Abstract
Being able to quantify the probability of large price changes in stock markets is of crucial importance in understanding financial crises that affect the lives of people worldwide. Large changes in stock market prices can arise abruptly, within a matter of minutes, or develop across much longer time scales. Here, we analyze a dataset comprising the stocks forming the Dow Jones Industrial Average at a second by second resolution in the period from January 2008 to July 2010 in order to quantify the distribution of changes in market prices at a range of time scales. We find that the tails of the distributions of logarithmic price changes, or returns, exhibit power law decays for time scales ranging from 300 seconds to 3600 seconds. For larger time scales, we find that the distributions tails exhibit exponential decay. Our findings may inform the development of models of market behavior across varying time scales.
Highlights
Complex movements in stock market prices affect the personal fortunes of people around the globe [1,2,3,4,5]
For all 30 stocks, we retrieve price time series with a second by second resolution from the Trade and Quote (TAQ) database provided by Wharton Research Data Services (WRDS)
As five stocks were replaced during this period, we focus on the 25 components that were consistently part of the Dow Jones Industrial Average (DJIA) between 02 January 2008 and 30 July 2010
Summary
Complex movements in stock market prices affect the personal fortunes of people around the globe [1,2,3,4,5]. A vast amount of data on financial decisions made in stock markets is available [25,26,27,28,29]. Previous studies have shown that distributions of returns observed in empirical data are consistent with power law decay [30,31,32,33,34,35,36,37,38,39,40,41,42], in contrast with widely used models that assume Gaussian behavior of these returns. Power law behavior has been observed in other economical and financial sectors of society [43, 44]
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