Volatility quantifies how much an asset's price moves. Most commonly, it is measured as the standard deviation of returns over a window, annualized. Higher volatility means bigger and more frequent price swings (up and down). It is symmetric: a volatile asset is not necessarily falling, just moving a lot. Implied volatility, derived from option prices, is the market's forward-looking expectation; realized volatility is what actually happened.
Calculating realized volatility: take the log returns of daily prices over N days, compute the standard deviation, multiply by sqrt(252) to annualize. A stock with 20% annualized volatility has typical daily moves of about 1.25% (sigma divided by sqrt of trading days per year). Crypto often runs at 60-100% annualized; equities usually 15-30%.
Implied volatility comes from solving the Black-Scholes model in reverse: given current option prices, what volatility makes the model match? VIX is the most famous implied-vol index, derived from S&P 500 option prices.
Volatility is the input to risk management. Position sizing, options pricing, value-at-risk calculations, and stop-loss placement all depend on volatility estimates. Misjudging volatility is one of the most common sources of trader blow-ups.
The BTC volatility alert endpoint tracks realized volatility for Bitcoin and fires alerts on >=3% one-hour moves. The correlation matrix endpoint shows how volatility relates across assets.