The Greek letter delta measures the relationship between underlying price changes and option price changes. It can be used as a measure of directional exposure and leverage – not only for single options, but also for option strategies and more complex option positions. This page explains how.

## Delta interpretation

Option delta measures by how much the value (market price or *premium*) of an option changes when the market price of the underlying asset (e.g. a stock) changes by one dollar. For more detailed explanation see the Option Delta Tutorial.

## Call option delta

Call option delta can reach values from zero (far out of the money options) to one (deep in the money options).

At the money options have delta around 0.50. This means that when the underlying stock increases by 1 dollar, the option's market price rises by 50 cents.

## Put option delta

Delta of put options can reach values between negative one (deep in the money puts) and zero (far out of the money puts).

At the money put options have delta around -0.50. When the underlying stock decreases by 1 dollar, the put option's value rises by 50 cents (same as with calls, just inverse).

## Delta of option spreads and combinations

Option delta is additive. Therefore, it is an effective tool for measuring directional exposure not only for a single option, but also for option spreads and more complex option positions – as long as all the options have the same underlying asset (because delta is the ratio of position value change relative to underlying price change).

To calculate total delta of a portfolio of options, add up all deltas of long options (all long calls and long puts) and subtract all deltas of short options (all short calls and short puts).

The result is total (*aggregate*) delta of the position. You can see an example here: Delta Hedging.

## Delta as measure of direction and leverage

If total delta is positive, the position has net long (bullish) exposure to the underlying asset (it makes a profit when price of the underlying asset rises).

If delta is negative, the position is bearish (it profits from decrease in underlying price).

Unlike the delta of a single option, total delta of an option strategy or portfolio of options can be higher than one or lower than minus one. Its value indicates not only the net direction of the exposure (bullish or bearish depending on delta sign), but also the leverage (the absolute size of delta).