Volatility
Quantitative Finance glossary · Derivatives Pricing & Volatility Surfaces
Definition
Annualised standard deviation of (log-)returns: σ_ann = σ_daily,√(252) under the iid assumption. Distinguish (i) realised vol from historical data (close-to-close, Parkinson, Garman-Klass, Yang-Zhang estimators progressively use intraday range), (ii) implied vol from option prices, (iii) instantaneous vol σ_t from stochastic-vol models. The three are not equal and their differences (variance risk premium = realised - implied) is itself a tradeable risk premium.
Volatility in plain English
Volatility measures how jumpy a price is — how much it bounces around, not which direction it's heading. Technically it's the standard deviation of returns (a stat for how spread-out the day-to-day changes are), scaled up to a yearly number by multiplying by √(252) since there are about 252 trading days in a year. The subtle thing is there are three flavors that rarely agree: volatility you measure looking backward at what actually happened, volatility the option market is pricing in for the future, and the true moment-to-moment wiggle. That gap matters — the difference between what the market fears and what actually happens is itself something traders bet on, like the spread between an insurance premium and the claims that really come in.
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