Delta Options

Option delta is one of the most popular and widely referenced option Greeks. 

Option Greeks quantify the variables that influence an option’s constantly changing price. "The Greeks" reflect how external factors impact an option’s value as market conditions change.

The Greeks represent different factors determining why options prices move relative to the underlying asset’s price. They measure an option's sensitivity to ever-changing external factors. The Greeks are dynamic and will fluctuate as price and information change.

There are five main Greeks, and each relates to either the option’s intrinsic or extrinsic value.

Delta and gamma depend on the option’s spot and strike price and are therefore derived from intrinsic value. Theta, vega, and rho are determined by time to maturity, volatility, and interest rates, all of which are components of extrinsic value.

What is delta in options? 

Option delta simply tells you how an option contract will react to price changes in different market scenarios.

Delta is the amount an options price should change based on a $1 move in the underlying stock.

Delta can be positive or negative. Call options have a positive delta between 0 and 1, while put options have a negative delta between 0 and -1. 

Delta as directional exposure

Delta represents the option’s directional exposure. A call option’s positive delta reflects the positive directional exposure to up moves in the underlying stock. 

All else equal, the higher the call option delta, the greater the impact of a positive move in the underlying security. 

For example, a stock trading at $100 has a $110 call option expiring in 60 days with a delta of 0.30 that costs $2.00. All else equal, if the underlying stock moves up to $101, the option should now be worth $2.30.

Why does delta change?

As expiration approaches, the delta of in-the-money options increases, and the option starts to trade and react closer to how the underlying stock would trade.

Out-of-the-money contracts will see their delta value decrease dramatically as expiration gets closer. As the underlying security moves further away from the strike price, the possibility of becoming in-the-money over the remaining life of the contract decreases.

Stated differently, out-of-the-money call options are less likely to move in-the-money as they get closer to expiration. Therefore, delta’s value decreases because there is a lower probability that the underlying security will be above the strike price at expiration.

As implied volatility increases, the delta of out-of-the-money options increases because market participants anticipate that the stock price will move more than expected.

As delta increases, the probability of out-of-the-money options moving into the money increases.

Call option delta example

If the stock goes up by $1 and you have an option contract with a delta of 0.5, the option price will increase by 50 cents, or $50 per contract. All else equal, if you have a delta of 0.3, then the $1 stock move should cause the options contract to increase by 0.3, or $30 per contract.

Delta relates an option’s price to a $1 move in the underlying security.

Delta as share equivalency

Delta represents the number of relative shares you would own by purchasing an option.

For example, buying a call option with a 0.50 delta is roughly equivalent to owning 50 shares of stock (and vice versa with put options as a -0.50 delta is like shorting 50 shares).

Thinking of delta as the equivalent number of shares owned helps simplify the concept of how delta in options pricing works.

Using the previous example of a $110 call option expiring in 60 days with a delta of 0.30 worth $2.00, if the underlying stock moves to $101, the option should now be worth $2.30. 

Owning 100 shares of the stock would have realized a $100 gain. The 0.30 delta option realized approximately 30 shares worth of value, or $30. 

So, a 0.30 delta call option is roughly equivalent to holding 30 shares.

An option with a delta of exactly 1 would be equivalent to holding 100 shares of stock.

Using delta for probabilities

Delta can also be used to estimate the probability a stock will be in-the-money at expiration. So, delta is often used as a substitute for the ITM probability. 

While delta is not as accurate as statistical probabilities, it is close enough that you can use it to make decisions about which strike price to select when creating and customizing different options strategies.

If a call option has a delta of 0.3, that 0.3 gives a reasonable approximation that there is a 30% chance the option will be in-the-money at expiration and a 70% chance the option is out-of-the-money at expiration. So, delta creates a good benchmark for probability estimates.

When selling options, delta provides a quick check or approximate representation of an option's probability of success.

A .30 delta has roughly a 30% chance of expiring in-the-money (or a 70% chance of expiring out-of-the-money).

Selling a .30 delta call option equates to a roughly 70% chance of success and a 30% chance of failure. 

Note that delta is used to estimate moneyness probabilities at expiration. An option that expires out-of-the-money may be in-the-money at times during the position's duration and vice versa.

One standard deviation equivalent to 0.16 delta

One standard deviation has an ~84% probability of expiring OTM. If we use delta as an approximate for probabilities, then the 0.16 delta is equivalent to one standard deviation. Assuming the probability distribution implied by the market is correct, then the relative distance the 0.16 delta option is from the spot price represents approximately 1 standard deviation.

We can see in the image below that an iron condor has a 68% chance of expiring OTM. This is because an iron condor has two short options: a short call and a short put. If both are sold at the 0.16 delta, or 1 std dev, than the normal distribution of probability for an iron condor expiring with a max profit is 68%.

It is important to note that standard deviation represents the historical movement of the stock's price, whereas Delta is implied by the market.

Delta when selling options

With option selling, you have to reverse your thinking regarding delta.

If you sell a call option, you have a short call option position with a delta of 0.3. This position gives you bearish exposure to the underlying security roughly equivalent to 30 shares of stock.

What is delta hedging?

Delta hedging is a neutral trading strategy used to generate income while staying nondirectional.

Because delta is a measure of the responsiveness of an option position to the underlying security, traders use delta neutral trading as a way to generate income while staying nondirectional or balanced. In practice, staying delta-neutral all the time is nearly impossible without continuous, dynamic re-positioning.

Next steps

Delta plays a significant role in virtually all options trading strategies. While you cannot look at just one option Greek when selecting the appropriate strike price for your options strategy, delta is a great place to start. 

Learn about the other options Greeks and how they impact options pricing.