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Realised volatility

Volatility measured from what prices actually did, as opposed to the implied volatility priced into options. Usually an annualised standard deviation of returns.

The standard recipe: take daily log-returns, compute their standard deviation over a window, multiply by sqrt(252) to annualise. A 20-day standard deviation of 0.85% gives 0.85 x sqrt(252) = 13.5% annualised.

The window is a genuine trade-off, not a detail. Ten days reacts fast and is noisy; 100 days is stable and slow. Comparing a 10-day realised number with a 30-day implied number is comparing different things, which is how people convince themselves options are cheap when they are not.

All estimators here assume returns are independent and that the mean is roughly zero over the window. Both are fine over short horizons and both break down over long ones, which is why realised volatility over a year is a weak forecast of the next year.

Related: close-to-close-volatility, parkinson-volatility, ewma, volatility-targeting

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