Options Education: Greeks

  Options educational content provided courtesy of ChartBender.

Why Delta is Important
Delta tells you the theoretical rate at which moves in the stock price will produce profits or losses in your position. See the graphs below. Some traders also interpret delta as the probability that the option will expire in-the-money.

Delta determines the color of the up arrow and the down arrow for the Direction row. You can see that the option in question must have a negative delta. As indicated, a rising stock price causes losses in this option position (up arrow, red). But a falling stock price causes profits in this option position (down arrow, green). If the colors were reversed, we'd know that the position has a positive delta.

The actual value of delta would tell us the theoretical magnitude of losses that are associated with an upward stock move, as well as the magnitude of theoretical profits associated with a downward stock move.

Gamma theoretically projects the amount by which your position's delta will change when the stock price changes by $1.00.

For example, if your position's gamma is $50, then your position delta will increase by $50 if the stock price increases by $1.00. And your position delta will decrease by $50 if the stock price falls by $1.00.

If your position's gamma is -$50, then your position delta will decrease by $50 if the stock price increases by $1.00. And your position delta will increase by $50 if the stock price falls by $1.00.

Why Gamma Is Important
Positive gamma means that the rate at which you profit will ACCELERATE as the stock price continues to move in your favor, while the rate at which you lose will DECELERATE as the stock price makes continued moves against you.

Negative gamma means that the rate at which you profit will DECELERATE as the stock price continues to move in your favor, but the rate at which you lose will ACCELERATE as the stock price makes continued moves against you. With negative gamma, a very stable stock price is your best friend.

Special note: Gamma has an inverse relationship to Theta.

Theta theoretically projects Decay P&L (i.e., Cost or Compensation for absorbing movement in the stock price.)

Theta is the theoretical amount of decay (i.e., cost or compensation) an option will produce in one day. As we discussed in Decision Making, you must absorb movement in the stock price (i.e., you must realize risk) in order to generate profit or loss from decay. That's why it can be helpful to view theta as the theoretically projected cost or compensation for realized risk. Positive theta theoretically projects how much compensation you will receive each day for absorbing stock movement. Negative theta theoretically projects how much it will cost you each day to absorb stock movement.

Why Theta Is Important
In addition to theoretically projecting decay, theta gives you an idea as to how your position will respond to movement in the stock price. This is because theta has an inverse relationship to Gamma. If, for example, you have a positive theta, you should expect to have a negative gamma. Negative gamma means movement in the stock price in one, and sometimes both, directions is undesirable. Positive theta typically means that you want very little or no movement in the stock price. The reverse is true if you have negative theta.

When you think of theta as theoretically projecting cost or compensation, you can ask yourself this: "For what am I being charged or compensated?" The answer is always the same: The risk posted to the position by changes in the stock price. If, for example, theta is theoretically projecting a relatively high level of compensation (i.e., a large amount of positive decay), it's because the market is expecting the underlying stock to be volatile, and potentially move quite a bit.

In our visual representation of the Greeks, theta determines the color of the top circle, as you would expect. If theta is positive, the circle is green indicating that the position will profit from decay. If the circle is red, it means theta is negative and the decay will produce losses in the position.

Interestingly, the color of the horizontal arrows in the direction row is also determined by theta. If decay has a green circle, then the horizontal direction arrows will also be green. This is a reminder that a +theta position benefits from a stable stock price. Conversely, if the decay circle is red, then the position will lose money if the stock sits still. Thus, the horizontal arrows in the Direction row will be red.

Vega theoretically projects Implied Volatility P&L (i.e., Cost or Compensation for Changes in Expected Risk).

Vega is defined as the theoretical dollar amount by which your position will change if implied volatility changes by one percentage point. (Recall from Option Behavior that changes in implied volatility will produce changes in the amount of time value.)

Left Graph. Vega is +5.00, which is the dollar amount by which the option contract will theoretically increase if IV increases by one percentage point. The vega of +5.00 also tells us that we will lose $5.00 from a one percentage point drop in IV.

Right Graph. IV has increased by five percentage points. The graph shows the theoretical increase of $25.00 in the XYZ Jan 35 Call. Had implied volatility dropped by five percentage points, down to 30%, the contract would have theoretically lost $25.00 in value.

Why Vega Is Important
Vega gives you an idea of how much you will pay, or be paid, if the market changes its opinion about the upcoming volatility of the stock price. As with all the Greeks, this information is good to know, but it will not tell you what your actual implied volatility profits or losses are.

The Grid to the left conveys that rising implied volatility will generate IV profits, and falling implied volatility will generate IV losses. Of course, depending on the position you have, the reverse could be true.

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