# Make Sure You Know This “Delta Accelerator”

You should know by now that there are several factors that affect the price of an option – not just the price movement of the underlying asset.

The variables that exist that account for the fluctuations of options price movement are known as the options “Greeks,” and we’ve covered many of these – Theta, a measurement of options time decay; Delta, how an option’s price will move with price movements in the underlying; and Vega, how sensitive an option is to the Implied Volatility associated with the underlying.

I’ve told you that Delta is the single most important factor in determining an option’s price. Today’s “Greek” shares a special relationship with the Delta, measuring the rate of change in the most important component in an option’s price.

I like to call it the “Delta Accelerator.”

### How Gamma Works

Gamma is the options “Greek” that shows how much the Delta will change with a \$1.00 movement in the underlying security.

Where Delta shows how much an option price will increase with the next \$1.00 move in a stock, Gamma measures how fast the Delta of that option price will increase after that \$1.00 move in the stock.

Let’s take a look at a hypothetical situation…

Say you are looking at a stock trading at \$45.20. You expect the stock to move higher, so you target a \$45 call option. The \$45 call is priced at \$2.00, with a Delta of 0.52 and a Gamma of .05.

Here is how things theoretically would work on a \$1.00 upward move on the stock…

The stock goes up to \$46.20. On Delta alone, the option will go up to \$2.52 (option at \$2.00 + Delta of 0.52 = \$2.52).

When the stock goes up another \$1.00 to \$47.20, the Delta now becomes 0.57. That increase is represented by the Gamma of 0.05 (0.52 + 0.05 = 0.57). The stock should then go higher by this \$0.57.

When the stock goes up another dollar to \$48.20, what happens to the Delta? If you added 0.05 to the Delta of 0.57, you should come up with 0.62 (0.57 current Delta + Gamma of .05 = 0.62).

### Understanding the Gamma-Delta Relationship

Delta and Gamma are the only two Greeks that are related to each other. Gamma is the only Greek that directly affects or determines the change of another Greek.

Delta is the single most impactful determinant of an option’s value. But the Delta isn’t static – as we’ve seen, the Delta of an option changes dynamically along with each change in the stock price.

The Gamma of an option helps us measure the magnitude at which the Delta changes.

Gamma is important for both directional and non-directional or hedging strategies.  Since a large part of what I do is straight directional trades (such as long call and long put trades), we’ll narrow our focus to a long option strategy.

Gamma is the same for both calls and puts and when you are long either, Gamma will be a positive number.

Gamma is going to be highest when the option is At the Money (ATM). ATM options will have a Delta of +/- .50 (+0.50 for calls and -0.50 for puts) and Gamma will always be the highest on the ATM options.

Gamma gets smaller the further in or out of the money the option goes.

The long option (call or put) has positive Gamma. As long as the stock goes in the needed direction, Gamma, though decreasing, will still result in the Delta increasing in value, which results in your option increasing in value.

Here’s a specific example…

### Here’s How the Delta and Gamma Work Together

Let’s take a look at how an option price increases on just the Delta and Gamma factors alone.

We’re going to look at a four-point move in Verizon Communications Inc. (NYSE:VZ), currently trading at \$44.33. Specifically, let’s pick the VZ December 2015 \$44 Call.

As you can see, the Delta is 52.02 or .52, so for the first point move in VZ, the option value should increase \$0.52, (again, just looking at the Delta & Gamma effects only) and go to a value of \$1.67 (\$1.15. +0.52 = \$1.67).

Each point higher after that adds Gamma of \$0.14 (actually 14.37% rounded down to be conservative) to the Delta amount.  So while the first one-point move increased the option \$0.52, the next one-point move higher will make the Delta \$0.66, (\$0.52 + \$0.14 = \$0.66). The third one-point move higher makes the Delta \$0.80. The fourth and last one-point move higher would make the Delta at that time \$0.94.

Add those Deltas up and you get a total increase in value on the option of \$2.92.

The original price of the VZ December 2015 \$44 Call was \$1.15. Add to this price the theoretical cumulative gain from just the Delta (as affected by the Gamma), and the option value becomes \$4.07.

From just the Delta and Gamma effects on the option value in this scenario, there is an opportunity for a theoretical gain of 253%, (\$2.92 gain divided by \$1.15 original cost = 253%).

I kept the Gamma constant to show you how this all plays out, but keep in mind the Greeks are as dynamic as the stock price, so they recalculate dynamically and it is likely the Gamma does not stay at \$0.14 on each dollar move.

### One Last Thing…

On your directional options trades, you want positive Gamma so the Delta increases and subsequently your option increases (assuming the stock goes in your anticipated direction).

For Long Calls:

Delta Value = Positive

Gamma Value = Positive

As your option goes further In the Money (ITM), the Gamma may decrease while the Delta works its way to 1.00.

For Long Puts:

Delta Value = Negative

Gamma Value = Positive

As your option goes further ITM, the Gamma may decrease while the Delta works its way to -1.00.

Gamma doesn’t necessarily show you if the option value will change, it helps you calculate by how much and how fast the option value will change. That’s why I call it the “Delta Accelerator.”

 An option’s Delta measures how its price will move with changes in the price of the underlying security. But Delta is not a static metric – it’s constantly changing as the underlying moves up and down. Gamma measures Delta’s rate of change. Here’s what you need to know: Gamma is a measurement of how fast the Delta changes after a one-point movement in the underlying stock The larger the Gamma, the more volatile the option’s price. Gamma is largest when an option is At the Money, where the slightest move in the underlying can have a big impact on an option’s price. Gamma is smallest on deep In the Money and Out of the Money, where changes in the underlying security have a smaller impact on its options.

Tom Gentile

### 3 Responses to “Make Sure You Know This “Delta Accelerator””

1. My rule of thumb for selection directional option trades is to purchase the expiration ~ 45 days out with the cheapest option price and the (near) highest gamma.