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The Option Greeks

The Greeks are various functions which show the sensitivity of Fair Value of an option to changes in market conditions. These functions are very helpful in assessing and comparing various option positions. They show what effect different variables will have on the fair value price of an option. The Greeks include Delta, Gamma, Vega, Theta, and Rho.


Delta is the rate of change of fair value of the option with respect to the change in the underlying asset price. Stated another way, it indicates the sensitivity of the option value to small changes in the underlying asset price.

For example, if the price of the underlying asset goes up by 1.00 and the fair value price of a call option on that asset goes up by .50, then Delta = 50% or .50. So the option is moving half as fast as the asset at these levels.

If Delta = 100% or 1.00, then the move in the option price would be as large as the move in the asset price. But remember that you paid MUCH less for the option than you would for the asset. So your ROI (return-on-investment) is much more magnified than if you had purchased the underlying asset itself.

Call deltas are positive - ranging from 0% to 100% (0.00 to 1.00); put deltas are negative - ranging from -100% to 0% (-1.00 to 0.00).

At expiration, delta will approach 100% (1.0) if the option is in-the-money; delta will approach 0% (0.0) if the option is out-of-the-money.

If you are purchasing options to open a position, you would like to have a large delta. Then as the asset moves in the direction you predicted, you would reap high gains for a low investment. But you must trade this off against the price of the option. For example, Delta is higher for options that are deeper in-the-money, but they are more expensive. Frequently, a good trade-off is achieved by options that are at-the-money or slightly in-the-money.

Delta is also a very important parameter to consider when you are using options to hedge a position, so that you can correctly determine your mix of assets and options. Delta is also known as the hedge ratio.


Delta also changes as the asset price changes. Another of the Greek parameters shows the sensitivity of the calculated Delta to small changes in the asset price. This parameter is called Gamma. Gamma is the rate of change of delta with respect to the underlying asset price. This parameter helps you to predict how delta will change as the asset price moves.

At-the-money options have the highest gammas. Gamma decreases as you go in-the-money or out-of-the-money. Gamma is sometimes used as a risk management tool to manage a large portfolio, because it tends to reflect the speed of an option. Options with high gamma are the most responsive to price movements, so they provide the most help in covering directional exposure.


Vega indicates the sensitivity of fair value of the option to small changes in the implied volatility. For ease of use, it is often expressed as the amount the option price would change with a one percentage point increase in volatility.

Vega is useful because volatility is one of the most important parameters determining the price of an option. Looking at historical volatility of the underlying asset price, implied volatility of the option price, and vega can help you determine which options are likely to yield the best rewards for you.

When an asset has very high volatility - be sure to look closely at vega. If you ignore this variable, you can be right about the asset moving significantly higher, yet the option you hold on that asset may move significantly lower due to a significant decrease in implied volatility.

Changes in volatility have a greater impact on options that are at-the-money, with a few months until expiration. The effect is less for options that are very close to expiration or very far from expiration. The effect is also less if the option is considerably in-the-money or out-of-the-money.


Theta indicates the sensitivity of the fair value of the option to small changes in time to expiration. For ease of use, it is often expressed as the amount the option price would decay in one day. It is shown as a negative number because the option loses time value as time passes. For a buyer of the option, this decay works against them; for a seller of the option, it works in their favor.

For people who are relatively new to options trading, this is a very important lesson to learn: options are a decaying asset. As you get closer to expiration, the level of decay accelerates. Many traders liquidate or roll-over their long positions when there is less than one month until expiration.


Rho indicates the sensitivity of the fair value of the option to small changes in the interest rate. For ease of use, it is often expressed as the amount the option price would change with a one percentage point move in the interest rate. This parameter generally does not have as large an impact as the other parameters discussed above.

The Greeks can be easily calculated for any option position using a good options analysis program like Option-Aid. Programs like this are a great investment that can pay for itself with a single trade. Trading options without a program like this, can cost you much more.

When you are analyzing potential option positions, it helps to have a computer program like Option-Aid that swiftly calculates volatility impacts, probabilities, statistics, and other parameters of interest. These programs can pay for themselves with the first trade that they help you with.

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