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So why doesn’t it trade that way? Why is it when a stock moves up by $1, I’m not $100 richer on my call option?
The answer is delta, one of the most important option Greeks you can learn.
Delta tells us how much the price of an option will change as the underlying stock or asset moves.
The thing is, delta doesn’t move in a straight line. In fact, it can move differently from one day to the next.
Despite what you may have heard, delta isn’t a hard concept to understand. In fact, by the end of this article, you’ll have many of the tools necessary to read, interpret, and use delta in your options trades.
What Is Delta?Delta is the amount an option’s price will change for every $1 increase in the underlying price.
Call options have positive delta, since they gain value as a stock rises. Conversely, put options have negative delta, since they lose value when a stock rises.
For call options, delta goes from 0 to 1, with at-the-money options at 0.5 delta.
For put options, delta goes from -1 to 0, with at-the-money options at -0.5 delta.
The further in the money a call option goes, the closer its delta gets to 1. Similarly, the further in the money a put option goes, the closer it gets to -1.
As call and put options go further out of the money, the deltas approach zero.
Take a look at this option chain for Apple (AAPL).
In this option chain, you can see the calls down the left side and puts down the right.
With Apple’s current price listed at the top as $172.55, that places the at-the-money split in between the $170 and $175 strikes.
The purple sections highlight in-the-money strikes, while the black sections denote out-of-the-money strikes.
The orange arrows illustrate the movement in delta from 0.01 to 0.92 for call options and -0.04 to -1.00 for the put options as each moves from out of the money to in the money.
Notice also how the deltas right at the break between the purple and black sections are close to 0.5 and -0.5.
Now, you may not have seen it immediately, but the rate at which delta changes varies from one strike to the next.
For example, the difference between the $170 and $165 call deltas is 0.12. However, the difference between the $165 and $160 deltas is only 0.09. This is what’s referred to as gamma.
Gamma is the rate of change of delta for every $1 increase in the underlying asset.
Here’s an easy way to think about it: If you’re driving a car, delta is your speed and gamma is your acceleration.
Why Is Delta Important?You can think of delta as the number of shares you control.
Yes, a call option with 0.5 delta technically controls 100 shares of stock. But it doesn’t act like that. It acts like it controls 50 shares of stock.
Here’s an example using the options chain for the S&P 500 ETF (SPY).
The $447 call option has a delta of 0.49.
Let’s assume the SPY moves higher by $1. That should mean the new price of the $447 call option would match the current price of the $446 call option.
Here’s how that math works:
The difference in price between the $447 call option and $446 call option is $0.62.
Why don’t the two match exactly?
Two reasons. First, the delta changes as the price of the underlying asset changes. So it’s probably more accurate to use a 0.50 delta for our calculations, since that’s the average of the two deltas.
Second, and more importantly, option prices are also determined by implied volatility.
And believe it or not, the implied volatility between those two options, even though they are so close together, is different.
The $447 call option has an implied volatility of 19.83%, while the $446 call option has an implied volatility of 20.10%.
If you did the calculations using vega, the Greek for measuring changes in implied volatility, you would find out that it contributes $0.13 to the option’s price.
So, adding the impact of delta and vega (implied volatility) gives us $0.49 + $0.13 = $0.62, the exact difference between the two option prices.
Pretty neat, right?
A Word on GammaI briefly touched on gamma earlier. Now I want to dig a little deeper.
This chart shows the gamma (blue line) and delta (red line) of a call option. The orange line denotes where the stock’s current price is (the at-the-money line).
Let’s start with the delta line.
As we discussed earlier, delta approaches zero for call options the further out of the money you go and approaches 1 the further in the money you go.
That’s what creates the S-shaped curve.
The slope of that curve is gamma.
And you can see that when an option is at the money, the curve is at its steepest point.
However, as you move further away from the stock’s current price, that slope decreases.
That’s why gamma has a bell curve shape with its peak at the money.
This tells us that the rate of change for delta is greatest at the money and decreases as you move away from the stock’s current price.
Using the car analogy, the car’s acceleration is greatest at the current stock price, and that acceleration decreases as you move further in or out of the money.
Why Delta Is CriticalIf you learn only one options Greek, I’d recommend it be delta.
Delta tells you how exposed your option is to changes in a stock’s price.
And since stocks tend to move around, this is extremely important.
I recommend you take some time and pull up a few option chains. Model out different options strategies (long and short options, spreads, etc.) and see how delta changes.
Then, email me with any questions you might still have on the subject.
While I can’t respond to every email, I promise to read them all.