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Probability of expiring in the money

The modelled chance that an option finishes with intrinsic value at expiration; close to its delta, and what most platforms display.

This is a point-in-time question: where is the underlying on one specific date? It ignores everything that happens in between, which makes it the right measure for a European-style position held to expiry and the wrong one for assessing whether a short strike will be tested.

Platforms compute it from the same model that produces the Greeks, so it inherits every assumption in that model — including the lognormal-assumption and the volatility used as input. Two brokers can show different numbers for the same contract.

Example: XYZ at $50, the 45-day $45 put shows a 22% probability of expiring in the money. That is the modelled chance XYZ closes below $45 on that one Friday, not the chance it visits $45 at any point.

Related: probability-of-touch, delta-as-probability, probability-of-profit, standard-deviation-move

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

How a call option's delta changes with the underlying priceAn S-shaped curve rising from zero, passing through about a half at the strike, and flattening near one.Delta of a call option1.000.5008090110120Out of the moneyAt the moneyIn the money1.00 means it moves one-for-one with the stockdelta ≈ 0.50 at the strikeStrike 100Underlying price
Delta across the range of prices. Delta says how much a call's price moves for a one-point move in the stock. Far below the strike it is near 0 and the option barely reacts; at the strike it is about 0.50; far above it approaches 1 and tracks the stock.

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