What is assignment probability for short options?
Assignment probability is the model-implied chance that a short option finishes in-the-money at expiration; it is commonly approximated by the absolute value of delta but reflects probability under risk-neutral pricing, not the real-world distribution.
Formula
|Δ| (Black-Scholes-Merton delta absolute value, as a rough proxy)Worked example
A 30-day NVDA $400 short put with delta −0.25 has an approximate 25% probability of finishing in-the-money at expiration, so it has a ~25% probability of assignment.
Common misinterpretation
Conflating "probability of touch" with "probability of finishing in-the-money." Probability of touch during the option's life is typically 2× the at-expiration probability. A 25% finish-ITM short put has a ~50% probability of being ITM at some point during its life, even if it eventually expires OTM.
Limitations
- Black-Scholes-Merton assumes lognormal returns and constant volatility; both fail near earnings or in regime shifts.
- American-style options can be assigned early, which delta does not directly model.
- For deep-in-the-money options, delta exceeds the true probability of finishing ITM because of the dividend-driven early-exercise incentive.
Tools that use this metric
Primary references
- Black & Scholes (1973). "The Pricing of Options and Corporate Liabilities."
- OCC — "Characteristics and Risks of Standardized Options"
References cite the source institution where the underlying definition or rule is published. OptionIncomeTools does not redefine standardized options terms; it ranks and presents data using widely accepted definitions.
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Educational only — not investment advice. See the disclaimer and methodology. Material methodology corrections are logged at corrections.