | -0.10 to -0.30 |
| Far out of the money | Near 0 | Near 0 |
Calls gain value when the stock rises, so their delta is positive. Puts gain when it falls, so theirs is negative. A call and a put at the same strike and expiration have deltas about one apart: a +0.53 call pairs with a -0.47 put.
A $100 stock with 30 days to expiration and a flat 30% implied volatility (model prices; real chains add skew):
Deltas add. A short option flips the sign of its delta, so a credit spread that sells the 95 put (-0.25, which becomes +0.25 when sold) and buys the 90 put (-0.10) has a net delta of about +0.15: it behaves like 15 shares per contract and gains a little as the stock rises. Summing every position's delta, adjusted for each stock's beta, gives the portfolio view described in beta-weighted delta.
Premium-selling rule sets commonly place short strikes by delta, for example a band of 0.15 to 0.30, because it puts strikes at similar implied odds on every stock regardless of price or volatility. The reasoning and the trade-offs between a wider and a tighter band are in delta bands for short strikes, and delta's relationship to the other Greeks is in options Greeks explained.
The option gains or loses about $0.30 for each $1 move in the stock, one contract behaves like about 30 shares, and the market prices roughly a 30 percent chance of the option finishing in the money.
A put gains value when the stock falls, so its price moves opposite to the stock. Put deltas run from 0 to -1, and selling a put flips the sign, giving the seller positive delta.
Only roughly. Delta and the model's probability of finishing in the money are close but not equal; for a 30-day 105 call on a $100 stock at 30 percent volatility, delta is about 0.31 and the model probability about 28 percent.