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  年化波動率formula_1定義為物件資產的年回報率的對數值的標準差。  一般的時間長度為T(年)的一段時間內的波動率formula_2則定義為:  因此,如果一種資產(如股票)在長度為P的一段時間內,日均的對數回報率的標準差為formula_4,那麼年化波動性為  在美國,通常認為formula_6(因為美國每年有252個交易日)。因此如果某資產的formula_7,那麼就可以算出年化波動率為  當然也可依上式算出月波動率等:formula_9時,  The formula used above to convert returns or波動性measures from one time period to another assume a particular underlying model or process. These formulas are accurate extrapolations of a random walk, or Wiener process, whose steps have finite variance. However, more generally, for natural stochastic processes, the precise relationship between volatility measures for different time periods is more complicated. Some use the Lévy stability exponent α to extrapolate natural processes:  If α = 2 you get the Wiener process scaling relation, but some people believe α < 2 for financial activities such as stocks, indexes and so on. This was discovered by Benoît Mandelbrot, who looked at cotton prices and found that they followed a Lévy alpha-stable distribution with α = 1.7. (See New Scientist, 19 April 1997.) Mandelbrot's conclusion is, however, not accepted by mainstream financial 計量經濟學家。
波動性(又稱“波幅”),指金融資產在一定時間段的變化性。通常以一年內漲落的標準差來測量。 光的波動性指兩列光波在空中相遇時發生疊加,在某些區域總加強,某些區域減弱,相間的條紋或者彩色條紋的現象。 金融市場中,投資的波動性與其風險有著密切的聯絡。