Futures & Options

A Glance At Gamma2 min read

May 19, 2021 2 min read
gamma option greek

A Glance At Gamma2 min read

Reading Time: 2 minutes

What Is Gamma?

As Delta changes with underlying price, Gamma is used to measure the rate of change of Delta. Gamma is the second derivative of the change in option price w.r.t change in the price of the underlying. In simpler words, one can use Gamma to help predict changes in the Delta of an option and to help assess the stability of Delta.

How Does Gamma Vary?

What is the Gamma of a call of strike Rs. 100? When the underlying price is closer to 0, the Gamma tends to 0. When the underlying price is closer towards infinity i.e. a very large number compared to Rs. 100 for example Rs. 1000, Gamma tends towards 0. However, when the underlying price is near 100, Gamma is greater than 0 and is at its highest when options are at-the-money.

Additionally, Gammas for ATM options decrease with increasing strike prices.

How Does Gamma Vary With Time to Expiry?

Gamma stays near 0 for deep OTM and ITM options throughout time. For an ATM option, Gamma approaches towards 0 when away from expiry but it is greater than 0 when expiry comes closer.

How Does Gamma Of A Call Vary with Volatility?

For a deep ITM and OTM call option, the Gamma stays near 0 for any volatility. Gamma for an ATM option is greater than 0 for low volatility and closer to 0 for high volatility.

Let’s Understand Gamma With An Example

We have a stock with the price at Rs. 450 and a Rs. 560 call priced at Rs. 10. Let’s assume that the option has a delta of 0.40 and a gamma of 0.01.

When the stock price increases to Rs. 451, this is what happens:

  • Option price moves by 0.40* Rs. 1 = Rs. 0.40 (delta multiplied by the difference in price). The new price of the call option becomes Rs. 10 + Rs. 0.40 = Rs. 10.40.
  • And delta becomes 0.40 + 0.01 = 0.41 (delta increases by the extent of the gamma).

 

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