# Option Delta and Option Gamma

Posted on Thursday, July 10, 2014 at 10:33 AM

The option “greeks” help explain how and why option prices move. Option delta and option gamma are especially important because they can determine how movements in the stock can affect an option’s price. Let’s take a brief look at how they can affect each other.

Delta and Gamma

Option delta measures how much the theoretical value of an option will change if the stock moves up or down by $1. For example, if a call option is priced at 3.50 and has an option delta of 0.60 and the stock moves higher by $1, the call option should increase in price to 4.10 (3.50 + 0.60). Long calls have positive deltas meaning that if the stock gains value so does the option value all constants being equal. Long puts have negative deltas meaning that if the stock gains value the options value will decrease all constants being equal.

Option gamma is the rate of change of an option’s delta relative to a change in the stock. In other words, option gamma can determine the degree of delta move. For example, if a call option has an option delta of 0.40 and an option gamma of 0.10 and the stock moves higher by $1, the new delta would be 0.50 (0.40 + 0.10).

Think of it this way. If your option position has a large option gamma, its delta can approach 1.00 quicker than with a smaller gamma. This means it will take a shorter amount of time for the position to move in line with the stock. Stock has a delta of 1.00. Of course there are drawbacks to this as well. Large option gammas can cause the position to lose value quickly as expiration nears because the option delta can approach zero rapidly which in turn can lower the option premium. Generally options with greater deltas are more expensive compared to options with lower deltas.

ATM, ITM and OTM

Option gamma is usually highest for near-term and at-the-money (ATM) strike prices and it usually declines if the strike price moves more in-the-money (ITM) or out-of-the-money (OTM). As the stock moves up or down, option gamma drops in value because option delta may be either approaching 1.00 or zero. Because option gamma is based on how option delta moves, it decreases as option delta approaches its limits of either 1.00 or zero.

An Example

Here is a theoretical example. Assume an option trader owns a 30 strike call when the stock is at $30 and the option has one day left until expiration. In this case the option delta should be close to if not at 0.50. If the stock rises the option will be ITM and if it falls it will be OTM. It really has a 50/50 chance of being ITM or OTM with one day left until expiration.

If the stock moves up to $31 with one day left until expiration and is now ITM, then the option delta might be closer to 0.95 because the option has a very good chance of expiring ITM with only one day left until expiration. This would have made the option gamma for the 30 strike call 0.45.

Option delta not only moves as the stock moves but also for different expirations. Instead of only one day left until expiration let’s pretend there are now 30 days until expiration. This will change the option gamma because there is more uncertainty with more time until expiration on whether the option will expire ITM versus the expiration with only one day left. If the stock rose to $31 with 30 days left until expiration, the option delta might rise to 0.60 meaning the option gamma was 0.10. As discussed before in this blog, sometimes market makers will look at the option delta as the odds of the option expiring in the money. In this case, the option with 30 days left until expiration has a little less of a chance of expiring ITM versus the option with only one day left until expiration because of more time and uncertainty; thus a lower option delta.

Closing Thoughts

Option delta and option gamma are critical for option traders to understand particularly how they can affect each other and the position. A couple of the key components to analyze are if the strike prices are ATM, ITM or OTM and how much time there is left until expiration. An option trader can think of option delta as the rate of speed for the position and option gamma as how quickly it gets there.

John Kmiecik

Senior Options Instructor

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