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Charm

The rate at which delta changes as time passes, holding price constant; it pulls out-of-the-money deltas toward zero and in-the-money deltas toward one.

Charm is the second-order Greek that describes decay of direction rather than decay of value. An out-of-the-money option loses delta simply because there is less time for it to come into the money; an in-the-money option gains delta for the same reason.

Hedgers notice it on Fridays and into opex. A book that is delta flat on Thursday can be meaningfully directional by Friday afternoon without the underlying having moved at all, which creates a predictable rebalancing flow into expiration.

Example: XYZ at $50 and you hold the $55 call at 0.20 delta with five days to go. Price does not move overnight. The next morning the delta is 0.17. Charm removed 0.03 of delta, or three share-equivalents per contract, for free.

Related: second-order-greeks, vanna, delta, opex-effects

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.

Educational only, not advice. Spotted an error? Post in Site Feedback.