Option Delta Calculation Explained (Simple Guide)

How much does an option change in value as its underlying stock price moves one way or the other? The answer to that is the delta calculation.

Delta is one of “the Greeks.” Those are statistical values that give you important info about options.

Other Greeks include theta, vega, and gamma.

As is the case with many other Greeks, delta changes with the underlying security. In other words, just because the delta is 0.65 when the stock price is at $50 per share, that doesn’t mean the delta will be at 0.65 when the stock price is at $55 per share.

In this guide, I’ll explain delta so that you can use it to manage risk when trading options.

What Is Delta?

You can think of delta as a ratio or a percentage. It tells you how much the value of an option will change when the underlying stock moves higher by $1.

Let’s say that Microsoft is currently trading at $106 per share. Next month’s $110 call option has a delta of 0.39.

That means if shares of Microsoft go up $1, then the call option will increase by $0.39 ($1 x 0.39) or 39% of the value of the change in the stock price.

Keep in mind: call option deltas are measured as positive numbers. Put options deltas are measured as negative numbers.

Why? Think about it: put options increase in value as the stock price goes down. They’re similar to a short position on the underlying stock.

So when the stock price goes up, the value of the put option should drop. How much it drops is determined by the delta.

Let’s look at another Microsoft example. Next month’s $105 put option delta is -0.43.

Note the negative sign in front of the delta. That’s important and expected with a put option.

If shares of Microsoft rise by $1, then you would expect the value of that put option to decrease by $0.43 ($1 x -0.43).

There’s also a difference in the value range between call options and put options.

For call options, the delta ranges from 0 to 1.

For put options the delta ranges from -1 to 0.

How Delta Changes With the Underlying Stock Price

Delta itself changes with the underlying stock price. The measurement of that change is called gamma.

For call options, the delta moves closer to 1.0 as the underlying stock gets further in the money.

For put options the delta moves closer to -1.0 as the underlying stock gets further in the money.

As a rule of thumb, options that are well into the money move on an almost 1:1 (call options) or 1:-1 (put options) basis with the underlying security.

On the other hand, options that are way out of the money usually have tiny deltas. The price won’t move much just because the underlying stock goes up or down by $1.

Number of Shares: Another Way of Looking at Delta

Some traders look at delta as a substitute for owning (or shorting) shares of stock.

Here’s how that works: a call option with a delta of .01 is the same as owning a single share of stock.

Why? Because if the stock goes up by $1, then the call should go up by $0.01 (.01 x $1).

Remember, though, options are traded in blocks of 100 shares. So you need to multiply the delta by 100 shares. That gives you just 1 share of stock (.01 x 100).

In the example above with Microsoft, the call option would be like owning 39 shares of Microsoft stock (0.39 x 100) and the put option would be like shorting 43 shares of Microsoft stock (-0.43 x 100).

Now do the math. If you own 100 shares of Microsoft at $106 per share and it goes up to $107 per share, then you just saw an unrealized gain of $100 ($1 x 100).

On the other hand, if you own that single call option contract that’s the equivalent of 39 shares of Microsoft stock, then you just earned $39 ($1 x 39).

That calculation, by the way, is called position delta. It’s usually used on multi-leg orders.

Position delta on a multi-leg order helps traders get a quick read of how much their overall position will move when the value of the underlying stock changes.

For example, let’s say that you enter into a long call spread on shares of Microsoft. You think the stock is poised to pop in the near future so you buy next month’s $110 call for $2.27 and sell next month’s $115 call for $0.91.

Your total investment is $136 ($227 – $91).

But what’s your position delta? To calculate that, you’ll need to look at the deltas of each option.

The delta for the $110 call option is 0.39. The delta for the $115 call option is 0.24.

So owning the $110 call option is like owning 39 shares of Microsoft stock (0.39 x 100). Owning the $115 call option is like owning 24 shares of Microsoft stock (0.24 x 100).

However, you sold the $115 call option, so that part of your delta calculation will be negative.

Therefore, your delta position is 39 – 24 = 15.

In other words, the whole position is like owning 15 shares of Microsoft stock.

Now, what happens when Microsoft increases by $1? You’ll see a $15 unrealized gain (15 x $1).

Position delta makes it a little easier to keep up with your multi-leg options strategies.

Delta: The Long and Short of It

As we’ve seen, sometimes the delta is positive and sometimes it’s negative. But is there a rule of thumb as to when it’s one way or the other?

Yes there is.

Here’s the breakdown:

  • Long call – delta positive
  • Short call – delta negative
  • Long put – delta negative
  • Short put – delta positive

Understanding when a leg is delta positive or delta negative is important when calculating the position delta. In the long call spread example above, the short call position was delta negative while the long call position was delta positive. Hence the subtraction to determine the equivalent number of shares in the overall position.

Analyzing Risk With Delta

You can also use position delta to analyze risk.

In the example above, ask yourself the following question: are you comfortable owning 15 shares of Microsoft stock?

Probably. There’s not much risk in that.

But let’s say your long call spread involved more contracts. If you had bought 10 $110 call options and sold 10 $115 call options, that literally changes the equation.

In that case, your exposure would be 150 shares of Microsoft stock (390 – 240 = 150).

Are you comfortable with that level of risk?

If not, then you have a couple of options.

You could short some shares Microsoft to mitigate the risk. Or, since you’re already an options player, you could buy more put options.

Alternatively, you could sell some of your long call options in the long call spread. That’s dangerous though because the short call options aren’t covered in the event that the stock skyrockets in value.

The good news is that there are plenty of ways you can adjust your risk and delta helps you determine your exposure.