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What is Gamma?

By News Canvass | Jun 07, 2023


  • Gamma represents the rate of change in options delta. Delta measures the rate of change in an options price compared to its underlying asset whereas gamma measures the rate of change in options delta over a period of time.
  • Options with high gamma will be more responsive to changes in the price of the underlying asset when compared to options with low gamma.

What is Gamma?

  • Gamma represents change of delta for a unit price change in the underlying stock or index. Gamma value also range between 0 and 1.
  • Gamma are linked to whether your option is long or short in the market. Gamma is the second level measure that measures the sensitivity of changes in delta to a unit change in the underlying stock price.

Concepts of Gamma

Few concepts that are relevant in Gamma are

  1. In the Money (ITM) : Call options are said to be In the Money when the current stock price is higher than the strike price of the contract
  2. Out of the Money (OTM) : Out of the Money means when the current stock price is lower than the strike price of the contract.
  3. At the Money (ATM) : means when both the values are equal.

Put options are ITM when the strike price s higher than the ongoing stock price.

Fundamentals of Gamma

Long Gamma

  • A Long Gamma position is any option position with positive gamma exposure. A position with positive gamma indicates the positions delta will increase when the stock price rises and it decreases when the stock price falls. Call and put purchase both have positive gamma. 
  • If the trader buys the call or put the trader will have the positive gamma exposure. Gamma will be subtracted from the positions delta when the stock price declines.

Short Gamma

  • A short Gamma position is any option position with negative gamma exposure. A position with negative gamma indicates delta will decrease when the stock price rise and increases when the stock price falls. Short Call and Short put positions have negative gamma. 
  • If the trader shorts a call or a put then the trader will have negative gamma exposure. Gamma will be added from the positions delta when  the stock price declines.

Example of Gamma

  • Gamma is extremely complicated to calculate most traders use spreadsheet and specialist software. Let us understand this with simple example. Suppose an underlying asset is trading at Rs 100 and its option has a delta of 0.3 and gamma of 0.2. The gamma of an option is often represented as a percentage.
  • In this example for every 20% move in the stock’s price the delta will be adjusted by a corresponding 20%. This means for every Rs 1 increase in the price of the underlying asset will cause the delta to increase to 0.5 by adding the gamma of 0.2 to current delta of 0.3.
  • Similarly 20% decrease in price of the underlying will result in corresponding decline in delta to 0.1 by subtracting the gamma of 0.2 from the current delta of 0.3.

Formula for Gamma

Gamma =  e[d21/2 + d*t ]/[(S*σ) * √(2p*t)]


  • d1= [ln (S / K) + (r + ơ2/2) * t] / [ơ * √t]
  • d = Dividend yield of the asset
  • t = Time to the expiration of the option
  • S = Spot price of the underlying asset
  • ơStandard deviation of the underlying asset
  • K =  Strike price of the underlying asset
  • r = Risk-free rate of return

Benefits of Using Gamma

  • Gamma can be effective in risk management. It is used as a hedging strategy. It helps the portfolio managers and traders who work with very large amounts of capital that require a certain level of precision. Gamma also asks for a base for other derivative metrics.

What is Gamma Used for?

  • Option Delta measure is only valid for short period of time. Gamma provides a more precise picture of how the option delta will change over time as the underlying price changes.  Gamma requires investment in dedicated software or dedicated tools.

How to Use Gamma

There are some ways to use gamma

  1. Measuring the volatility of delta
  • A higher gamma indicates a greater potential change in delta. This simply means that the price of the option is likely to be more volatile. Essentially when making use of    delta of the probability of being in the money at expiration, gamma can show the volatility of the probability delta provides.
  1. Gamma and Long Options
  • Since Gamma Measures the rate of change of delta and delta measures the options sensitivity to the underlying, gamma can indicate how the changes in the options value can potentially accelerate. When the Gamma is high option value can accelerate when the stock moves up or down which in turn accelerates profits or losses for a long position
  1. Gamma and Short Options
  • When the gamma is high, the risk for option sellers is likely to increase. This is because a higher gamma indicates an accelerated movement of the underlying which can make options exercise drastic profit and loss swings,  Thus a short uncovered option has increased risk when the gamma is high.


  • The trader must understand the concept of gamma function because it helps in the correction of convexity problems. Delta of an option is useful for a shorter time period while gamma helps a trader over a longer time horizon as the underlying price changes.
  • It is to be noted that the value of the gamma approaches zero as the option goes either deeper into the money or deeper out of the money.  It is thus a valuable tool in helping traders forecast changes in the delta of an option or an overall position. Gamma will be larger for at the money options and goes progressively lower.
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