Probability of assignment calculator
The chance a short put or call finishes in the money, beside the delta it is usually mistaken for.
Dollars per share
Dollars per share
Of this option, %
Calendar days
Chance of assignment
17.2%
in the money at expiration
Chance it expires worthless
82.8%
the full credit kept
Delta
0.15
often read as the chance
Chance of touching
34.3%
the strike, before expiry — rule of thumb
Expected move
$10.53
one standard deviation, 45 days
Strike distance
0.95
standard deviations from the price
How each figure is worked out
- Chance of assignment is N(−d₂) for a put and N(d₂) for a call, where d₂ = [ln(price ÷ strike) − σ²t ÷ 2] ÷ σ√t, σ is the implied volatility and t is days ÷ 365. It is the lognormal model an option chain’s greeks come from, with the interest rate taken as zero — over 45 days a 4% rate moves the answer by a small fraction of a point.
- Delta is N(−d₁) for a put and N(d₁) for a call. It is often quoted as the probability of assignment, and it is close but not the same: for an out-of-the-money put, delta runs a little below the chance of finishing in the money, and for an out-of-the-money call a little above it.
- Chance of touching is about twice the chance of finishing in the money — a rule of thumb, not a model. It matters more than assignment for anybody using a stop, which fires on the way rather than at the end.
- Expected move is price × σ × √t: one standard deviation over the period. Strike distance is how many of those separate the strike from the price.
Which implied volatility to use
The implied volatility of the option you are selling, as your broker’s chain shows it — not the stock’s overall IV or its IV rank. Out-of-the-money puts usually carry a higher implied volatility than options at the money, and using the lower figure understates the chance of assignment.
Assignment before expiration
US equity options are American-style, so a short option can be assigned on any day it is in the money. Early assignment is uncommon until an option is deep in the money with little time value left, or, for a short call, just before an ex-dividend date. The figures above are about expiration.
What it leaves out
A model, not a forecast. It assumes volatility stays at the figure you typed and that prices move without jumps. Stocks gap on news, which is why PutWatch’s screen rejects any candidate with an earnings date inside the trade. Dividends and interest are ignored.
Other calculators
Cash-secured put — Premium, capital required, breakeven and annualized return on one put.
Short strangle — Both breakevens, estimated buying power and the return on it.
PutWatch runs this arithmetic on several hundred names every weekday and publishes a top ten from them — the daily screen.
Research and education, not investment advice. Selling options can lose more than the premium received. See the disclaimer.