# Delta

## Basic Points

- Delta is a first-order Greek which measures the sensitivity of an option's price to movement in the underlying security.
- Delta is the dominant Greek responsible for the price of an option.
- Gamma, vanna, and charm are all second-order Greeks which relate directly to delta. This means that hedging delta also indirectly hedges these higher-order Greeks.
- All options have a delta rating, and this determines how much is made or lost as the underlying security’s price moves.
- Delta has nothing to do with volume, but it is at the core of the mechanics of how options work. For example, delta can be used to approximate the percentage that an option will expire worthless or not: a 20-delta option has about an 80% chance of expiring worthless.
- As another example, a 20-delta option would have about the same reward/risk as holding 20 shares.

## Advanced: Analytic Use Cases

There are a few different key ways to use delta. For one, it shows the percentage stake of an underlying. Instantaneously, and factoring out nonlinear considerations, a +30 delta call will have the same profit and loss from movement in the underlying as being long 30 shares. Likewise, a -30 delta put will instantaneously have the same PnL as being short 30 shares in that underlying. Gamma and other forces, however, cause the amount of deltas to change as movement occurs in the underlying, time, and implied volatility.

Another use for delta is that it can be used to estimate the probability that an option will expire in the money. For example, a +30 delta call will have about a 30% chance of expiring in the money. As another approximation, the probability of touch is roughly double that, meaning that there would be about a 60% chance of an option's underlying security to touch that strike at some point during the life of its contract.

## Expert: Understanding Delta

In general, deltas are a practical way to develop criteria for strategies, such as buying at 50 delta and writing at 25 delta for a debit vertical. Delta also adjusts the range for skew and kurtosis, which are distortions from the usual standard distribution of returns on a bell curve that would be overlooked on a strategy that is simply using fixed strike distances in between spreads rather than delta ranges.

Approximately, an option is near 50 delta right at the money, which is when the underlying is equal to the strike price. In this way, deltas can inform about moneyness, which is the relation of a strike to the money. For example, if we say that an option moved from 30 to 20 delta, then we know that it moved from out of the money to *further* out of the money. And this is without even needing to know whether it was a call or a put. However, lognormal effects (the options market pricing in an unlimited price ceiling and a finite price floor for the underlying) will often cause put deltas near the money to be lower than call deltas.