Volatility describes the variability of an underlying security's returns. In options, it is commonly quoted as an annualized percentage. Historical volatility measures movement already observed; implied volatility is inferred from an option price using a pricing model. Neither specifies the direction of the next move.
Historical volatility (HV)
Historical, or realized, volatility is calculated from observed returns over a stated period. One common method takes the standard deviation of daily logarithmic returns and multiplies it by the square root of an assumed number of trading days per year, often 252.
For example, a daily standard deviation of 1.5% gives approximately 1.5% × √252 = 23.8% annualized volatility. That is a measurement under the chosen convention, not a promise about next year's movement. Different lookback windows, return definitions and annualization methods can produce different results.
Implied volatility (IV)
IV is the volatility input that makes a selected model reproduce an observed option price, given the other inputs. These normally include the underlying price, strike, time remaining, interest rates and expected dividends. The model must suit the contract's exercise and settlement terms.
A broker may calculate IV from a bid, ask, midpoint or another price estimate. Wide spreads and stale quotes can therefore make displayed IV noisy. American-style options need a model that accounts for early exercise; a plain European Black–Scholes calculation can miss that value.
| Measure | Starting point | Main limitation |
|---|---|---|
| Historical volatility | Past underlying returns over a chosen window | The past window may not represent the coming period |
| Implied volatility | Option price, contract terms and a model | Reflects pricing assumptions and market conditions, not a guaranteed forecast |
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How a volatility change affects an option
Higher IV generally increases the value of a plain long call or put when other inputs are unchanged. Vega estimates the local sensitivity. If vega is $0.12 per share per one volatility percentage point, an IV increase from 20% to 23% implies an approximate $0.36 increase per share, or $36 for a standard 100-share contract, from that change alone.
That is a local estimate, not a guaranteed fill or total profit. Vega itself changes, and the underlying price and time remaining can move simultaneously. Around earnings, a fall in IV can offset a favorable stock move.
Why strikes and expirations have different IVs
The basic constant-volatility Black–Scholes model uses one underlying volatility across strikes. This is a model assumption, not a requirement that market prices must satisfy. Applying the model separately to observed prices commonly produces different IVs by strike: a volatility skew or smile. Differences across expirations form the volatility term structure.
Compare like-for-like contracts, quote times and model inputs. High IV alone does not prove an option is overpriced, and low IV alone does not make it a bargain. Try the implied volatility calculator and read its assumptions alongside the result.
