We study the statistical properties of volatility---a measure of how much the market is likely to fluctuate. We estimate the volatility by the local average of the absolute price changes. We analyze (a) the S&P 500 stock index for the 13-year period Jan 1984 to Dec 1996 and (b) the market...

We study the volatility of the S&P500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log-normal function. Further, using detrended fluctuation analysis we show that the volatility is power-law correlated with Hurst exponent $\alpha\cong0.9$.

We analyze the fluctuations in the gross domestic product (GDP) of 152 countries for the period 1950--1992. We find that (i) the distribution of annual growth rates for countries of a given GDP decays with ``fatter'' tails than for a Gaussian, and (ii) the width of the distribution scales as a...

We study the distribution of fluctuations over a time scale $\Delta t$ (i.e., the returns) of the S&P 500 index by analyzing three distinct databases. Database (i) contains approximately 1 million records sampled at 1 min intervals for the 13-year period 1984-1996, database (ii) contains 8686...

It is commonly believed that the correlations between stock returns increase in high volatility periods. We investigate how much of these correlations can be explained within a simple non-Gaussian one-factor description with time independent correlations. Using surrogate data with the true...

The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period Jan 1994 -- Dec 1995. A sample of 40 million data points is extracted, which is...

We analyze daily prices of 29 commodities and 2449 stocks, each over a period of $\approx 15$ years. We find that the price fluctuations for commodities have a significantly broader multifractal spectrum than for stocks. We also propose that multifractal properties of both stocks and commodities...

We investigate the two components of the total daily return (close-to-close), the overnight return (close-to-open) and the daytime return (open-to-close), as well as the corresponding volatilities of the 2215 NYSE stocks from 1988 to 2007. The tail distribution of the volatility, the long-term...

We address the question of how stock prices respond to changes in demand. We quantify the relations between price change $G$ over a time interval $\Delta t$ and two different measures of demand fluctuations: (a) $\Phi$, defined as the difference between the number of buyer-initiated and...

We analyze the memory in volatility by studying volatility return intervals, defined as the time between two consecutive fluctuations larger than a given threshold, in time periods following stock market crashes. Such an aftercrash period is characterized by the Omori law, which describes the...