Understanding How Options Move With the Underlying Stock (Part 3)

02/05/2010 12:01 am EST


More Options Intuition

Underlying stock has a delta of either +1.00 or -1.00, depending on whether our position is long or short. So, what’s the gamma of underlying stock? Zero. It has no rate of change in its delta. Likewise, deep ITM options and deep OTM options have small gammas because their “moneyness” (i.e., their delta) shouldn’t fluctuate very much on moves in the stock.

Deep ITM options are more like stock, with a delta very close to +1.00 or -1.00 that doesn’t change very fast. And deep OTM options are closer to worthless, with a delta very close to zero that also doesn’t change very fast. In this way, you can think of gamma as the speed of the delta.

Deep ITM or deep OTM options have small gammas, and thus, slow-moving deltas. This means their deltas are stable and change very little compared to ATM options, whose gammas are the highest, thus giving them fast-changing deltas.

Natenberg, again, says it best:

“The gamma is a measure of how fast an option changes its directional characteristics, acting more or less like an actual underlying position. Since directional risk is always important, the gamma is [a very] important risk measurement. Indeed, an option position can change its directional risk dramatically, even if a trader takes no action in the marketplace.”

Since gamma is always a positive number for both calls and puts, buying options gives you a positive gamma position. You are long gamma and can benefit from big and quick price movement in your delta direction, whether you are net long delta, or net short delta. When you sell options, you are short gamma and can suffer because of big, quick moves against your delta position.

This may not mean much for single option positions, but for large complex positions, the gamma number becomes a vital single reference for risk evaluation, much like a barometer can instantly tell you something meaningful and useful about complex weather conditions. Gamma describes a trader’s exposure to leverage so that they will know how quickly their position could morph into a nightmare. You could think of gamma as the “gears” of leverage because they can ratchet up your delta exposure quickly on a big move.

For instance, think of a trader being short many deep OTM puts. The options have a low delta, and thus, a low probability of getting near the money. But the trader, in aggregate, has a short gamma position that can grow in size if those options move closer to the money since gamma increases for ATM options. If the market makes a swift move lower, this position will “gear” up and cause large potential losses for this trader. This is what happened to hedge funds of Victor Neiderhoffer, on two occasions I believe.

Natenberg on the “bottom line” of gamma:

“A large gamma number, whether positive or negative, indicates a high degree of risk. A low gamma number indicates a low degree of risk. Every option trader learns to look carefully not only at current directional risk (the delta), but also at how that directional risk will change if the underlying market begins to move (the gamma).”

Natenberg says that a large gamma number can hurt you, and that fits with my trader example above where a guy who thought he had the market outsmarted sold “too many” puts. But how can it hurt to have a large positive gamma?

Well, this just means you are long a lot of options and a move away from the money for those options means you have increased your chances of losing a good chunk of that money. It’s something pro option traders take very seriously, and they don’t want to be long too much premium any more than they want to be short too much.

Curvature and Acceleration

Gamma is one of the option trader’s most important risk management tools. The second derivative of the option pricing model, it tells traders how sensitive their positions are to directional movement. Since most option pros tend to carry what we call “delta neutral” positions, it seems at first glance that they should not be worried about the market moving in either direction.

But since delta changes ever so slightly with moves in stock, option traders are forced to continuously adjust the hedges on their positions when those changes add up because of position size or big percentage stock moves. They do this by either buying or selling the underlying stock to get the delta position back to neutral. This is often called “gamma scalping” because in a relatively stable market with no surprises like a big change in volatility, it is a profitable adjunct to the option trader’s primary goal of volatility arbitrage.

There’s a lot to learn about gamma that I cannot begin to explain here. We haven’t even touched on how time and volatility figure into determining both delta and gamma, or how gamma changes. But I will close with some simple descriptions that have helped me picture their power and usefulness as concepts and tools.

Delta is often called the “slope” of an option. And gamma is sometimes described as the “curvature” of the option because as the underlying price changes, the option delta changes too in a non-linear way—sort of the way I used the “gearing” analogy. You engineers and other quantitative types should readily understand this stuff.

Click to Enlarge

For us non-quant types, I like the way Natenberg once explained it to us in class at the CME in the mid-90s. He said you can think of delta as the “speed” of the option and gamma as its “acceleration.”

That I can relate to.

By Kevin Cook, contributor, ONN.tv

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