⚡ Gamma: The Accelerator That Drives Your Option Price Changes

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If $\Delta$ is your car’s speed, then Gamma ($\Gamma$) is your acceleration. Gamma is the rate of change of Delta.

Gamma is a highly important, yet often misunderstood, Greek because it explains why an option’s price sensitivity isn’t fixed.

What Gamma Measures

$\Gamma$ measures how much an option’s $\Delta$ will change for every $1 move in the underlying stock price.

  • Example: A call option has a $\Delta$ of 0.50 and a $\Gamma$ of 0.10. If the stock price rises by $1.00, the option’s $\Delta$ instantly increases to 0.60 ($0.50 + 0.10$). If the stock price falls by $1.00, the $\Delta$ instantly decreases to 0.40 ($0.50 – 0.10$).

This non-linear change is what makes option trading so leveraged and why Gamma is the ultimate risk metric.

The Gamma Curve: Where Risk is Highest

Gamma is not uniformly distributed across strikes. It follows a highly concentrated curve:

  1. Maximum Gamma: $\Gamma$ is always highest for options that are At-The-Money (ATM). These are the options where the probability of finishing ITM is balanced (near 50%), meaning small stock moves have the largest impact on that probability.
  2. Zero Gamma: $\Gamma$ approaches zero for options that are deep ITM or deep OTM, as their $\Delta$ is already near 1.00 or 0.00 and has little room left to change.

Gamma Risk and the Trader

  • Long Options (Buying Calls/Puts): You have positive Gamma. This is good! When the stock moves in your favor, your $\Delta$ increases, meaning your option gains more speed and makes more money faster.
  • Short Options (Selling Calls/Puts): You have negative Gamma. This is dangerous! When the stock moves against you, your $\Delta$ increases, causing your option to rapidly accelerate its losses. This is why selling ATM options close to expiration is extremely high-risk.

Gamma and Expiration

Gamma behaves aggressively as expiration approaches. For ATM options, $\Gamma$ spikes sharply during the last week of trading. This means the $\Delta$ of that option can swing from 0.50 to 0.90 (or 0.10) with minimal stock movement, creating a Gamma Risk known as the “pinning risk” right before expiration.

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