Zipf's law distributions in Korean financial markets

We investigate the rank distribution and the cumulative probability for stock prices, and the probability density of price returns for stocks traded the Korean Stock Exchange (KSE) and the Korean Securities Dealers Automated Quotations (KOSDAQ) market. We show that the upper tails of the distributions can be fitted with a power-law and find that, the rank distribution scales approximately as a, power law with exponents alpha = -0.99 (p -> small) and -1.33 (p -> large) for the KSE and alpha = -1.31 for the KOSDAQ These values are similar to those of stock prices traded on the Tokyo Stock Exchange (TSE). In addition, the cumulative probability distribution follows a power law with the scaling exponent beta = -1.23 (KSE) or -1.45 (KOSDAQ). In particular, the evidence shows that the probability density of normalized price returns for two kinds of assets almost has the form of an exponential function, which is similar to the result for the TSE and the New York Stock Exchange (NYSE).