How Gamma Affects Short-Term Option Positions

by Mark Wolfinger | April 28, 2010 9:16 am


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Owning a short position in a near-term option comes with high positive time decay, meaning that the value of the option is quickly eroding as time passes. But it is a high-risk/high-reward scenario, and the extra risk this type of position carries is not immediately apparent.

Here’s a recent e-mail I received from a reader:

“I know people who are trading spreads and condors on ‘weekly’ options. As a beginner, I can see the advantage of a very short time exposure to market change, but I can also see the disadvantage in the speed with which you may have to carry out any position management. What are your thoughts? Would you recommend them?”

I do not recommend trading options with only a short time till expiration. And I’ll explain why.

Theta, a measure of time decay, is a wonder to behold when it works in your favor. But there’s another important option Greek that’s affected as expiration nears: gamma. Gamma measures the rate at which an option’s delta changes.

In case you are unfamiliar with the concept that a sudden change in delta, i.e., gamma, can wreak havoc on your position, let’s look at some data.

For this example, I’ve chosen a generic stock, currently trading near $56 per share, and the June 60 call option, which expires in 60 days. These options trade with an implied volatility of 30.


June 60 Calls; IV = 30

th value How Gamma Affects Short Term Option Positions

Th Val = Option fair value as calculated

First, we see two obvious patterns. As the stock moves higher (from $56 to $62), the call option increases in value. As time passes (60 days down to only two days), the option loses value.

This data represents the typical situation. When the option is out of the money (OTM), delta moves toward zero as time passes. Why? With less time remaining before the option expires, there is a reduced probability that the stock will move past the strike price ($60 in this example), and thus, less chance the option will be in the money (ITM).

Delta provides a good approximation of the probability that the option will be in the money at expiration. A delta of 6 denotes a 6% chance. (Note that maximum delta value is 100, and when the call is at the money, the delta remains near 50, which makes sense, because the option has an equal chance of being ITM or OTM at expiration.)

Next compare those results with the option delta when the stock is at $62 (above the strike price). As time passes, delta rises, indicating an increased chance of finishing ITM. Delta for a call option increases as the stock moves higher, and decreases as it moves lower.

Because delta represents a good approximation of how much the option price changes when the underlying stock moves by 1 point, it’s important to recognize how an option’s delta can change. The topic of this article is explosive gamma, and understanding why delta can change so quickly. 

Unless there’s very little chance that the stock can move enough to change the moneyness (ITM versus OTM) of an option, gamma increases as time passes. This is most apparent when the stock is trading ATM. With two days remaining, the 30 gamma, coupled with the 50 delta, tells you that this option is going to move toward 0 or 100 delta very quickly. 

When 60 days remain, gamma increases at a moderate pace. If you are short that option and the stock rallies, the option will increase in value and you lose money. But that loss is small when compared with being short that two-day option.

A significant price increase in the stock results in your short option quickly moving point for point with the stock.

At a price of $61, delta is more than 80. How do we know? Delta is now 50 and the 30 gamma makes delta 80 when the stock is one point higher at $61. Gamma is not constant, and also increases as the stock increases. Thus, delta is more than 80.

If you plan to be short very short-term options, you must understand the risk that comes along with the benefit of time decay.

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  3. Don’t Let Delta and Gamma be Greek to You:
  4. How to Avoid the Wrath of Gamma at Expiration:
  5. Expiration Day and Gamma – What You Need to Know:
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