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Implied volatility and the volatility smile
Every option has a price, and behind that price is a single number the market is really arguing about: how much is this thing going to move before expiry? That number is implied volatility. It's not measured from history — it's backed out of the price traders are actually willing to pay right now. And when you plot it across strikes, it makes a shape that shouldn't exist in theory but always does in practice.
Reading volatility backwards
An options pricing model (Black-Scholes) takes some inputs — price, strike, time, rates, and volatility — and spits out a fair option price. Flip it around: you already know the price the option is trading at, so you solve for the one input you can't observe — volatility. The answer is implied volatility (IV): the market's consensus guess at future movement, expressed in the model's language. High IV means options are expensive because big moves are expected; low IV means the market is calm.
The smile
In a perfect Black-Scholes world, IV would be the same for every strike — one flat line. It never is. Plot IV against strike and you get a smile (or, in equities, a lopsided "smirk" that's steeper on the downside): IV dips near the at-the-money strike and climbs toward the out-of-the-money wings. The market is telling you it thinks big moves are more likely than the tidy bell curve assumes — and that it fears crashes more than melt-ups.
Implied volatility is the market's bet on future movement, read out of an option's price. The smile is proof the market doesn't believe the textbook — it pays extra for the tail risk of big moves.
Why it matters
- It's a fear gauge. A steepening smile means the market is paying more for protection — often before it's obvious why.
- Same option, different "cheapness." Two options can look similarly priced yet carry very different IV; the smile tells you which strike the crowd is really crowding into.
- It feeds everything downstream — the Greeks, expected-move calculations, and the ATM straddle that markets use to price a session's likely range.
Price is what you pay; implied volatility is what you're actually buying. Once you read options in IV instead of rupees, a wall of numbers turns into a live map of what the market expects — and what it's afraid of.