Options Delta

What delta measures

Delta is the rate of change of an option's price with respect to the underlying. Calls have positive delta and puts have negative delta.

It also approximates the option's equivalent share exposure, which is why traders talk about a position being 50 deltas.

Why it is not a true probability

Delta rises toward 1 for deep in-the-money calls and toward 0 far out of the money, but its relationship to the chance of expiring in the money is approximate and changes with volatility and time.

• At short expirations delta can change very quickly.
• High implied volatility spreads delta across strikes.
• The probability proxy ignores drift and the shape of the distribution.

FAQ

Is delta the probability of expiring in the money?

It is often used as a rough proxy, but the relationship is not exact and changes with volatility and time.

Can delta exceed 1?

For most single options delta stays between 0 and 1 for calls and -1 and 0 for puts; deep in-the-money options approach the boundary.

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