Delta is the most quoted number on an options screen and the most misread. It answers one narrow question exactly, and four others only approximately.
The exact definition
Delta is the rate of change in an option's price for a one-dollar move in the underlying, holding everything else still. A call with a delta of 0.40 gains roughly forty cents when the stock rises a dollar, and loses roughly forty cents when it falls one.
Calls have deltas between 0 and 1, puts between −1 and 0. The sign encodes direction; the magnitude encodes how much of the move the option participates in. An at-the-money option sits near 0.50 in absolute terms because it is roughly a coin flip whether it finishes in the money.
Deep in the money: absolute delta approaches 1 — the option behaves almost like the shares.
Far out of the money: delta approaches 0 — the option barely responds, because there is little chance of it paying.
At the money: near 0.50, and the most sensitive point to changes in the stock.
The share-equivalent reading
A more useful interpretation for position sizing is that delta also expresses equivalent share exposure. One contract covering 100 shares with a delta of 0.40 moves like 40 shares. A ten-contract short put at delta −0.30 moves like being long 300 shares, in the opposite direction to the obligation it represents.
This is why a portfolio of options with small individual positions can add up to more market exposure than intended. Deltas are additive across legs, so a four-leg structure has one net delta that can be read the same way.
Why delta does not stay put
Delta is a local measurement: it is the slope of the option's value at the current stock price, not a constant. As the stock moves, delta changes, and the rate of that change is gamma.
This is why a short option's apparent risk grows as the stock approaches its strike. The delta that looked comfortable at two dollars away is a different, larger delta once the stock arrives. Any position sized from delta at the moment of entry is sized at its most benign point.
Where the "delta as probability" reading breaks down
Delta is often used as a shorthand for the chance of finishing in the money, and it is close to the risk-neutral probability under the model the calculator uses. Close, but not the same thing, and the difference matters at the edges.
More importantly, the probability of finishing in the money is not the probability of making money. A short put with a delta of −0.20 finishes out of the money most of the time and still loses money on the occasions it does not, because the loss is larger than the premium collected. Delta tells you about the outcome's likelihood; it says nothing about its size.
Questions
Is delta the same as probability of profit?
No. Delta approximates the modelled chance an option finishes in the money. Probability of profit is the chance the whole position is profitable at expiration, which is a different range of prices once premiums and multiple legs are included.
What does a negative delta mean?
The position gains when the underlying falls. Short calls and long puts have negative delta; short puts have positive delta because they profit as the stock rises.
Does delta change after I open the position?
Continuously, with the stock price and with time. Delta is a snapshot, and for options near the money the snapshot changes fast — which is what gamma measures.