Is delta the same as probability of assignment?

No. Delta is the option's hedge ratio — how much its price moves for a $1 move in the stock. It happens to sit close to the risk-neutral probability of finishing in-the-money, which is why it gets used as a stand-in, but the two are different quantities. For a put, |delta| is N(-d1) while the probability of finishing in-the-money is N(-d2), and N(-d2) is always the larger of the two. Delta understates your real assignment odds, every time.

How big is the difference between delta and assignment probability?

It depends almost entirely on volatility and time. On a 30% implied-vol stock at 30 days to expiry, a 10-delta put has roughly an 11.6% chance of finishing in-the-money — a gap of about 1.6 percentage points, small enough to ignore. On a 136% implied-vol name at the same delta and tenor, that same 10-delta put is closer to 19%. The gap scales with volatility multiplied by the square root of time, so it grows on exactly the contracts that pay the most premium.

Why do brokers show delta instead of assignment probability?

Delta is a required output of every option pricing model, so it is already on the screen and costs nothing to display. It is also useful for its actual purpose, which is position sizing and hedging. Some platforms do show a separate probability-of-ITM figure, but delta is the number that appears everywhere, so it became the default proxy through availability rather than accuracy.

Is levelbox's chance of assignment finished?

No, but it is better than it was. We compute it from the contract's own implied volatility, and now apply a skew correction that turns a vanilla option price into a true digital — the piece that was missing before, which biased the number high and overstated the chance of assignment on steeply skewed names. Where a chain is too thin to measure the skew reliably, we fall back to the uncorrected figure and flag it in the app as possibly overstated. Where the chain quotes both calls and puts we back the forward out of put-call parity, which handles dividends and borrow cost; otherwise we assume neither, which is a small understatement. We still only model assignment at expiry, not early assignment. And the skew correction itself rests on the closed-form maths, not yet on a backtest — that would need stored historical option chains, which we do not keep.

Should I stop using delta to pick strikes?

No — delta is still a perfectly good way to select a strike consistently across names, and it is what most option chains are sorted by. Keep using it to pick the strike. Just stop reading the number itself as a probability, and check the actual assignment probability separately, because on a high-volatility name the two can differ by 10 percentage points or more.

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General Option Selling

Delta Is Not Your Chance of Assignment

22 July 2026 · 9 min read

Delta is not your probability of assignment. It is close to it on calm, low-volatility stocks — usually within a percentage point or two — and meaningfully wrong on volatile ones, always in the same direction: delta understates the real chance of being assigned. A 10-delta put on a quiet stock finishes in-the-money about 11.6% of the time. The same 10-delta put on a name trading at 136% implied volatility finishes in-the-money closer to 19% of the time.

If you sell puts by picking a delta, that gap is worth understanding, because it is largest on exactly the contracts that look most attractive.

What delta actually measures

Delta is a hedge ratio. It answers the question: if the underlying moves one dollar, how much does this option's price move? (The other Greeks each answer a different one.) A put with a delta of −0.10 gains roughly $0.10 for every dollar the stock falls. That is its job, and it does it well.

It is not a probability of anything. It became a probability proxy because it is already sitting on every option chain, free, and for the moderate-volatility, short-dated contracts most people trade, it lands close enough to the real number that nobody noticed the difference mattered.

The convention is so entrenched that "I sell 10-deltas" and "I take a 10% chance of assignment" are used interchangeably in almost every options forum you will read. Those are not the same statement.

Why the two numbers differ

In the Black-Scholes framework, two closely related quantities fall out of the same equation:

|Delta| for a put is N(−d₁)
The probability the put finishes in-the-money is N(−d₂)

And d₂ = d₁ − σ√T, where σ is implied volatility and T is time to expiry in years.

Because d₂ is always smaller than d₁, N(−d₂) is always larger than N(−d₁). The two are separated by roughly:

gap ≈ φ(d₁) · σ · √T

Everything you need to know is in that expression. The gap grows with volatility and with the square root of time. It has nothing to do with the direction of the stock, your thesis, or the quality of the company. It is pure arithmetic, and it always runs the same way — against the seller.

