Options Basics: Wrapping Up the Greeks - Gamma

Here with an introduction to gamma—the fourth part of his discussion on the Greeks—is options expert Russ Allen of Online Trading Academy.

In the last few articles, I’ve been describing the forces that affect option prices. Each has a measurement whose name is a Greek letter, and collectively they are called “the Greeks.” Here again is the table listing them:

Greek Name: Measures option price change resulting from:

Delta—Changes in the current price of the underlying asset

Vega—Changes in expectations for future price change in the underlying asset

Theta—Drop in option price due to the passage of time

Rho—Changes in the risk-free interest rate

Gamma—Change in Delta due to changes in the current price of the underlying asset

Earlier, I discussed Delta and Vega; last week we talked about Theta and Rho. As I mentioned then, there is one other force that can also be involved—dividends.

If the underlying asset for an option is a stock or exchange traded fund that pays a dividend, then the payment of that dividend will have a predictable effect: the stock or ETF should go down in price by the amount of the dividend. This is another one of those relationships that must be true because if it weren’t, there would be an opportunity for arbitrage (risk-free profit). A free market does not allow this. It pays us for taking risks. Any risk-free opportunity is actually a defect in the market.

Let’s say that a $100 stock is about to pay a $1 dividend. Tomorrow is the “ex-dividend date.” This means that anyone who buys the stock tomorrow does not get the dividend. Whoever owns the stock at the close of business today, the day before the ex-dividend date, receives the dividend, no matter how long they’ve owned the stock (even if that’s only one second).

Tomorrow morning, the stock would be expected to open for trading at $99, one dollar less than its closing price today. At that price, the stock would be considered unchanged. Anyone who owned the stock from today would then own something that was worth one dollar less, but they would be due the one dollar dividend in cash. So, $99 worth of stock and $1 worth of cash equals the former $100 price of the stock, for no net change in net worth.

If it were not true that the stock dropped by the value of the dividend, then it would be a simple matter to buy the stock just before the ex-dividend date, hold it just long enough to be recorded as the owner, collect the dividend, and then sell the stock again for a risk-free profit. That type of opportunity could not last long. Everyone who knew about it would want to buy stocks on the day before the ex-dividend date, and sell them the next day. The stock’s price would soon take on the same pattern of dropping on the ex-dividend date, as everyone tried to sell at the same time.

By the way, the actual payment of the dividend takes a few days after the ex-dividend date. The payment itself has no effect on the stock price.

So, we know that there will be a drop in the stock price when a dividend happens. How does this effect option prices? Well, since a drop in underlying price will make calls cheaper and make puts more expensive, when it is known that a drop will occur, the effects will be priced into the options ahead of time. If it is known that a stock will pay a dividend before a particular option expiration date, then all of that stock’s calls for that expiration date will be cheaper, and all of its puts more expensive, than they would be otherwise. The dividend is in effect priced in by making the difference between call and put prices that much greater than they would otherwise be.

NEXT PAGE: Here Comes Gamma

Oddly enough, as far as I can determine there is no Greek letter to describe the effect of dividends, even though they can be even more important than interest rates, which do have their own greek (Rho). There is a greek called Phi which includes the effect of interest rates netted against dividends, but none for the dividends themselves. So when trading options on a stock or ETF that pays dividends, we have to work out the dividend effect for ourselves. We have to understand that the calls are higher and the puts are lower in price until the ex-dividend date. This difference will go away abruptly on the ex-dividend date.

The only Greek that we haven’t yet tackled is Gamma. This is a second-order greek, because it describes the change not in the price of an option, but in the Delta of an option, which is itself another greek.

Gamma is rarely the basis for a trade. Usually our option positions are designed to take advantage of an expected movement in the stock price (Delta effect); or of an expected change in implied volatility (the Vega effect); or simply of time decay (the Theta effect). Gamma is not usually a prime consideration.

Still, its effect is important and we should have a basic grasp of it.

Gamma shows how an option’s Delta will change when the underlying stock price changes. For example, say a call option priced at $2.00 has a Delta of .50 and a Gamma of .06. A one-dollar increase in the underlying price would increase the call’s price by fifty cents (Delta effect). But the next dollar increase in the stock price would have a larger effect on the option’s price. Gamma shows how much larger. In this case, after that first one-point move, the price of the call now stands at $2.00 + $.50 = $2.50. Its new Delta value is the old Delta value of .50 plus the old Gamma value of .06, or .56. This means that the second dollar increase in the underlying will increase the call’s price by $.56 instead of $.50.

Once the underlying begins moving in the right direction for your long option position, each additional dollar of price movement adds more to your profits than the last one. This is true both for call options (with increasing underlying prices), and for put options (with decreasing underlying prices). So the Gamma effect means that when owning any kind of option, when you win, you win at an accelerating rate; and when you lose, you lose at a decelerating rate. When you are in the position of owning options rather than writing them, the bigger the Gamma the better, all else being equal. For option writers, the opposite is true.

This acceleration does stop at a certain point—the point at which the Delta reaches its maximum value of 1.00. After that, the option is changing just as fast as the stock and can not change any faster. So the option’s Gamma becomes zero as its Delta settles in at a rate of 1.00 for calls, or -1.00 for puts.

So here is the summary for Gamma:

Greek name: Gamma

Force acting on option price: Change in underlying price

Unit of measure: Point change in the options’s Delta for a one-point increase in the underlying price.

Sign: Positive for both puts and calls

Notes: Adding the Gamma to the Delta of an option gives the expected new Delta after a one-point increase in the underlying price. Subtracting the Gamma gives the new Delta after a one-point drop in the underlying.  For a given expiration date, at-the-money (ATM) options have the highest Gamma. For a given strike price, options with a nearer expiration date have higher Gamma values if near the money, and lower Gamma values if away from the money. For at- or near-the-money options, Gamma increases over time. For others, it decreases. A high gamma value helps long option holders and hurts option sellers (both puts and calls).

Over the last few weeks. We’ve covered all of the forces that move options, and the Greeks that measure the magnitude of those forces.

By Russ Allen, Instructor, Online Trading Academy