Stock Market · Options Theory

Gamma. Delta's rate of change

If delta tells you how much an option moves per ₹1 in the underlying, gamma tells you how much the DELTA changes per ₹1 move. Gamma is the second derivative, the acceleration.

What gamma measures

Gamma = change in delta / change in underlying price

Example: ATM Nifty call has delta 0.5 and gamma 0.002.

Nifty rises 100 points. New delta = 0.5 + (0.002 × 100) = 0.7.

The option now moves ₹0.70 per point, up from ₹0.50. As the option goes more ITM, it accelerates.

> Gamma is the reason buying options has convex payoffs. Winners accelerate as they go ITM.

Where gamma is highest

• ATM options have the highest gamma
• Gamma explodes as expiry approaches for ATM options
• Deep ITM and far OTM have low gamma

Gamma and expiry risk

In the last 2–3 days before expiry, ATM options' gamma goes extreme. A 1% move in Nifty can cause ATM options to double or halve in value. This is why expiry week options trading is particularly explosive.

High gammaexplosive option price moves for ATM options near expiry

Gamma scalping

Professional option traders sometimes buy high-gamma options (ATM, near expiry) and continuously hedge delta, as the underlying moves, they lock in profits from the gamma-driven option price moves. This strategy profits from volatility itself.

Gamma for sellers

Option sellers HATE gamma. High gamma means their short option positions can move against them explosively. This is why selling options near expiry ATM is particularly dangerous. Gamma risk is maximum.

Takeaway. Gamma = how fast delta changes. ATM options have highest gamma. Near expiry, gamma explodes. ATM options become extremely sensitive to small market moves. Buyers benefit; sellers are exposed.