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Market volatility modeling for short time window

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  • de Mattos Neto, Paulo S.G.
  • Silva, David A.
  • Ferreira, Tiago A.E.
  • Cavalcanti, George D.C.

Abstract

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.

Suggested Citation

  • de Mattos Neto, Paulo S.G. & Silva, David A. & Ferreira, Tiago A.E. & Cavalcanti, George D.C., 2011. "Market volatility modeling for short time window," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3444-3453.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:20:p:3444-3453
    DOI: 10.1016/j.physa.2011.04.031
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    Cited by:

    1. de Mattos Neto, Paulo S.G. & Cavalcanti, George D.C. & Madeiro, Francisco & Ferreira, Tiago A.E., 2013. "An ideal gas approach to classify countries using financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(1), pages 177-183.
    2. Ramos, Antônio M.T. & Carvalho, J.A. & Vasconcelos, G.L., 2016. "Exponential model for option prices: Application to the Brazilian market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 161-168.
    3. Christoph J. Borner & Ingo Hoffmann & John H. Stiebel, 2023. "On the Connection between Temperature and Volatility in Ideal Agent Systems," Papers 2303.15164, arXiv.org.

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