Volatility (finance)

In finance, volatility (usually denoted by σ) is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market prices. Implied volatility looks forward in time, being derived from the market price of a market-traded derivative (in particular, an option). Volatility as described here refers to the actual volatility, more specifically: actual current volatility of a financial instrument for a specified period (for example 30 days or 90 days), based on historical prices over the specified period with the last observation the most recent price. actual historical volatility which refers to the volatility of a financial instrument over a specified period but with the last observation on a date in the past near synonymous is realized volatility, the square root of the realized variance, in turn calculated using the sum of squared returns divided by the number of observations. actual future volatility which refers to the volatility of a financial instrument over a specified period starting at the current time and ending at a future date (normally the expiry date of an option) Now turning to implied volatility, we have: historical implied volatility which refers to the implied volatility observed from historical prices of the financial instrument (normally options) current implied volatility which refers to the implied volatility observed from current prices of the financial instrument future implied volatility which refers to the implied volatility observed from future prices of the financial instrument For a financial instrument whose price follows a Gaussian random walk, or Wiener process, the width of the distribution increases as time increases. This is because there is an increasing probability that the instrument's price will be farther away from the initial price as time increases.