What is Delta?

Delta is one of four main measures of risk for options, and measures the rate of change of an options price given a $1 change in the underlying assets price. In simpler terms, Delta shows how much an options price will increase or decrease if the underlying asset changes by $1.

Delta signifies directional risk. Positive delta equates to being long, and negative delta equates to being short. This can be seen in the relationship between delta and different options. Delta ranges from 0 to 1.0 for long calls and short puts, and from 0 to -1.0 for long puts and short calls. This can be slightly confusing, so I'll make it clearer with an example in a bit.

A high delta means a larger change in the option price in relation to the underlying asset’s price movement. In other words, the higher the delta, the higher the magnitude of change in an options price when the underlying assets price changes.

For example, if a long call option has a delta of 0.50, a $1 increase in the underlying will increase the price of the option by approx. 0.50, if no other factors change.

This is an approximation because Delta is not constant, whenever the underlying asset changes, so does delta. This relation is represented by Gamma, another measure of risk. Gamma measures the rate of change of Delta based on movement in the underlying. I will discuss Gamma in depth in a later article.

Additionally, Delta also changes as Implied Volatility changes. This is why a $1 move in the underlying does not mean the option price will change the exact delta amount, as other factors (IV, Gamma) will not remain constant, and when these factors change, so does delta,

Earlier on, I said Delta represents directional risk. This means if you have a long position, for example a long call, and have a delta of 0.50, and the underlying increases by $1, your option price will increase by approx. 0.50. On the other hand if the underlying decreases by $1, your option price will decrease by approx 0.50.

There are many ways to utilize delta for portfolio management. Because delta represents directional risk, we can use it for hedging, limiting potential losses. Delta neutral or 0 Delta positions can also be opened so price movements in the underlying cause no change to the position, allowing profit from volatility or time decay. Both of these strategies will be discussed in future articles.

Delta also varies on the relationship between an options strike and the underlying assets price. Generally, the further in the money an option is, the higher the delta is, and the further out the money an option is, the lower the delta. This means, as an option approaches being In the money, the delta approaches 1.0 for long calls and short puts, and -1.0 for short calls and long puts.

If an option is near the money or at the money, the delta will be close to 0.5 (for long calls and short puts) and -0.5 (for short calls and long puts).

Delta also has a rough correlation to the probability of an option being In the money. For example, if I have a short call, and the delta is -0.25, there is an approx. 25% chance the option will be in the money, meaning an approx. 75% chance it is out of the money.

When selling options, the goal is to have the option expire OTM, so it is worthless, and the seller can keep the premium. This means selling ITM or ATM options comes with more risk, but with potential for higher profit.

There is greater risk when selling ITM/ATM options because the underlying asset has to move a certain amount for the option to be OTM, which is ideal. But I digress. I will make an article in the future about selling options, where I will discuss this concept in greater detail.

Key Points: The main takeaways from this article are that:

Delta measures the rate of change of an options price given a $1 change in the underlying assets price. Delta signifies directional risk.

Positive delta equates to being long, and negative delta equates to being short.

The further OTM an option is, the lower the delta is, and the closer ITM an option is, the higher the delta gets, approaching 1 or -1, depending on the position.

Thank you for reading, and I hope you have a better understanding of Delta.