Volatility and the bell curve

Two roads to the same city

Imagine two stocks, both at ₹1,000 today and both at ₹1,000 a month later. One moved ₹5 a day, calmly. The other jumped ₹40 up, ₹35 down, ₹50 up… every day. Same start, same end — very different rides.

Volatility measures the size of the bumps. It doesn't say which direction — only how much things swing.

Why does an option trader care? Because an option is a bet on reaching a price. A jumpy market is more likely to reach far-away strikes, so options on jumpy things cost more.

Measuring it: standard deviation

Volatility is the standard deviation of daily percentage moves, scaled up to a year:

1. 1

   Take daily % changes

   e.g. +0.6%, −1.1%, +0.3%, −0.4%, +0.9%… for the last few months.

2. 2

   Find their standard deviation

   Say it comes out to 0.8% — a "typical" daily move.

3. 3

   Scale to a year

   Multiply by √252 (trading days in a year ≈ 15.9). 0.8% × 15.9 ≈ 12.7% annual volatility.

That's historical volatility — what the market actually did.

Implied volatility: what the market expects

There's a second kind. Option prices are set by buyers and sellers. If you take an option's market price and ask "what volatility would make the pricing model spit out this price?", you get implied volatility (IV) — the market's expectation of future bumpiness.

India VIX is simply NIFTY's 30-day implied volatility. India VIX at 13 means the options market expects NIFTY to move with about 13% annual volatility. VIX at 25 means fear is high and options are expensive.

The bell curve: turning % into points

Here's the useful bit. If daily moves are roughly random, the place NIFTY ends up after some days spreads out like a bell curve (a normal distribution). And bell curves follow a famous rule:

• About 68% of outcomes land within 1 standard deviation (1σ) of today.
• About 95% land within 2σ.
• About 99.7% land within 3σ.

To get 1σ in points for any period:

1σ = spot × volatility × √(days ÷ 365)

NIFTY at 22,400, IV 13%, 30 days: 22,400 × 0.13 × √(30/365) ≈ 835 points.

≈68% chance: 21,565 – 23,235

≈95% chance: 20,730 – 24,070

≈99.7% chance: 19,895 – 24,905

So, according to the options market, there's about a 68% chance NIFTY is between 21,565 and 23,235 in 30 days, and about a 95% chance it's between 20,730 and 24,070.

Why traders love this

Picking strikes to sell. A seller who wants high odds might sell options beyond 2σ — strikes the market thinks have only about a 2.5% chance of being reached on each side.

Sanity-checking a buy. If you buy the 23,300 call expiring in a week, 1σ for 7 days is only about 22,400 × 0.13 × √(7/365) ≈ 403 points. You're betting on a move of more than 2σ in a week — possible, but you now know it's a long shot.