What is Gamma? The Acceleration of Option Price Changes
Using the gear analogy, the transmission ratio between a stock and an option is Delta. The transmission ratio between a stock and Delta is Gamma. Therefore, Gamma describes the acceleration of changes in an option's value.
Gamma indicates how much an option's Delta changes for every $1 change in the stock price (assuming all other factors remain constant). For example, if Gamma = 0.03, it means that when the stock price rises or falls by $1, the option’s Delta will increase or decrease by 0.03.
Since Delta represents the sensitivity of the option price to stock price changes, a change in Delta further amplifies the movement of the option price:
Assume an initial Delta of 0.57. If the stock price increases by $1, Delta becomes 0.57 + 0.03 = 0.61. If the stock price moves another $1 in the future, the option price change will increase from $0.57 to $0.61. The option is accelerating.
Conversely, if the stock price decreases by $1, Delta becomes 0.57 - 0.03 = 0.54. A future $1 move in the stock price would result in the option price changing less, from $0.57 to $0.54. The option is decelerating.
How to Interpret Positive and Negative Gamma?
In the examples above, the Gamma readings were all positive, but negative Gamma is also a possibility.
Positive Gamma: Buying an option position has positive Gamma. With positive Gamma, stock price and Delta move in the same direction. If the stock price rises, Delta increases; if it falls, Delta decreases.
Negative Gamma: Selling an option position has negative Gamma. With negative Gamma, stock price and Delta move in opposite directions. If the stock price rises, Delta decreases; if it falls, Delta increases.
Applying this concept to all four types of option positions leads to the following conclusions:
Buying Options (Positive Gamma): When the price moves in your favor, the position profits accelerate. When the price moves against you, the position’s losses decelerate.
Selling Options (Negative Gamma): When the price moves in your favor, the position profits decelerate. When the price moves against you, the position’s losses accelerate.
An analogy: Positive Gamma when buying options adds "icing on the cake," while negative Gamma when selling options is like "kicking you when you’re down."
The Relationship Between Time, Price, and Gamma
Gamma readings are highest near at-the-money (ATM) options, while they decrease for both deep in-the-money (ITM) and out-of-the-money (OTM) options. This means that ATM options have the highest Delta sensitivity to stock price changes, causing even small price movements to result in significant option price changes.
As expiration approaches:
For options near the ATM region, the Gamma curve steepens, and Gamma readings increase.
For deep ITM or OTM options, the Gamma curve flattens, and Gamma readings approach zero.
This implies that as expiration nears, ATM options experience extreme price fluctuations, significantly impacting profits and losses. Meanwhile, Gamma has minimal influence on deeply ITM or OTM options.
Is a Sudden Increase in Gamma a Good Thing?
For positive Gamma positions, some may see higher Gamma readings as an opportunity for parabolic profit growth when prices move in their favor. However, don't forget that if the price moves against you, losses will also escalate at a parabolic rate.
For this reason, monitoring Gamma and controlling Delta sensitivity risk is crucial for conservative investors—unless you have a strong rationale for taking on Gamma risk.
How to Eliminate Gamma Risk? Close the position early.
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