The 20-delta shortcut: what it estimates and what it does not
The 20-delta shortcut is a rough call-exposure guide. It is not a forecast of assignment or a guarantee of whole-position profit.
By OptionsKing. Publisher and editorial methods.
What you will learn
By the end of this lesson, you should be able to:
- Compare delta with modeled finish odds.
- Calculate repeated exposure under independence.
- Separate keep-credit odds from total profit.
Compare call delta with the model's separate finish probability on the same chain. Then repeat the probability calculation across multiple hypothetical cycles. Keep the distribution, independence assumption and distinction between option profit and stock-plus-option profit visible throughout.
Checking it
The model's actual probability of finishing in the money is N(d2), a different term from the delta N(d1) sitting next to it. Both come out of Black and Scholes (1973), Journal of Political Economy 81(3), 637 to 654. Here they are on the same chain.
| Strike | Delta | Delta says you keep | Model says you keep | Shortcut error |
|---|---|---|---|---|
| $60 | 0.431 | 56.9% | 60.7% | 3.8 points |
| $62 | 0.306 | 69.4% | 72.7% | 3.4 points |
| $63 | 0.252 | 74.8% | 77.9% | 3.0 points |
| $64 | 0.203 | 79.7% | 82.3% | 2.7 points |
| $65 | 0.162 | 83.8% | 86.1% | 2.3 points |
| $66 | 0.127 | 87.3% | 89.3% | 1.9 points |
| $68 | 0.074 | 92.6% | 93.9% | 1.3 points |
On these non-dividend-paying model calls, delta exceeds risk-neutral ITM probability by one to four percentage points. This does not establish a conservative shortcut for puts, dividend-adjusted calls, or real-world assignment.
On the strike we care about, 0.20 delta implies 80 percent and the true figure is 82.3 percent. A 2.7 point miss, in the direction that costs you nothing. Round the shortcut and it is right to within a rounding error.
Where the gap comes from
d1 and d2 are separated by one term: the volatility times the square root of the time remaining. On this contract that is 0.28 times the square root of 45 over 365, which is 0.098.
So the gap widens with volatility and with time. A 0.20 delta call on a 70 percent volatility biotech nine months out has a much larger gap than three points, and a 0.20 delta weekly has almost none. If you sell 30 to 60 day contracts on 20 to 40 percent names, the shortcut holds. Take it to LEAPS and stop trusting it.
The error that actually costs money
The repeated-cycle calculation assumes unchanged probabilities and independent outcomes. Actual cycles share market regimes and changing inputs. Use the calculation to understand repeated exposure, not to forecast a particular year's assignment count.
Not the three points. This one.
82 percent is a per-trade number, and you do not place one trade.
Roll this position eight times a year, which is what a 45-day cycle gets you, and the chance of going the whole year without a single assignment is 0.823 to the eighth power. That is 21 percent. Four years out of five, the seller with an 82 percent win rate gets assigned at least once, and the expected count is 1.4 assignments a year.
Now do the same to the touch number. A 35.3 percent touch rate per cycle means the chance of getting through a year without the stock ever trading through your strike is 0.647 to the eighth, which is 3 percent. Ninety-seven times out of a hundred, a seller running this position for a year watches it go against them at least once.
Nobody is surprised by the three-point discrepancy in the table. Everybody is surprised by these two.
Two more things delta is not
It is not a forecast. Delta is derived from the option's own price, so reading probability off it is asking the market what the market thinks. When implied volatility is 28 because everyone is braced for something, delta already contains that fear, and it will read the same whether the fear was justified or not.
It is not the probability of a profitable trade. Delta approximates the chance of finishing in the money, so one minus delta is roughly the chance of finishing out of the money. Those differ, because a covered call with the stock down $4 has kept its credit and lost money. Delta has an opinion about the option. It has none about your position.
Cluster B takes the same contract apart from the Greeks side and lands in the same place from a different direction.
The version worth memorising
- Delta as a percentage is your assignment odds, plus a couple of points of slack in your favour. Good enough for choosing a strike at the screen.
- Double it for the odds of a scare. 0.20 delta means a 40 percent chance the stock touches your strike, and the true figure here is 35.3 percent.
- Raise it to the power of your cycles per year before you tell anybody your strategy wins 80 percent of the time.
Check your understanding
Does an 82.3 percent per-cycle keep rate imply an 82.3 percent chance of an assignment-free year?
Show the explanation
No. Under eight identical independent cycles, multiply 0.823 by itself eight times, giving about 21 percent. Real cycles need not satisfy those assumptions.
Common questions
Does 0.20 delta really mean an 80 percent chance of keeping the premium?
It is a rough call-model shortcut. This example has 0.203 delta and 82.3% modeled OTM probability. That is not a guaranteed full-credit rate, assignment rate, or combined-position win rate.
Why is delta not exactly the probability of finishing in the money?
For a non-dividend-paying European call, delta uses N(d1) and risk-neutral ITM probability uses N(d2). Longer time and higher volatility can widen the difference; neither expression is automatically a real-world frequency.
If I sell 0.20 delta calls all year, how often do I get assigned?
Treating the example's eight cycles as identical and independent gives about 1.4 ITM endings on average and roughly 21% probability of none. Actual assignments and dependence can differ.
Is a lower delta always a safer strike?
Safer from assignment, yes, and it pays proportionately less. The $68 strike keeps its credit 93.9 percent of the time for $18, against 82.3 percent for $62 at the $64 strike. You are buying a higher win rate with income, at roughly a fair price.
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 Screening and probability 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.