How much does an option move when the stock moves?

The Greeks are not advanced mathematics dressed up in Greek letters. Each one answers a plain question of the form "if only this changes, what happens to my option?" We will not derive a single formula. We will read the dials.

Delta answers the first and most important question: how much does the option's price change when the underlying moves $1?

The number and its range

• Call deltas run from 0 to +1. A call gains when the stock gains.
• Put deltas run from −1 to 0. A put loses when the stock gains.

Worked: stock at $100, a 30-day $100 call priced at $2.30 with delta 0.50.

• Stock to $101 → option ≈ $2.80 (+$0.50 per share, +$50 per contract).
• Stock to $99 → option ≈ $1.80 (−$50 per contract).

A put on the same stock with delta −0.50 does the reverse: the stock rises $1, the put loses about $0.50.

Delta tracks moneyness

Delta is essentially a smooth version of the ITM/ATM/OTM classification from Unit 2:

Plotted against strike, delta traces a flattened S-curve: near 1 on the deep-ITM side, sliding through 0.50 at the money, tailing to near 0 far out.

Delta as share equivalence

This is how professionals actually use it. Multiply delta by the multiplier and the number of contracts and you get your position delta — your exposure restated in shares:

4 contracts × 100 × delta 0.35 = 140 share equivalents

A desk does not think "I own four call options." It thinks "I am long the equivalent of 140 shares, and that number will change if the stock moves." Restating options exposure in shares is the single habit that turns options from a mystery into a position you can size.

Delta as a rough probability

You will hear a 0.30-delta call described as having "about a 30% chance of finishing in the money." It is a serviceable rule of thumb and worth knowing, with two caveats stated honestly:

• Delta is an approximation of a different model quantity than the actual probability of finishing ITM. They are close for typical contracts, not identical.
• It is a model output under model assumptions, not a measured fact about the world. It inherits every assumption baked into the pricing model, including the implied volatility you fed it.

Use it as a rough gauge of where a contract sits. Do not use it as a forecast.

The problem with delta

Everything above assumed delta holds still. It does not. The moment the stock moves, delta itself changes — which means the $50-per-dollar exposure you measured is only true for the very next dollar. That instability has its own Greek, and it is the next lesson.

In the data

Delta is published for every contract on a chain. Apple's is below, in the Terminal's options view, as the Δ column on each side.

Open Apple's chain with IV and the Greeks in the EODHD Terminal

It is signed: calls run from 0 to 1, puts from 0 to −1, so a far out-of-the-money call might read 0.10 and a deep in-the-money put −0.88. And it is quoted per share of the underlying, the same way the premiums are, so a position delta needs the 100-share multiplier applied on top. Adding up deltas across calls and puts nets long against short, which is either exactly what you wanted or a serious miscount.

Try it now

1. In the chain above, open one expiry and read the call delta down the column from the lowest strike to the highest. Confirm the S-curve: near 1 at low strikes, near 0 at high ones.

2. Pick a contract and compute its share-equivalent exposure: delta × 100 × the number of contracts you are imagining. Say the answer as "I am long ___ shares' worth."

3. Compare a 0.50-delta contract and a 0.10-delta contract on the same expiry. For a $1 move, one earns $50 per contract and the other about $10 — yet the second one costs far less. Note that the cheaper contract is cheaper because it does less, not because it is a better deal.