Volatility
Historical Volatility (HV)
Also called: realized volatility, statistical volatility, RV
Historical volatility is the annualized standard deviation of an underlying's past returns over a set window, such as 20 or 30 trading days. It measures how much the price actually moved, in contrast to implied volatility, which measures how much option prices expect it to move.
HV is computed from daily log returns: take their standard deviation over the window and multiply by √252 to annualize. A 20-day HV of 25% means daily closes have recently been moving with roughly a 1.6% one-standard-deviation change.
The IV–HV spread is a core volatility-trading input. When IV sits well above HV, options are pricing more movement than the stock is delivering, and short-premium strategies collect the difference if the gap holds. When HV exceeds IV, options have been underpricing realized movement.
Formula
HV = stdev( ln(P_t / P_t−1) ) over N days × √252
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Frequently asked questions
Why is implied volatility usually higher than historical volatility?
Option sellers demand compensation for the risk of sudden large moves, so IV carries a volatility risk premium over realized volatility most of the time. The premium widens into events and narrows in calm markets.
What window should I use for historical volatility?
Match it to the option you trade: 20–30 days for monthly options, longer windows for LEAPS. Short windows react quickly but are noisy.