Historic what does volatile mean measures a time series of past market prices. For a financial instrument whose price follows a Gaussian random walk, or Wiener process, the width of the distribution increases as time increases.
Since observed price changes do not follow Gaussian distributions, others such as the Lévy distribution are often used. These can capture attributes such as “fat tails”. For any fund that evolves randomly with time, the square of volatility is the variance of the sum of infinitely many instantaneous rates of return, each taken over the nonoverlapping, infinitesimal periods that make up a single unit of time. Thus, “annualized” volatility σannually is the standard deviation of an instrument’s yearly logarithmic returns.
252 trading days in any given year. The formulas used above to convert returns or volatility 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. Much research has been devoted to modeling and forecasting the volatility of financial returns, and yet few theoretical models explain how volatility comes to exist in the first place. In today’s markets, it is also possible to trade volatility directly, through the use of derivative securities such as options and variance swaps. Volatility does not measure the direction of price changes, merely their dispersion.
It is common knowledge that types of assets experience periods of high and low volatility. That is, during some periods, prices go up and down quickly, while during other times they barely move at all. This is termed autoregressive conditional heteroskedasticity. Whether such large movements have the same direction, or the opposite, is more difficult to say.
8th time since 1974 at this reading in the summer of 2014. Some authors point out that realized volatility and implied volatility are backward and forward looking measures, and do not reflect current volatility. To address that issue an alternative, ensemble measure of volatility was suggested. This measure is defined as the standard deviation of ensemble returns instead instead of time series of returns.
There exist several known parametrisation of the implied volatility surface, Schonbucher, SVI and gSVI. Using a simplification of the above formula it is possible to estimate annualized volatility based solely on approximate observations. Suppose you notice that a market price index, which has a current value near 10,000, has moved about 100 points a day, on average, for many days. The average magnitude of the observations is merely an approximation of the standard deviation of the market index. Realistically, most financial assets have negative skewness and leptokurtosis, so this formula tends to be over-optimistic.
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