There are four Greeks of Options. These are Delta, Gamma, Vega and Theta.
In this article we will discuss about Gamma and its effect on Options Prices.
Gamma is the derivative of Delta. It measures the rate of change of delta in relation to the change in the price of the underlying instrument such as stock. Gamma is expressed as a percentage. In other words it is the rate of change of the rate of change (Delta). In simple terms, how fast delta changes with respect to the underlying price.
Gamma is constantly moving up and down in relation to underlying stock price. Gamma helps options trader in figuring out (indirectly) how much he/she will gain or lose in option based on the movement of the stock since gamma effects delta.
Gamma value is close to zero for deep in-the-money or way out-of-the money options. Similarly gamma is highest for at-the-money options.
Lets’ say stock XYZ is trading near $38 and October 40 Call option is selling for $2.
Lets’ also assume that October 40 call option has a delta of 0.50 and a gamma of 0.10 which is equivalent to 10 percent. Lets’ assume that XYZ moves to $39. This means delta will move to 0.55 (increase of 10%) and if XYZ moves to $37 then delta will move to 0.45 (decrease of 10%).
As the option approaches expiry date the gamma of at-the-money options increases while the gamma of in-the-money and out-of-the money options decreases.
How Volatility Affects Gamma
Besides the effect of time on the value of gamma, volatility also has the effect on gamma which in turn effects the change in delta of the option.
Effect of Low Volatility in Gamma
When volatility is low the gamma of at-the-money options is high.
When volatility is low the gamma of way out-of-the-money and deep-in-the-money options is close to zero.
Effect of High Volatility in Gamma
When volatility is high the gamma of all options strikes prices are stable and do not fluctuate as much.
In the Black-Scholes model in the equation for the calculation of gamma the volatility is the part of the denominator. Since volatility is in the denominator, therefore, when volatility increases the gamma decreases and vice-versa.