Understanding Gamma: The key to making profitable options trades

Having got a proper grip of Delta, let us now proceed to understand Gamma which is one of the Greeks. It is one of the ‘options Greeks’ along with Delta, rho, Theta and Vega. Delta is how much an option’s premium (price) will change given a one-point move in the underlying asset's price. Gamma describes the rate of change in an option’s Delta per one-point move in the underlying asset’s price. Therefore, Gamma is a measure of how the rate of change in option’s price along with fluctuations in the underlying price. The higher the Gamma, the more volatile the price of the option is.

Gamma is an important measure of the convexity of a derivative’s value in relation to the underlying asset. It helps assess the different types of risk in options portfolios.

Key points of Gamma

• Gamma is the rate of change for an option's delta based on a single point move in the delta's price.

• If Delta is the first order derivative of premium, Gamma is the second order derivative of premium.

• Gamma is at its highest when an option is at the money and is at its lowest when it is further away from the money.

• Gamma is also highest for options closer to expiry.

• Gamma is used when trying to gauge how movements in the underlying asset will affect an option's moneyness.

• Delta-gamma hedging immunizes an options position against moves in the underlying asset.

Let us consider an example for better understanding.

Nifty Spot = 19530; Strike = 19600; Option type = CE; Moneyness of option = Slightly OTM; Premium = Rs 54; Delta = 0.37; Gamma = 0.0018; Change in spot = 70 points; New spot price = 19530 + 70 = 19600.

Now let’s see what the new delta would be, new premium and new moneyness, let’s figure this out –

Change in Premium = Delta * change in spot 0.37 * 70 = 25.9 (round it to 26); New premium = 54+26 =80.

Rate of change of delta = 0.0018 units for every 1point change in underlying; Change in delta = Gamma * Change in underlying i.e 0.0018*70 = 0.126; New Delta = Old Delta + Change in Delta i.e 0.37 + 0.126 = 0.496.

New Moneyness = ATM

When Nifty moves from 19530 to 19600, the 19600 CE premium changed from Rs 54 to Rs 80, and along with this the Delta changed from 0.37 to 0.496.

Observe that with the change of 70 points, the option transitions from slightly OTM to ATM option. Which means the option’s delta must change from 0.3 to somewhere close to 0.5. This is exactly what’s happening here.

(The author is a homemaker, who dabbles in stock market investments in free time)