Delta: Breaking Down the First of the Greeks

Delta Pointers Delta is a numerical value that describes an option in several interesting and useful ways, such as how much the option's price should move for a $1 move in the underlying stock, how much the option is almost exactly like its stock, and what the probability is of the option being in-the-money by expiration.

A short definition of delta would be the sensitivity of an option's price to changes in the underlying price. A shorter definition would be the speed of the option. If an option has a delta of 0.500, you can think of this as 50% and it means that if the underlying stock moves $1 (higher or lower), the option price will move only 50 cents (again, higher or lower).

Delta is calculated within an option pricing model by a function that compares the option strike price to the underlying stock price and accounts for probability and the passage of time. That mouthful sounds complicated, but if you know a little about options already, you can break this down step-by-step. First, comparing the option strike price to the underlying stock tells you about its value. Since an option gives you the right to be long or short the stock, its value is comprised of intrinsic value (the real worth it has if it is in-the-money) + time value (the worth it has due to future possible price movement).

Second, the option pricing model assigns a probability to every option that quantifies the likelihood of that option finishing in-the-money (ITM). This number is the delta, and it changes dynamically as underlying prices change and time passes. The number produced by the pricing model is between 0.000 and 0.999, and traders speak of 0.103 as a “10-delta” and 0.591 as a “60-delta.”

The INs, ATs & OUTs of the Money

At-the-money (ATM) options have deltas of around 0.500 (a “50-delta”), which means they have roughly a 50% probability of finishing in-the-money come expiration. This makes sense because buying an ATM option is like a coin toss. We have a 50/50 shot at being right about a $40 stock moving up or down tomorrow or next month and causing either the 40 call or put to move in-the-money.

What deltas do out-of-the-money (OTM) options have? Less than 0.500, as you might have guessed, because they should theoretically have less than a 50% chance of finishing ITM. So with stock at $40, the $45 call might have a delta of .300 (a “30-delta”), and the $35 put might have a delta of -0.300 (also a “30-delta” but of the put variety).

Correspondingly, that means ITM options should have deltas of greater than 0.500 because they have more than a 50% chance of finishing ITM. So with the stock at $40, the $35 call might have a delta of 0.700, and the $45 put might have a delta of -0.700. Deep ITM calls and puts have deltas really close to 0.999 and -0.999, so the $25 call might have a delta of 0.95 and the $55 put might have a delta of -0.95. By the way, why do puts have a negative sign in front of them?

Calls Have Positive Delta, Puts Have Negative Delta

The next thing we need to learn about delta is how it's calculated differently for puts and calls. And the only real difference we need to worry about is that calls have positive delta to indicate their inherent long position and puts have negative delta to indicate their inherent short position. We mark calls on the probability scale from 0.000 to +1.00, and puts from 0.000 to -1.00, with the whole numbers +1.00 and -1.00 representing the stock itself. Traders speak of stock as a “100 delta” position because the next one-thousandth up from 0.999 is 1.00.

What do all little options want to be when they grow up? A full 100 shares of stock, of course! In other words—assuming options had feelings and wishes—they'd want to finish in-the-money… which means they'd want to have a delta equal to that of +1.00 for calls, or -1.00 for puts. Until expiration day, and we know the final destiny of those yet-to-mature options, their deltas tend to stay within the probability scale of +0.999 to 0.000 for calls, and -0.999 to 0.000 for puts.
And here's how the delta of an option moves as the underlying stock price moves: if stock moves from $40 to $44, the delta of the 40 call might move from 0.50 to 0.65, while the delta of the 40 put might move from -0.50 to -0.35. Notice that as the stock price rose, the call gained in delta value while the put lost delta value.

Delta Tells You How an Option is Similar to its Stock

Since options want to grow up to be like stock, but they have this funny tendency to follow the stock back and forth as if it's a tug of war between the calls and the puts, delta could be described as a measure of who's winning. Delta tells you minute-by-minute how far each side has come and how far each little strike still has to go to become a full 100 deltas.

Options that are deep ITM have deltas close to 0.999 for calls and -0.999 for puts because they are nearly 100% like the underlying stock.

Traders might speak of these deep options as “100 delta” or as “trading for parity” because they have almost no time value relative to their large intrinsic value. They might also call them “an exercise” because they are so likely to be exercised at expiration, or sooner if there is a dividend event or they are part of a hedge that needs to be unwound. Options that are deep OTM have deltas close to 0.000 and thus they have almost zero equivalence to the underlying stock.

As the underlying stock price changes, an option's delta must change too. As stock rises, call deltas move away from zero, closer to +1.00, and put deltas move away from -1.00, closer to zero. As stock falls, call deltas move away from +1.00, closer to zero, and put deltas move away from zero, closer to -1.00.

How to Use Delta to Gage Option Buying vs. Selling

Some traders may use changes in delta to figure out if options are being bought or sold. Since option markets are so liquid and competitive, option prices tend to move in lock-step during the trading day with their stocks. So you would expect all “30-delta” options to move about 30 cents for every $1 move in the underlying stock. A $1 up move would have the calls up 30 cents and the puts down 30 cents, and vice versa for a $1 move lower in the stock.

What if the stock moved $1 higher and the 30-delta calls only moved 15 cents higher? Someone was probably selling those calls (trading them on or near the bid) and the market makers were perfectly willing to let them do so. What if the stock moved $1 lower and the 30-delta puts moved 50 cents higher? It's likely that someone was buying those puts (at or near the ask price) because they moved far higher in price than their delta would dictate was fair value.

Three Ways to Think About Delta That Make It Such a Great Tool

Here's a handy reference guide to delta to help you remember its power…

1. Delta is the rate of change of the option relative to its underlying stock—in essence, the speed of the option.

2. Delta is the probability the option will finish in-the-money—i.e., how likely is it the option will end up trading for parity because it is virtually equal to a position in the stock from the strike price?

3. Delta is the “hedge ratio” or equivalence to the underlying stock—i.e., it tells you how much stock you need to buy or sell to exactly hedge an option position.

Note: This content was previously published by the Options News Network.¹It has been edited slightly from the original version. The Options News Network was previously affiliated with OptionsHouse, LLC, through our mutual parent company, PEAK6 Investments, LP.

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