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Standard deviation move

A move scaled in units of implied volatility; one standard deviation contains about 68% of outcomes under the model's assumptions, two about 95%.

Options pricing describes the future as a distribution, and the standard deviation is its width. Strike selection by standard deviation — sell the one-sigma strike, buy the two-sigma wing — is the standard way to compare trades across underlyings of different prices and volatilities.

The percentages come from a normal distribution of returns, and real markets have fatter tails. Two-sigma events occur meaningfully more often than 5% of the time, and the discrepancy is concentrated on the downside, which is precisely where short-premium traders place their risk.

Example: XYZ at $50 with 30-day implied volatility of 25%. One standard deviation is $3.58, two is $7.16. The 16-delta put near $46.40 is approximately the one-sigma strike, which is why selling 16-delta options is such a common default.

Related: expected-move, delta-as-probability, lognormal-assumption, probability-itm

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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