Option Greeks


The Greeks are risk measures that can help you choose which options to buy and which to sell. With options trading you must have an idea of the direction of the underlying as well as a view of the direction of implied volatility, and then factor in the timing.

The Greeks help you tailor your strategy to your outlook. Spreads, for instance, can help option buyers reduce theta and vega risk. Understanding the Greeks gives you even more of an edge in this zero sum game of options trading.

Option prices can change due to directional price shifts in the underlying asset, changes in the implied volatility, time decay, and even changes in interest rates. Understanding and quantifying an option's sensitivity to these various factors is not only helpful -- it can be the difference between boom and bust.

The option "greeks" come from the pricing model (normally the Black-Scholes model) that gives us implied volatility and quantifies these factors. Delta, theta, and vega are the greeks that most option buyers are most concerned with.


Delta is a measure that can be used in evaluating buying and selling opportunities. Delta is the option's sensitivity to changes in the underlying stock price. It measures the expected price change of the option given a $1 change in the underlying.

Calls have positive deltas and puts have negative deltas. For example, with the stock price of Oracle (ORCL) at $21.48, let's say the ORCL Feb 22.5 call has a delta of .35. If ORCL goes up to $22.48, the option should increase by $0.35.

The delta also gives a measure of the probability that an option will expire in the money. In the above example, the 22.5 call has a 35 percent probability of expiring in the money (based on the assumptions of the Black-Scholes model). But note: This does not give us the probability that the stock price will be above the strike price any time during the options life, only at expiration.

Delta can be used to evaluate alternatives when buying options. At-the-money options have deltas of roughly .50. This is sensible, as statistically they have a 50 percent chance of going up or down. Deep in-the-money options have very high deltas, and can be as high as 1.00, which means that they will essentially trade dollar for dollar with the stock. Some traders use these as stock substitutes, though there are clearly different risks involved.

Option Greeks delta example

Deep out-of-the-money options have very low deltas and therefore change very little with a $1 move in the underlying. Factoring in commissions and the bid/ask spread, low delta options may not make a profit even despite large moves in the underlying. Thus we see that comparing the delta to the options price across different strikes is one way of measuring the potential returns on a trade.

Option sellers also can use the delta as a way to estimate the probability that they will be assigned. Covered call writers usually do not want to be assigned and so can use the delta to compare the probability with the potential return from selling the call.

Advanced traders often use "delta neutral" strategies, creating positions where the total delta is close to zero. The idea is these positions should profit regardless of moves up or down in the underlying. This approach has its own risks, however, and generally requires frequent adjustments to remain delta-neutral.

To review, delta is the option's sensitivity to the underlying price. The delta tells us how much an options price will change with a $1 move in the underlying. At-the-money options have a delta of roughly .50 and therefore will change roughly $.50 for every $1 change - up or down - in the underlying stock.


Theta is the option's sensitivity to time. It is a direct measure of time decay, giving us the dollar decay per day. This amount increases rapidly, at least in terms of a percentage of the value of the option, as the option approaches expiration. The greatest loss to time decay is in the last month of the options life. The more theta you have, the more risk you have if the underlying price does not move in the direction that you want.

Option sellers use theta to their advantage, collecting time decay every day. The same is true of credit spreads, which are really selling strategies. Calendar spreads involve buying a longer-dated option and selling a nearer-dated option, taking advantage of the fact that options expire faster as they approach expiration.

We can look at JDS Uniphase (JDSU) as an example. Going into earnings, the implied volatility was highest for the May options, up at 64 percent. Theta for the at-the-money calls was -.04 and for out-of-the-money calls was -.03. June options had an implied volatility of 50 percent and the theta the ATM calls was -.02 and for OTM calls was -.01.

Thus a calendar spread consisting of buying a June call and selling the May call would give you a positive theta of +.02. Whereas simply buying a May ATM call would give you a theta of -.04.

A JDSU May ATM call spread against an OTM call (a vertical spread: buying ATM, selling OTM) would gives you a theta of -.01, still negative, but much reduced.


Vega is the option's sensitivity to changes in implied volatility. A rise in implied volatility is a rise in option premiums, and so will increase the value of long calls and long puts. Vega increases with each expiration further out in time.


The gamma metric is the sensitivity of the delta to changes in price of the underlying asset. Gamma measures the change in the delta for a $1 change in the underlying. This is really the rate of change of the options price, and is most closely watched by those who sell options, as the gamma gives an indication of potential risk exposure if the stock price moves against the position.


Rho is the option's sensitivity to changes in interest rates. Most traders have little interest in this measurement. An increase in interest rates decreases an options value because it costs more to carry the position.

Using the Greeks to Buy a Call

Buying stock is a relatively easy process. If you think it is going up, you buy it. But when using options, there are several additional layers of complexity and decisions to be made - what strike?, which expiration? We can use the Greeks to help us make these decisions.

First we can look at the delta. The at-the-money call will have a delta of .50. This tells us two things. One, the option will increase (or decrease) by $.50 for every $1 move in the underlying stock. If a stock is trading for $25 and the 25 strike call (delta of .50) is trading for $2, then if the stock goes to $26, then the option should be worth roughly $2.50.

Out-of-the-money calls will have a delta of less than .50 and in-the-money calls have a delta greater than .50 and less than 1.

Two, the delta tells the probability of expiring in the money. A deep-in-the-money call will have an option close to 1, meaning that the probability that it will expire in the money is almost 100 percent and that it will basically trade dollar for dollar with the stock.

Theta is greatest for the near-term options and increases exponentially as the call approaches expiration. This works against us in buying short-dated options. It also gives us the least amount of time for our position to work out. Buying longer-term options - at least two to three months longer than we plan on holding the option - usually makes sense from this perspective.

We must balance this out with the vega of the call. The further out in time you go out, the higher the vega. The practical import of this is that if you are buying options with higher implied volatility (often the case before earnings, or when professional money managers are purchasing in big blocks), you have more exposure using those longer-dated options.

So, we are still left with the question of which option to buy. The answer, as with most things, is which one will give you the most bang for the buck. First, for any given underlying, look for the option with the lowest implied volatility. This will have the lowest relative theta and vega exposure, and will be the best return on investment.

The next step is to do a comparison of the delta, theta and vega relative to the actual options price. Deep-in-the-money calls have the highest delta and lowest theta and vega, but they are probably not the best compared to the price of the option. They also have the most total capital tied up and thus at risk.

Far out-of-the-money options, on the other hand, can also have low vega and theta, and always have a low delta, but again, those values may not be the best relative to the price of the option. And their probability of profit is very low.

"Near the money" options, two to three months out (depending on how long you want to hold the option) usually provide the best relative delta, theta, and vega compared to the price of the option - the most bang for the buck. Most option traders do not do this much analysis to just buy a call, and that is exactly the reason that doing so can make you a more profitable trader.

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