Two traders can look at the same stock and buy calls that behave nothing alike. One buys a deep in-the-money call that tracks the stock almost dollar for dollar. The other buys a far out-of-the-money call that barely moves until the stock runs. The number that tells them apart is delta, and it is printed on every row of the chain.
Moneyness
Moneyness is how far a strike sits from the stock price, and on which side. A $150 call on a stock at $160 is $10 in the money. A $170 call is $10 out of the money. The chain's M% column gives the same thing as a percentage of the stock price, so a strike 5% below the stock reads minus 5.0 whatever the stock costs. That matters because a $10 move is a lot on a $100 stock and nothing on a $1,000 one; the percentage is what carries across stocks.
Delta
Delta is how much an option's price changes when the stock moves $1. A call with a delta of 0.50 gains about 50 cents when the stock rises $1 and loses about 50 cents when it falls $1. Call deltas run from 0 to 1. Put deltas run from 0 to minus 1, because a put gains when the stock falls. Some platforms print deltas as whole numbers, 50 instead of 0.50; the meaning is the same.
Delta follows moneyness. A deep in-the-money call behaves like the stock and has a delta near 1. A far out-of-the-money call barely reacts and has a delta near 0. An at-the-money call sits close to 0.50, usually a touch above it. Plot delta against the stock price and you get an S-shaped curve.
The same $100 strike with 90, 30 and 7 days left. Delta runs from near 0 far out of the money to near 1 deep in it, passing about 0.50 at the strike. Drag volatility up and the S flattens; switch to Put and the curve sits one lower, from minus 1 up to 0.
Time changes the shape. With months to go the S is gentle, and a few dollars of movement shifts delta only a little. In the last days it turns into a step: an at-the-money option snaps toward 0 or 1 on small moves, because there is no time left to come back. Higher volatility works like more time and flattens the S. Read down the call side of a live chain and you see the same curve, Delta falling from near 1 at the lowest strikes to near 0 at the highest.
Delta in shares
Because one contract covers 100 shares, delta also tells you how much stock an option is standing in for. A 0.50 delta call moves like 50 shares, a 0.90 delta call like 90. Owning five 0.30 delta calls is roughly like owning 150 shares, for as long as the deltas stay where they are. They do not stay put: as the stock rises, calls move deeper into the money and their deltas climb, which is a big part of why a winning call's gains speed up. Module 5 gives that change its own name, gamma.
Delta as a rough probability
Traders also read delta as a rough guide to the chance the option finishes in the money. A 0.25 delta call has something like a one in four chance of ending above its strike; a 0.90 delta call is very likely to. It is an approximation, not a promise: delta runs a little above the model's true chance, by an amount that grows with volatility and time.
A $100 strike call with 30 days left. The two lines nearly overlap, which is why traders use delta as a quick probability. Push volatility or days up and delta pulls further above the true chance.
The gap is small enough that professionals choose strikes by delta rather than by dollar amount. The 25 delta put means the same thing on any stock at any price in any market: an option about one in four to finish in the money. The $300 put tells you nothing until you know the stock price and how much it moves.
Why the chain beats a guess
You cannot look at a strike and know its delta. Delta depends on the stock price, the days left, and how much the market expects the stock to move, all at once. A call $10 out of the money can be a 0.40 delta on a jumpy stock with a month to run and a 0.05 delta on a quiet one with a week. The chain has already solved that for every strike, and it re-solves it as the stock moves. When you want the 25 delta call, you scan one column for the row nearest 0.25 instead of guessing which strike that might be today. Delta and its neighbors Gamma, Theta and Vega each get their own lesson in Module 5.
The maths: delta is a slope
Delta is the slope of the option's value against the stock price: dollars of option value per $1 of stock. You can estimate it from two prices, one dollar either side of today: delta ≈ (C(S + 1) - C(S - 1)) / 2, where C(S + 1) is the option's value with the stock $1 higher.
Worked example, from the model the charts use: a $100 strike call with 30 days left, at 30% volatility and a 4% rate, is worth about $3.08 with the stock at $99, $3.59 at $100 and $4.15 at $101. Delta ≈ (4.15 - 3.08) / 2, about 0.53. The model's exact delta at $100 is 0.532.
In the model, delta is N(d1) and the chance of finishing in the money is N(d2), where N turns a number of standard deviations into a probability and d2 = d1 - v × √T. In the example d1 is about 0.08 and d2 is about zero, so delta is 0.53 while the chance of finishing in the money is 0.50. The gap, v × √T, grows with volatility and time, which is the gap you can open up in the second chart. The interest rate and an extra half of v squared inside d1 are why an at-the-money delta sits a little above 0.50.
Your turn
Open the AAPL chain on the expiration in the question. Read the Delta of the at-the-money call, then scan up the out-of-the-money calls and find the strike whose Delta is closest to 0.25. Then read the at-the-money put delta on the other side of the same row, with its minus sign.
What comes next
This module is the free sample. Module 2 starts with forward prices, carry and put-call parity, the rules that tie every price on the chain together, and Modules 3 to 7 cover how pricing models think, volatility, the Greeks one at a time, dynamic hedging and position risk. Modules 8 to 12 build spreads for a volatility view and a directional view, then cover arbitrage and early exercise, the volatility surface, and hedging in the real world, and the whole course comes with any ApexVol plan, including the free trial.