## Gamma And Volatility

**Gamma with respect to change in volatility:**

When volatility is low, the Gamma of At-the-money (ATM) options is high, while the Gamma for deep In-the-money (ITM) or Out-of-the-money (OTM) options approaches 0. This phenomenon arises because when volatility is low, the time value of such options is low, but it goes up dramatically as the underlying stock price approaches the strike price.

When volatility is high, Gamma tends to be stable across all strike prices. This is due to the fact that when volatility is high, the time value of deep In or Out-of-the-money options is already quite substantial. Thus, the increase in the time value of these options as they move nearer to At-the money will be less dramatic and hence the low and stable Gamma.

Keeping constant, the strike 16500, spot at 16500 and days to expiry 17, let us calculate how changes in volatility changes the gamma of an option.

As volatility increases, there will be an increase in the price of the options and vice versa. Thereby, we can see that as volatility decreases, call Delta decreases and put Delta increases.

The Gamma too increases. High Gamma values mean that the option tends to experience volatile swings.

**GAMMA WITH RESPECT TO CHANGE IN RATE OF INTEREST RATE**

Strike 16500 spot 16500 days to expiry 17 Volatility 17%

As the interest rate decreases, we can find Gamma increasing for the ATM call and put.