# The Many Uses of Option Delta

In an option chain, the delta for a given option strike price can vary from -1 to +1. Call options have a positive delta for option buyers somewhere between 0 and +1. Calls increase in value when the underlying increases in value. Put options have a negative delta somewhere between 0 and -1 as Put option prices have an inverse correlation to the underlying price.

Note that the signs on these relationships are reversed for option sellers who are short contracts. An option seller that is short a Call will have delta exposure between 0 and -1, while a Put seller will have delta exposure between 0 and +1.

### What is Delta?

Option traders already have some familiarity with the set of option Greeks like delta, theta, and gamma. For those unfamiliar, the option Greeks are calculated values that approximate how option price may be expected to change given a change in input such as underlying price move, time decay, and implied volatility.

Perhaps the most popular and versatile of the Greeks is the delta. It tells us how much the price of an option can be expected to change given a \$1 move in the underlying stock. For example, if we’re long a Call option with a delta of 0.60, we might expect the option’s price to increase by \$0.60 if the underlying share price increases by \$1.00.

### How is Delta Calculated?

We can think of delta as the ratio of option price change and share price change.

Mathematically it is stated as

Delta = (O1 – O2) / (S1 – S2) where:

• O1 is the changed price of the option,
• O2 is the initial price of the option,
• S1 is the changed price of the underlying stock, and
• S2 is the initial price of the underlying stock

Fortunately, our option trading platforms can take care of the calculations.  You may have to configure your trading platform to include delta as one of the values shown in the option chain.

### Strike Selection and Probability

Option strike prices can be “in-the-money,” “out-of-the-money,” or “at-the-money.” An option with a strike price close to the underlying price is considered “at-the-money.” An option that is “at-the-money” will have a delta that is very close to 0.50.

Keep in mind that the delta itself changes with a change in the underlying price. We can generally expect the it to increase when an option moves further in-the-money.

One of the more common uses for delta is to help traders select strike prices. If we’re bullish on a stock and would like to buy a Call option rather than the shares, delta can help us select a Call strike price.

Delta can also estimate the probability of a particular share price at expiration. For example, a Call option with a delta of 0.80 suggests that the underlying has an 80% chance of being at or above that strike price at expiration. Or conversely, a 20% chance that the underlying will be below the option strike price at expiration. More rigorous calculations are available for price probability, but delta serves as a handy “back of the envelope” approximation.

We could buy an out-of-the-money Call with a low delta — for example, 0.10. With that low delta, the option’s price would be lower, and we’d have greater leverage. But the tradeoff is a much lower probability of the stock being at the strike price or higher at expiration. We could have a much higher probability trade by buying a deep ITM option with a delta of 0.80. This second alternative would be less speculative as the high delta option will track the underlying much better and be a better proxy for the stock.

## Position Delta

Position delta can estimate the profit or loss on an entire option position relative to \$1 changes in the stock price.  This can be very helpful in assessing the directional risk of an entire position or even an entire portfolio.

Position delta can be estimated as follows:

Position Delta = Option Delta x Number of Contracts Traded x 100

Position delta can tell us the actual dollar amount that we might expect a position or portfolio to change given a certain change in the underlying’s price.  Again, our trading platforms can be configured to do all these calculations.

### Summary

Delta estimates the change in the price of an option based on a change in the underlying stock price. It can give us an approximation for the probability that an option will expire in-the-money.  And lastly, delta can help traders assess directional risk on an entire position or portfolio.