Delta is the Greek of underlying price change.
Delta is defined as the amount that value of an option will change when the underlying security increases by one dollar. For example, stock XYZ is trading at $200 per share. if a call option is selling for $1.55 and has a delta value of 0.30, and the price of the stock increases to $201, then the option will increase to $1.85 based on the change in price.
Some people think of Delta as the rate of change, or price velocity.
If you have studied higher level math or science, you’ll recognize Delta as the variable that usually represents change or difference in values.
Delta values for puts are between 0 and -1.0. When Delta is 0, it means that the strike price is so far out of the money that a one dollar change in the underlying won’t impact the price of the put. When this happens the option will have zero value. An example would be an $80 put for a security trading at $100 the day before expiration. There is virtually no chance of the security going below $80, so whether the underlying trades at $100 or $99, the put price won’t change.
If a put has a Delta value of -1.0, the opposite is true- for every one dollar change in underlying price, the put will move a dollar in the opposite direction. When Delta reaches -1.0, the option will have no time value left, it will be priced solely on its intrinsic value. For example, if you look at the value of a $120 put for a security trading at $100 the day before expiration, the put will likely have a value of $20 ($120-$100). If the stock drops to $99, the option price will go up to $21, a dollar for dollar change in the opposite direction.
Call Delta values are between 0 and 1.0 with the same type of extremes, just positive instead of negative. A Delta value of 0 means price changes of one dollar have no impact on the call price, and a Delta value of 1.0 means the call will move dollar for dollar with the underlying price.
As you can see from the discussion so far, Delta is a signed value- it can be positive or negative. However, for puts it is always negative, and for calls it is always positive. If the price of an underlying security goes up, the price of that security’s puts will go down (negative), and the call will go up (positive). As a result, many people don’t pay much attention to the sign because it is assumed- you always know which sign it is.
Another standard practice is to think of Delta as a value between 0 and 100 and forget about it as a decimal, similar to a percent calculation. You learn early in school that 0.50 equals 50%, and most people discuss Delta the same way. If someone is looking for a 30 Delta option, they are looking for a call with a Delta value of 0.30, or a put with a delta value of -0.30. Going forward, I’ll refer to Delta as a positive value between 0 and 100, even though in option tables, it is always displayed as a decimal. For many reasons that you’ll soon see, it actually is simpler.
Virtually all options that are being traded have Deltas nowhere close to 0 or 100. You’ll notice that the examples I used were for options with strike prices very far from the underlying price with no time left for the underlying price to get to the strike price. Traders trade options when the outcome isn’t yet fully determined with the expectation that the underlying price will end up at expiration at a price that pays off for their strategy.
The ultimate unknowns are options with a strike price equal to the underlying. Generally, these options have Delta values very close to 50. If the underlying price goes up one dollar, the call option will go up 50 cents and the put option will go down 50 cents. As option strike prices go into the money, the Delta value increases above 50. As option strike prices move out of the money, the Delta value decreases below 50.
Another relationship of note is that put and call Delta values add up to 100 for a given strike price. If a call strike has a 30 Delta, the put for the same strike will have a 70 delta. You could do this with positive and negative decimal values: call Delta decimal value minus one equals the put Delta decimal value. (In our above example: 0.30 – 1.0 = -0.70). This is one reason people like to skip the decimals and positive and negative signs.
So far, we have talked about Delta as a way to understand the impact of underlying price movement. While this key attribute of delta is very helpful, it is only the start of the many uses of Delta. Delta can be used as a probability indicator, and to quantify risk.
Delta indicates probability of expiring in the money
Delta has a second use that many people think of as more useful than the first. The Delta of the option is roughly equal to the current probability that the option will expire in the money. For example, a 30 Delta option has a 30% chance to expire in the money. In our earlier examples, we hinted at how a 0 Delta option had virtually no chance to expire in the money, and a 100 Delta option was virtually guaranteed to expire in the money. The Delta value is the market’s way of communicating what the current odds are based on current conditions.
This probability is always based on the current market expectation. As expectations change, the probability will change as well. Expectations change based on price movement, news, time, and a variety of lesser factors.
