Volatility

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Volatility most frequently refers to the standard deviation of the continuously compounded returns of a financial instrument with a specific time horizon. It is often used to quantify the risk of the instrument over that time period. Volatility is typically expressed in annualized terms, and it may either be an absolute number or a fraction of the mean. Volatility can be traded directly in today's markets through options and variance swaps. For a financial instrument whose price follows a Gaussian random walk, or Wiener process, the volatility increases as time increases. Conceptually, this is because there is an increasing probability that the instrument's price will be farther away from the initial price as time increases. However, rather than increase linearly, the volatility increases with the square-root of time as time increases, because some fluctuations are expected to cancel each other out, so the most likely deviation after twice the time will not be twice the distance from zero.

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