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Delta neutral

A position whose net delta is around zero, so small moves in the underlying have no first-order effect on its value.

Neutrality is a snapshot, not a state. Any position with gamma stops being delta neutral as soon as the underlying moves, which is why the phrase always implies maintenance: you are neutral now, and you will not be in an hour.

Being delta neutral does not mean being risk free. The position still carries vega, theta and the second-order Greeks, and those are usually why it was put on. Neutrality just removes the directional bet so the other exposures can be traded cleanly.

Example: long ten XYZ $50 straddles with XYZ at $50.00. Net delta is roughly zero because the calls and puts offset. XYZ moves to $51 and the calls gain delta faster than the puts lose it, leaving the position long about 200 share-equivalents. Neutral lasted one dollar.

Related: delta-hedging, position-greeks, gamma, gamma-scalping

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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