Volatility, from first principles

Volatility is one word doing eight different jobs. Before any of the rest of this site makes sense, you need to know which volatility a sentence is talking about — because historical volatility, implied volatility and realised volatility can be three very different numbers on the same afternoon, about the same index, and every one of them is correct.

What is core volatility? Core volatility is the family of measures that quantify how much an asset's price moves, expressed as an annualised standard deviation of its returns. The family splits by what data it is computed from: historical and realised volatility look backward at prices that already happened, implied volatility is extracted forward from option prices, and expected and forward volatility are statements about periods that have not begun.

What is Volatility?

What is Volatility? At its core it is the annualised standard deviation of an asset's returns — a measure of how far price typically strays from its own p…

Dispersion of returns Beginner →

Historical Volatility

Historical Volatility is the annualised standard deviation of an asset's past close-to-close log returns over a chosen window — a purely backward-looking …

Past dispersion, close-to-close Beginner →

Realized Volatility

Realized Volatility is the volatility an asset actually delivered over a past period, measured from its realised price path — the quantity an option selle…

What the market actually did Intermediate →

Implied Volatility

Implied volatility is the volatility figure that, when fed into an option pricing model, makes the model output the option's current market price exactly …

The volatility an option's price implies Beginner →

Expected Volatility

Expected volatility is a forecast of how much an asset will move over a future period, produced by a statistical model from the return history — which mak…

A forecast of future dispersion Intermediate →

Forward Volatility

Forward volatility is the volatility the option market implies for a future window between two dates T1 and T2, extracted from the two spot implied volati…

Volatility of a future window Advanced →

Annualized Volatility

Annualized volatility is a short-period volatility rescaled to a one-year horizon by multiplying by the square root of the number of periods in a year, be…

Volatility rescaled to one year Beginner →

Intraday Volatility

Intraday volatility is the dispersion of an asset's returns measured within a single trading session, revealing a U-shaped pattern — violent at the open, …

Dispersion within a single session Intermediate →

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Frequently asked questions

What is core volatility?

Core volatility is the family of measures that quantify how much an asset's price moves, expressed as an annualised standard deviation of its returns. The family splits by what data it is computed from: historical and realised volatility look backward at prices that already happened, implied volatility is extracted forward from option prices, and expected and forward volatility are statements about periods that have not begun.

How many core volatility pages does VolatilityGyan have?

VolatilityGyan documents 8 concepts under Core Volatility, each with a plain-English definition, a professional explanation, the formula with every variable defined, an original diagram, worked NIFTY examples, its limitations, common mistakes and at least twenty frequently asked questions.

Where should I start with core volatility?

Start with What is Volatility?. What is Volatility? At its core it is the annualised standard deviation of an asset's returns — a measure of how far price typically strays from its own path, which says how much a market moves and deliberately nothing about which direction it moves.