Gamma — the accelerator

If delta is speed, gamma is acceleration

Delta told us how fast an option moves. But delta changes as the market moves — remember how the call gained ₹58 for a 100-point move, not the ₹53 delta predicted? That's gamma at work.

Gamma = how much delta changes for a 1-point move in the underlying.

The 22400 CE (7 days, NIFTY 22,400) has gamma ≈ 0.00099. Tiny number, big effect:

1. 1

   NIFTY at 22,400

   Delta ≈ 0.53.

2. 2

   NIFTY rises 100 points

   Delta grows by about 0.00099 × 100 ≈ 0.10.

3. 3

   NIFTY at 22,500

   Delta is now ≈ 0.63. Each further point up earns you more than the last one did.

For an option buyer this is lovely: when you're right, you speed up; when you're wrong, you slow down (delta shrinks as the option goes OTM). That curve-in-your-favour is called being "long gamma".

Where gamma lives

Two things jump out:

1. Gamma is highest at the money. That's where delta is changing fastest — the option is balanced on the edge between expiring worthless and expiring with value.
2. Gamma explodes near expiry. With 30 days left, ATM gamma is about 0.00047. With 1 day left it's about 0.0026 — more than five times higher. With a day to go, a 100-point move swings an ATM call's delta from about 0.5 to 0.75 (or down to 0.27) — and in the final hours the swings are even bigger.

Look back at the delta chart in the previous lesson: the purple 1-day curve was almost a vertical cliff at the strike. A steep cliff in delta is a tall spike in gamma — two views of the same thing.

Why sellers fear expiry-day gamma

Option sellers are short gamma: the curve works against them. When the market moves against a seller, their losses grow faster and faster.