How large the gap gets

Here is the difference between |delta| and the true risk-neutral probability, in percentage points, for a 10-delta put:

	σ=15%	σ=30%	σ=45%	σ=60%	σ=80%	σ=136%
7 DTE	+0.4	+0.7	+1.1	+1.5	+2.1	+3.7
30 DTE	+0.8	+1.6	+2.5	+3.4	+4.6	+8.6
90 DTE	+1.4	+2.9	+4.5	+6.3	+8.8	+17.2

Read the top-left corner and the convention looks fine. A 10-delta put on a 15%-vol utility at a week to expiry really is about a 10.4% chance. Nobody was ever hurt by that approximation.

Read the bottom-right corner and the convention falls apart. At 90 days on a high-volatility name, "10 delta" can mean a 27% chance of finishing in-the-money. That is not a rounding error. That is a different trade from the one you thought you were putting on.

The problem: the error is largest where the premium is richest

This is the part that matters practically, and it is not a coincidence.

Implied volatility is what you get paid for. High-IV names offer fat premium precisely because the market expects large moves. So when you scan a chain for the best yield on capital, you are steering directly toward the names where the delta-as-probability shortcut breaks down worst.

The approximation holds up fine on the names nobody wants. It breaks down on the ones everyone does. A screener that ranks by premium and reports risk as delta is, structurally, understating risk more on the candidates it ranks highest.

A real example

Our own screener had this bug until last week, so this is not hypothetical.

A recently-listed semiconductor ADR was showing in our AI Buildout theme at 136% implied volatility. The screener picked the strike closest to 0.10 delta and displayed, as it had always done, a 10% chance of assignment.

The actual risk-neutral probability that put finished in-the-money was 20.5%.

Not 10%. Not 12%. Double. And it was the highest-volatility, highest-premium name on the board — exactly the one a yield-sorted screen would put in front of you first, and exactly the one our risk number was furthest from the truth on.

At other strikes on the same name the pattern held: 14% delta was really 26%, 21% delta was really 35%. On leveraged index ETFs in the same run, 30-delta puts came out at 38%.

We were not slightly wrong on the safe names. We were badly wrong on the risky ones.

What we show now

The screener computes the risk-neutral probability the put finishes in the money — the digital N(−d₂), including the skew and forward corrections described below — from the strike, the time to expiry, and the contract's own implied volatility. It displays that as chance of assignment. Delta is still shown next to it, as a percentage, so you can see both numbers and the gap between them on every card.

Worth stating plainly: it is the risk-neutral probability, not a forecast. It is what the option market's own prices imply, given no view of ours about where the stock is going. We deliberately publish the market's number rather than an in-house estimate. We built an adjusted estimate too — one that corrected for expected drift and blended implied with realised volatility — measured it against actual outcomes, found it worse calibrated than the plain market number, and did not ship it. That is the whole reason to backtest a model before displaying it.

What we fixed, and what is still wrong

The section you are reading used to describe a bias we knew about and had not corrected. We have corrected it now. The honest move is to show both — the gap, and the fix — rather than quietly edit the gap away.

The skew correction now ships. We price off the contract's own implied volatility, so we sit on the smile at that strike. The step we used to skip was the second one: a vanilla put price is not a digital, because implied volatility changes with strike. The true probability is

P(S_T < K) = N(−d₂) + e^(rT) · vega · ∂σ/∂K

Equity puts skew downward — lower strikes carry higher implied vols — so ∂σ/∂K is negative, the correction term is negative, and the uncorrected number was biased high: it overstated the chance of assignment, by a point or two on a 30-vol name and considerably more where the skew is steep. We now measure the local slope off the chain we already fetch and apply that term. On a recent run it moved 1,082 of 1,105 candidates.

The other 23 are the honest part. On a thin chain there are too few usable strike prices to measure a trustworthy slope, and a bad slope applied confidently to a risk number is worse than no slope at all. So on those names we fall back to the uncorrected figure and mark it in the app — a small flag that says the number may be overstated and the true chance is a little lower.

Dividends and borrow cost. For a dividend payer the true forward is lower than a naive carry-forward, which makes assignment slightly more likely than a no-dividend model reports — a bias in the opposite direction to the skew one. Where the chain quotes both a call and a put at the same strike, we now back the forward out of put-call parity, which captures the dividend and the borrow cost together without needing a separate dividend feed. Where it does not, we fall back to assuming neither, and the small understatement remains.

It only models assignment at expiry. Early assignment is a real feature of American options and we do not model it. In practice it is rare on an out-of-the-money put, and the research says holders under-exercise rather than over-exercise, so the omission probably works in the seller's favour. Probably is not certainly.

