Understanding How Options Move With the Underlying Stock (Part 2)

02/04/2010 12:01 am EST


Learning Greek, One Letter at a Time

If it isn’t obvious yet, you have to understand delta to grasp gamma. You could probably go on to learn about the other two important “Greeks,” theta and vega. But you can’t really get gamma unless you know delta. So if any of this is the least bit confusing so far, make sure you go and read the option delta code before you proceed.

In the above example, a $10 move meant that the gamma of 0.03 was multiplied by 10 to yield 0.30. Hence, 0.30 was subtracted from the 130 call delta. But, this was actually occurring on the way down in real time. So, for every dollar-point drop from $130 to $120, the 130 call delta was losing approximately 0.03 of value, and thus, the option was losing value in its premium at a slightly slower and gradually decreasing rate as the stock price dropped. Think of a boy going down a slide with a slowdown in speed as he gets near the bottom and you’ll get the idea.

Conversely, the 130 put would have gained about -0.30 delta points, likely going from around -0.50 (since it was ATM before the $10 drop) to around -0.80, pushing this put deeper in the money (ITM). Since put deltas are always negative, the subtraction or addition of gamma makes them move either deeper ITM (toward -1.00), or deeper OTM (toward zero).

You may have noticed I said that the put “gained” -0.30 delta points. How can a negative be a gain? Well, if you’re a put, it’s what you want to be when you grow up—more like a real, live underlying short position with a -1.00 delta! So, keep in mind that a mathematical loss of -0.30, taking you from -0.50 to -0.80, is actually a gain in the put’s delta value. The diagram below should help you visualize this.

Click to Enlarge

To summarize, gamma tells you how much delta changes relative to stock. When stock rises $1, delta increases mathematically by the amount of gamma. When stock falls $1, delta decreases mathematically by the amount of gamma.

Remember, since gamma is always a positive number—added or subtracted to delta depending on stock rise or stock fall, respectively—put deltas will increase mathematically toward zero on stock rise and decrease mathematically toward -1.00 on stock fall. But, again, mathematical “losses” for put deltas are actually moving them more in the money, closer to -1.00, where their value increases.

In our AMZN example, if stock rose $10 to $140, the ATM 130 put would have probably “lost” about -0.30 delta points as 0.30 was added mathematically to a delta of -0.50, resulting in a new delta of -0.20. The ATM put would have lost delta points because the stock’s rise caused it to lose “moneyness,” decreasing its value.

One of the best options instructors in Chicago is Sheldon Natenberg, author of the option trader’s bible, Option Volatility and Pricing. Shelly had a great and simple way of explaining many market concepts, and his quote below got me thinking years ago about how to see the logic of delta and gamma without thinking about the math.

“This corresponds to our intuition that as the underlying price rises, ATM calls move into the money and ATM puts move out of the money.”

As (hopefully) the graphic above illustrates.

By Kevin Cook, contributor, ONN.tv

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