Delta explained: sensitivity, share equivalents and probability
Delta is a local price sensitivity. Convert it into position exposure while keeping its probability interpretation separate.
By OptionsKing. Publisher and editorial methods.
What you will learn
By the end of this lesson, you should be able to:
- Calculate a local price estimate.
- Compose stock and signed option delta.
- Distinguish sensitivity from probability.
Read the units first: option price change per dollar of underlying movement. Multiply by the contract size and reverse the sign for a short position. The covered-call example then combines stock and option exposure, showing why the net changes as the stock moves.
Reading one: the price sensitivity
The October 17 $72.50 call on UBER carries a delta of 0.331 with the stock at $68.40.
UBER goes to $69.40 and the option goes from $1.53 to about $1.86. Roughly 33 cents on the dollar, so $33 per contract.
It is only approximate, and it is approximate in one direction. The real move was 35 cents, not 33, because delta itself changed as the stock rose. The rate at which delta changes is gamma, and it is the reason this reading is a first-order estimate rather than a formula.
Reading two: share equivalents
This is the reading that changes how you think about a book, and it is the one most retail traders never adopt.
Delta 0.331 on one contract means that contract behaves like 33.1 shares of stock, right now, for small moves. Not 100 shares. Not one contract. Thirty-three shares.
Now compose the covered call. You are long 100 shares, each with a delta of exactly 1.00, and short one call at 0.331.
- Shares: +100
- Short call: -33.1
- Net: 66.9 share-equivalents
So the covered call you thought was a 100-share position is a 67-share position. It rises and falls about two thirds as fast as the stock. That is precisely what you sold: a third of your directional exposure, for $153.
Everything about position sizing gets clearer in this unit. Adding up share equivalents across a whole book is the only way to answer "how long am I, actually".
Reading three: probability, approximately
Delta is close to the probability that the option finishes in the money. Close, not equal.
The true model probability for this contract is 0.293. Delta says 0.331. That is 3.8 percentage points of overstatement, and the gap is systematic rather than random. The next page works through where it comes from and when it gets big enough to matter.
For a rule of thumb it is fine. A 0.30 delta short call is roughly a 70 percent chance of expiring worthless. Just do not build a spreadsheet on it.
Delta across the chain
| Strike | Delta | Share equivalents | Modeled odds of finishing ITM |
|---|---|---|---|
| $70 | 0.455 | 45.5 | 41.2% |
| $72.50 | 0.331 | 33.1 | 29.3% |
| $75 | 0.227 | 22.7 | 19.5% |
| $80 | 0.089 | 8.9 | 7.3% |
Deep in the money, delta approaches 1.00 and the option tracks the stock nearly dollar for dollar. Far out of the money it approaches zero and the contract barely notices the stock at all. At the money it sits near 0.50, and that is where it changes fastest.
Signs, and the thing that trips everyone
Long calls are positive delta. Long puts are negative. Short positions flip both: a short call is negative delta, which is the position most people on this site actually hold.
The mistake worth naming: a short put has positive delta. You want the stock to go up. That feels wrong to anyone who associates puts with bearishness, and it is the single most common sign error in a beginner's position sheet. Every Greek flips when you sell rather than buy, and that page is worth reading before you total up a book.
What delta will not tell you
Delta describes a small move near current inputs, not a fixed hedge ratio for a large gap. It also does not summarize volatility or time exposure. Recalculate after substantial price changes and examine the other Greeks before extrapolating a loss.
Anything about volatility, anything about time, and nothing at all about the size of the move. A 0.331 delta says the option gains 33 cents on the first dollar. It says nothing about what happens on a nine dollar gap, which is the move that decides whether the position was sized correctly.
Check your understanding
Why does a covered call's 66.9-share delta not cap its downside at that amount?
Show the explanation
It is a local snapshot. As the stock falls and the call moves farther out of the money, its offsetting delta shrinks. The combined holding can approach the full 100-share downside exposure.
Common questions
What does a delta of 0.30 mean?
For a long call, 0.30 means an approximately $0.30 per-share price increase for a small $1 stock rise, other inputs fixed, or about 30 share-equivalents per standard contract. Probability is a separate, model-dependent approximation.
What is the delta of a covered call?
The shares minus the short call. Long 100 shares at delta 1.00 each against a short 0.331 delta call gives 66.9 share-equivalents, so the position moves about two thirds as fast as the stock.
Is a short put positive or negative delta?
Positive. You profit when the stock rises, because the put you sold loses value. This catches people out constantly, since puts feel bearish and selling one is a bullish position.
Does delta stay the same?
No. It changes as the stock moves, as time passes and as implied volatility shifts. The rate of change against the stock is gamma, and on a near-dated at-the-money option it is large enough that delta from an hour ago is already stale.
Sources
Rules and thresholds above were checked against these documents on August 4, 2026. Exchange and broker rules change. Confirm anything you are about to act on with your own broker.
Keep reading
Do the math on your own trade
Every price in this article is an illustrative worked example, not a quote. Read The Greeks for the rest of the series, and the disclaimer before you act on any of it. Selling options carries real risk of loss, and the loss can be far larger than the premium you collected.