Gamma - Γ

• Gamma measures delta's sensitivity to changes in the stock price, in other words "the speed of speed" or acceleration of the options position.
  
  

  Gamma =

  rate of change in delta rate of change in underlying asset price

• By knowing the gamma of an option, we know how quickly the delta will change and how quickly we should adjust our position in advance of this.
• Gamma is significant because it helps the trader measure risk, particularly for delta neutral traders.  Gamma effectively shows us how quickly the odds change of the option expiring in the money. 
• Gamma tends to be large when the option is near the money (NTM).  This means that the delta is highly sensitive (when the option is NTM) to changes in the stock price.  In other words the odds of the option changing from being OTM to ITM or vice versa are high.  Therefore, it is logical that ATM options have higher gammas.
• When options are deep in the money (DITM), the delta is close to 1 and is not too sensitive itself to changes in the underlying asset price.  Therefore, the gamma of DITM options is low.
• Similarly, gamma is low for deep out of the money (DOTM) options.
• The gamma for puts and calls is always identical and can be positive or negative.
  
  

  Underlying Asset Price	Delta	Gamma
  ATM	Around 0.5	High
  NTM	Around 0.5	High
  Deep ITM	Around 1 (high)	Low
  Deep OTM	Low	Low