From the June 01, 2007 issue of Futures Magazine • Subscribe!

It’s all Greek to me

To make money consistently by trading options, it’s important to understand how options prices move and what moves them, because as many beginning traders will attest, it can be very frustrating to watch a stock or futures contract take off while the corresponding options contract wastes away.

“It’s very intuitive to think if the value of the stock changes, the value of the options will change,” says Dan Passarelli, instructor at Peak 6 University. But options values are like an algebra equation, and there are six variables that determine an options price: The price of the underlying, the strike price, days until expiration, volatility, interest rates and dividends paid in the case of equity options.

To solve that equation, options traders use the Greeks. Regardless of your strategy, knowledgeable traders understand and use the Greeks to structure winning trades and to determine profitable entry and exit points.


There is not necessarily a linear relationship between an option’s value and the price of the underlying stock or futures contract. Instead, each option has a delta that describes the theoretical relationship between the two. Delta tells you how far the value of an option is likely to move based on a $1 move in the price of the underlying stock or futures contract. Delta is expressed as a range between zero and 1.00, and the higher the delta, the more closely related the movement of the option would mimic that of the underlying asset. If an option has a delta of .90, and the underlying moves $1, the option would increase in value by 90¢. An option with a delta of .25 would move 25¢ for each $1 move in the underlying.

“The trader’s definition is: The delta is the percent likelihood of an option expiring in-the-money,” Passarelli says, adding that to a retail trader, delta is the most important of the Greeks because direction of the underlying has a greater and more immediate effect on the option’s price. “If I want my call’s value to be affected more by the movement of the stock price, I would buy a call with a bigger delta,” he says. If the stock rallies, you are going to make more money, but if you are wrong, that losing trade will be more expensive.

Lee Lowell, a futures and options specialist for Mt. Vernon Research, says, “New traders tend to buy options with smaller deltas because they are cheaper on a dollar basis,” but he warns that they are cheaper for a reason: they are less likely to expire in the money. Traders who want to risk less capital might buy out-of-the-money calls, but they need to know that the option is not going to move as fast as the underlying stock, and that the likelihood of it expiring in-the-money is less than 50%; so while you risk less money, there is a smaller chance of success.

Options with higher deltas are going to be more expensive, deep in the money and close to expiration. “The only time you’d every find an option with 100% delta is on the last trading day and if it is in-the-money,” says Patrick Yon, senior market analyst for New World Trading. “Then it is moving on a one-to-one basis with the underlying asset.”

Floor traders use delta to figure out how much of the underlying to buy to hedge a position. “If you have 1,000 shares of Microsoft and you want to write calls against that, you can use delta if you want to know how much to hedge,” Yon says, adding if Microsoft had a .50 delta and you wanted to hedge 100%, you would buy options two-to-one against the stock. Note one equity option controls 100 shares of stock, but in the futures market, one option controls one futures contract.


All options lose their value as time passes, a concept called time decay. Theta measures the rate of time decay. Theta is not a constant; the decay of an at-the-money option’s value accelerates to zero as the option approaches its expiration date. Options with low theta values are decaying slowly and typically have a longer time until expiration than options with high theta rates.

“To an option buyer, time is the enemy because the options are going to lose value every day whether the market moves in your direction or not,” Lowell says. “It’s a race to see if the market is going to move in your favor or if time decay is going to overtake the profitability.” Lowell explains that if IBM shares are at $100, and you bought a two-month call at a $105 strike price for $1, you are not going to make any money unless the stock goes higher than $106 within the next 60 days. If the stock is at $105.30 with 10 days to expiration and the option is worth 50¢, you would still be losing money even though the stock moved in your direction. On the flip side, the option seller is sitting back and watching time decay working for him.

Selling options outright is one of the riskiest options strategies. “You are taking the same exposure that you do with a future or a stock, so you don’t want to leave that position exposed for too long,” Yon says, adding professionals look to sell out-of-the-money options that are decaying rapidly to limit their exposure to a short time. “I look for a good theta level, one that is decaying rapidly and also one that doesn’t have a lot of time left on it. I don’t usually go out more than 30 days.”

The premiums you can collect on such an option are not huge because the options are close to expiration and typically out-of-the-money. But “if you are willing to sell an option that is a little bit in-the-money, you want to take little more risk; that option has a high theta value on it,” Yon says, and you can collect more premium. Theta is typically expressed on one day basis, but it’s not unusual to see a seven day theta value, so pay attention.


Delta indicates how far the value of an option is going to move, expressed as a percentage of a move in the underlying. Gamma tells you how fast an option’s delta is going to respond to that movement in the value of the underlying. Options with high gammas have deltas that are very responsive to changes in the underlying asset, and conversely options with small gammas have deltas that are not.

Gamma is not as important to retail traders because small changes in the value of the underlying asset are unlikely to affect the value of a small portfolio. However, gamma can be very important to traders who manage large options portfolios.

“You want your deltas to always be moving for you. And as an option buyer, that’s what you get,” Lowell says. “As an option seller, deltas can work against you.” Lowell explains that the more gamma you have, the faster your deltas are going to move. As an options seller, you will have negative gamma. If you are bearish, you want the market to go down, but if the market goes up, you will be getting shorter and shorter the market at a faster pace. If you are an options buyer and you are bullish and the market is going up, you will be getting longer and longer the market, in your favor, at a faster pace.


Vega, while not really a Greek symbol, is used in options pricing models to measure the rate of change relative to the volatility input. There are two types of volatility: historical and implied. Historical volatility is a mathematical measurement of price movements through time and basically is a standard deviation. Implied volatility, the one used in the options pricing model, is essentially the measure of supply and demand for the options.

Most retail players don’t look at vega, Lowell says. “Volatility moves are usually overshadowed by the directional move,” he says, and if you are buying 10 lots, that vega probably wouldn’t affect you.

However, he does warn beginning traders about buying overpriced options before an earnings announcement, only to see the value collapse after the event because of implied volatility. “It happens all the time.”

“Vega can just explode,” says Gregory M. Jensen, executive vice president of Spread Trade Systems Inc. And that explosion can be triggered by events such as earnings statements, employment reports or news events that increase the value of the calls and the puts, “and vega is a way to measure that,” he says. Jensen examines historical charts for specific patterns that surround earning reports, and says that volatility typically climbs, spikes and falls after the event. “Vega is a tool to measure how expensive the option is relative to the fear factor,” and he uses it to identify entry and exit points.


Rho is a measure of the fair value of an option based on interest rate movement, and because interest rate changes are typically small and predictable, it is usually of interest to traders looking to hedge an investment in commercial property and longer-term options, such as long-term equity anticipation securities (LEAPs).


Using the Greeks is a good way to determine the timing, the amount of risk and the potential movement of an option strategy. “No matter how you trade, the Greeks can help you measure how that strategy is going to perform based on the underlying asset and that’s the main use no matter which Greek you are using,” Yon says.

But know when to say when. “The Greeks can be overused by the engineers and the accountants of the world,” Jensen says. And regardless of the model, the market is always right.

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