What is assignment probability for short options?
Delta is not assignment probability. Delta is an option-price sensitivity to the underlying, sometimes used as a rough proxy for the risk-neutral probability that the option finishes in-the-money at expiration. Actual assignment additionally depends on the entire price path, remaining extrinsic value, dividend timing, borrow conditions, and the option holder's exercise decisions. On OptionIncomeTools, four different probabilities are surfaced separately: (1) market-implied finish-ITM proxy from |delta| or Black-Scholes N(d2); (2) model-estimated physical probability from real-world return distributions; (3) probability of touching or breaching the strike before expiration (path-dependent); (4) probability of assignment at or before expiration, which is not directly modeled for American-style equity options and is only warned about near ex-dividend dates for deep-ITM short calls.
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.
Related glossary entries
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Educational only — not investment advice. See the disclaimer and methodology. Material methodology corrections are logged at corrections.