The skew correction rests on the maths, not yet on a backtest. We can show N(−d₂) beats delta against real historical outcomes, because that only needs past prices. We cannot yet show the same for the skew term, because validating it needs stored historical option chains and we do not keep those. The correction is justified by the closed-form relationship above — which we checked against a direct numerical computation — not by a calibration test. That distinction matters. Blurring it here would be exactly the kind of overclaim this section exists to avoid.

None of this is something we would rather have hidden. Each item is on our backlog with the reason it is not done yet, and this section keeps getting shorter.

Update, 22 July 2026: the skew correction described above shipped the same day this post went up. An earlier version of this section said the number was biased low because we ignored the smile — wrong on both counts: we were already on the smile, and the missing term biased the number high, not low. We corrected the direction, then built the fix. Getting the direction backwards in a section about honesty was worse than getting it backwards anywhere else, which is why we did not leave it sitting on the backlog.

What to do with this

Nothing dramatic. Delta remains a perfectly sensible way to choose a strike — it is consistent across names, and it is what every chain is sorted by. Keep using it for that.

The change is in how you read it:

On a low-vol, short-dated put, delta and assignment probability are close enough to treat as one number.
On a high-IV or longer-dated put, they are not. Look up the actual probability before deciding you are comfortable with the risk.
When a contract looks unusually well-paid, assume the gap is wide, because the same volatility driving the premium is driving the gap.
And a single-contract probability is not a monthly one. Sell the same 0.10-delta strike every few days and the odds of being assigned at least once compound into a very different number from the one on the chain.

And the framing that matters most for a wheel seller: if you sold the cash-secured put because you would genuinely be happy owning the stock at that strike, a higher assignment probability is not a worse trade. It is the plan, working more often than you expected. The problem is only ever assignment on a name you did not actually want — which is a question about the company, not about the Greeks.

Analytical and educational only — not investment advice. The probabilities described here are model outputs under standard Black-Scholes assumptions, not predictions. Options carry risk of substantial loss, including having stock assigned to you at a price well above the market.

Common questions

Is delta the same as probability of assignment?: No. Delta is the option's hedge ratio — how much its price moves for a $1 move in the stock. It happens to sit close to the risk-neutral probability of finishing in-the-money, which is why it gets used as a stand-in, but the two are different quantities. For a put, |delta| is N(-d1) while the probability of finishing in-the-money is N(-d2), and N(-d2) is always the larger of the two. Delta understates your real assignment odds, every time.
How big is the difference between delta and assignment probability?: It depends almost entirely on volatility and time. On a 30% implied-vol stock at 30 days to expiry, a 10-delta put has roughly an 11.6% chance of finishing in-the-money — a gap of about 1.6 percentage points, small enough to ignore. On a 136% implied-vol name at the same delta and tenor, that same 10-delta put is closer to 19%. The gap scales with volatility multiplied by the square root of time, so it grows on exactly the contracts that pay the most premium.
Why do brokers show delta instead of assignment probability?: Delta is a required output of every option pricing model, so it is already on the screen and costs nothing to display. It is also useful for its actual purpose, which is position sizing and hedging. Some platforms do show a separate probability-of-ITM figure, but delta is the number that appears everywhere, so it became the default proxy through availability rather than accuracy.
Is levelbox's chance of assignment finished?: No, but it is better than it was. We compute it from the contract's own implied volatility, and now apply a skew correction that turns a vanilla option price into a true digital — the piece that was missing before, which biased the number high and overstated the chance of assignment on steeply skewed names. Where a chain is too thin to measure the skew reliably, we fall back to the uncorrected figure and flag it in the app as possibly overstated. Where the chain quotes both calls and puts we back the forward out of put-call parity, which handles dividends and borrow cost; otherwise we assume neither, which is a small understatement. We still only model assignment at expiry, not early assignment. And the skew correction itself rests on the closed-form maths, not yet on a backtest — that would need stored historical option chains, which we do not keep.
Should I stop using delta to pick strikes?: No — delta is still a perfectly good way to select a strike consistently across names, and it is what most option chains are sorted by. Keep using it to pick the strike. Just stop reading the number itself as a probability, and check the actual assignment probability separately, because on a high-volatility name the two can differ by 10 percentage points or more.