Probability of underlying touching the strike price
There is another probability indicator from Delta that is lesser known. For out of the money options, the probability that the option will touch the underlying price before expiration is roughly equal to two times Delta. For example, an option with a 35 Delta has a 70% chance of the underlying touching the strike price. Once an option is in the money, you can double the difference of the Delta from 100 to determine the probability it will touch the other way. So, an option with a delta of 60 has an 80% chance that the underlying will touch its strike price: (100-60) x 2 = 80. Either way, this is a probability that many option traders don’t consider. Security prices go up and down, and options that have strike prices close to the underlying price could have the underlying price cross the strike price several times before expiration.
Why does touch probability matter? Mainly, it matters because you need to know what to expect. If you sell a 30 Delta option, you expect that it will expire worthless, because it has a 30% chance of expiring in the money. However, it also has a 60% chance of having the underlying touch the strike price of the option, whether or not it ends in the money or not. If your strategy is buy back the option if/when it goes in the money, you would likely do this 60% of the time, which might not be a profitable strategy. Knowing the odds as you open a position helps you determine a workable strategy for when to react and how to manage what happens as you approach expiration.
Delta as Equivalent Shares
Taking the total Delta can also give an account owner a good idea of what the equivalent number of shares would be for an option contract or portfolio of option contracts. For example, an option contract with a Delta of 30 will move the same as 30 shares of the underlying asset. Adding up contracts can allow a trader to determine how many share equivalents are in a total portfolio. I use this measure every day to determine how I want to adjust the make-up of my option portfolio.
Using Delta value to quantify risk
When you have a single option position and use Delta to determine the probability of expiration in the money or touch, in a way you are determining the riskiness of your position based on whatever strategy you are implementing. If you have a 60% chance of success, you have a 40% risk of failing.
But what about when you have many different options contracts open at once? What will the impact of a price change be to your total position? By totaling the Deltas of each position, the overall impact of the various positions can be seen. If you are trying to hedge your positions to avoid having price movement negatively impact your position, the total Delta can give you an indication of how well your position is hedged. If you are trying to magnify a move in one direction, the total Delta can indicate how much movement overall you can expect. We’ll talk about the calculations involved on other pages of the website, but I can tell you that understanding the overall Delta of my portfolio was a game-changer in how I think about managing my positions.
Limitations of the Delta value
While I consider Delta to be the most important and most useful of the greeks, it has its limitations that you have to always be aware of.
As mentioned earlier, Delta is a calculated value, based on current market prices. The market changes all the time, and Delta changes with it. Even at the extremes of 0 and 100 delta values, prices can change to switch an option in or out of the money due to an unforeseen event that causes an extreme price move.
Delta for price movement doesn’t compare equally from one underlying security to another. Since the value is based on a one dollar change to the underlying (regardless of the value of the underlying), an equal percentage increase to two different securities may have a very different impact on options with the same Delta value. For example, if you owned an option contract on a security with an underlying price of $20, and another contract on a security that has an underlying price of $2000, you will get a very different reaction for a 1% price movement when each contract has the same Delta value. If both contracts had a 50 Delta, the $20 security would move 20 cents and the option would move 10 cents. Meanwhile, the $2000 security would move $20 and the option would move around $10. So, you can’t easily add up Delta values between differing securities to know what to expect. Typically, this issue is handled by weighting the Delta values based on price and volatility correlation. We discuss this elsewhere as well.
Delta as a price move indicator is only valid for a one-dollar underlying move. The move in price will cause Delta to change to a new value and a different amount of movement for the next dollar of underlying price movement. Fortunately, we have another Greek, Gamma, that helps us understand how much to expect Delta to change. We’ll cover that on the Gamma webpage.
What is the Best Delta?
I’m often asked what the best Delta is to use when trading options. There is no universal answer, because it depends on what the objective of the trading strategy being used is. Is the goal to expire worthless, or to expire in the money? In all the strategies I share, I always discuss what Delta values I use for the trade and why. Hopefully, this view will help to show why Delta values are critical data for opening and managing trades.
