Market volatility modeling for short time window

The gain or loss of an investment can be defined by the movement of the market. This movement can be estimated by the difference between the magnitudes of two stock prices in distinct periods and this difference can be used to calculate the volatility of the markets. The volatility characterizes the sensitivity of a market change in the world economy. Traditionally, the probability density function (pdf) of the movement of the markets is analyzed by using power laws. The contributions of this work is two-fold: (i) an analysis of the volatility dynamic of the world market indexes is performed by using a two-year window time data. In this case, the experiments show that the pdf of the volatility is better fitted by exponential function than power laws, in all range of pdf; (ii) after that, we investigate a relationship between the volatility of the markets and the coefficient of the exponential function based on the Maxwell–Boltzmann ideal gas theory. The results show an inverse relationship between the volatility and the coefficient of the exponential function. This information can be used, for example, to predict the future behavior of the markets or to cluster the markets in order to analyze economic patterns.