What is Color?
Color is an options "greek" that measures the rate at which gamma will change over time. More specifically, it is the third order derivative of an option's value, once to time and twice to the option's price. Gamma measures the change in delta in response to a one unit price move in the underlying asset, and delta measures how a derivative moves in response to a price change in the underlying.
Color is also known as gamma decay or the derivative of gamma with respect to time (DgammaDtime).
- Color measures the rate at which gamma will change over one year. It can be converted to a daily amount by dividing by the number of days in a year.
- Color is important for gamma-hedging as it shows how gamma will change.
- Color is a third order derivative measuring gamma, and gamma measures changes in delta. Delta is the sensitivity of the price of an option to changes in the underlying asset's price.
Options greeks measure many characteristics of options pricing, from how fast the options price changes with respect to the price changes in the underlying asset, called delta, to the rate of decay of the option's time value, called theta.
To understand color, it is important to first understand gamma, since color is measuring how gamma will change over time.
Gamma measures the rate of change in an option's delta per one-point move in the underlying asset's price. Delta is a first derivative, gamma a second, and color a third. Color is an important trait to monitor when maintaining a gamma-hedged portfolio because it helps the trader to gauge the effectiveness of the hedge over the passage of time.
Gamma is also used when trying to gauge the price movement of an option, relative to the amount it is in or out of the money. When the option being measured is deep in or out of the money, gamma is small. When the option is near or at the money, gamma is at its largest. Gamma is also larger the closer to expiration, and smaller the further away it is from expiration.
Traders who use a gamma-hedging options trading strategy use color to capture information on the gamma of an option per year. The daily figure can be found by dividing the result by the number of days in the year.
Color provides a more reliable figure when the option is far from expiration. However, as expiration draws near, color becomes more volatile, can change intraday, and is less reliable.
Borrowing from physics, if delta is the velocity of options price movement with respect to the underlying, then gamma is the acceleration. Since the third derivative is a bit hard for non-scientists to grasp, we can move these greeks down one level. Now consider gamma to be the velocity of delta and therefore color is the acceleration of gamma.
Gamma expands as expiration draws near and color measures it. Gamma also expands as the option moves closer to at the money, and color also measures this. If gamma is small because the option is far from expiration or the underlying asset is far from the strike price, then color will reflect this.
Example of Color in Option Trading
Assume that an option has a delta of 0.65. That means that for each $1 move in the stock price, the option is expected to move $0.65, all else remaining equal.
Now assume that this option has a $10 strike price and the underlying is currently trading at $11. The stock price is going up, and soon reaches $12, putting the stock even more in the money. The delta of the stock is now 0.90.
An in the money option will also see its delta increase as the time to expiration draws nearer. In any case, for each dollar move in the stock, the option is now moving $0.90. The difference between the old delta and the new is what gamma is measuring. Gamma increased by 0.25. Note though, gamma will start to decrease the closer delta gets to one, because once delta is at 0.90 it can only increase by 0.10, which is less than what it was increasing before.
Color is an extension of gamma, measuring how much it moves over time. Color shows how much gamma is expected to change. The daily amount shows how much the gamma is expected to change each day. A color of 0.03 means gamma will fluctuate approximately 0.03 per day. A reading of 0.1 means gamma will fluctuate 0.1 per day.
As the price approaches expiration, color is more prone to rapid change and is therefore not as reliable.