What is color?
Color is an optional “Greek” that measures the rate at which gamma changes over time. Color is also known as gamma attenuation or a derivative of gamma with respect to time.
- Color measures the rate at which gamma changes over time, for example one year.
- Colors can be converted to daily quantities by dividing by the number of days in a year.
- Color is important for gamma hedging because it shows how gamma changes.
- Color measures gamma and measures the change in delta. It measures the price sensitivity of an option to changes in the price of the underlying asset.
More specifically, color is a cubic function of the value of an option, once for the price of the option and twice for the price of the option. Gamma measures changes in the delta in response to price fluctuations in one unit of the underlying asset, and delta measures how derivatives fluctuate in response to price fluctuations in the underlying asset.
The option Greek letter measures many characteristics of the option price, from the rate of change of the option price with respect to the price change of the underlying asset called the delta to the rate of time value of the option called theta.
Color measures how gamma changes over time, so it is important to understand gamma first in order to understand color.
Gamma measures the rate of change of the optional delta for each point of movement in the price of the underlying asset. Delta is the first derivative, gamma is the second derivative, and color is the third derivative. Color is an important property to monitor when maintaining a gamma hedge portfolio, as it helps traders measure the effectiveness of hedges over time.
Gamma is also used when trying to measure price fluctuations of an option by comparing it to the amount of money it is inside or outside of money. Gamma is small when the option being measured is deep in the money or outside the money. Gamma is maximized when options are nearby or costly. Gamma also increases as it approaches the expiration date and decreases as it moves away from the expiration date.
All long position options have a positive gamma and all short options have a negative gamma.
Traders who use the gamma hedge options trading strategy use color to get information about the gamma of options per year. The daily number can be calculated by dividing the result by the number of days in the year.
Colors provide a more reliable number if the option is not about to expire. However, as the expiration date approaches, the color becomes more volatile and can change during the day, making it less reliable.
Other tertiary Greek letters include the rate of change in gamma for underlying asset prices, Ultima, and Zoma.
Borrowing from physics, gamma is accelerating if Delta is the rate of movement of option prices relative to the underlying asset. Third-order derivatives are a bit difficult for non-scientists to understand, so these Greeks can be lowered by one level. Now consider gamma as the velocity of the delta. Therefore, the color is the acceleration of gamma.
As the expiration date approaches, the gamma expands and the color measures it. As the option approaches at the money, gamma also expands and color measures this. If the gamma is small because the option expires far away, or because the underlying asset is far from the strike price, the color reflects this.
Color example in options trading
Suppose the option delta is 0.65. That is, for every $ 1 of stock price movement, the price of the option is expected to move $ 0.65, and everything else remains the same.
Now assume that the strike price for this option is $ 10 and the underlying asset is currently trading at $ 11. Stock prices are rising, reaching $ 12 soon, and stock prices will rise further. The stock delta is now 0.90.
With the in-the-money option, the delta also increases as the time to maturity approaches. In any case, for every dollar the stock moves, the option moves $ 0.90. The difference between the old delta and the new delta is what gamma measures.Gamma increased by 0.25 [$0.90 – $0.65].. However, when the delta reaches 0.90, it increases by 0.10, so the gamma begins to decrease. This is because it is less than what was previously increasing.
Color is an extension of gamma that measures the amount of movement over time. The color indicates how much gamma is expected to change. The daily amount indicates how much gamma is expected to change per day. A color of 0.03 means that the gamma fluctuates by about 0.03 per day. A reading of 0.1 means that the gamma fluctuates by 0.1 per day.
As prices approach expiration, colors tend to change rapidly and therefore become less reliable.