Fluctuations of trading volume in a stock market

We consider the probability distribution function of the trading volume and the volume changes in the Korean stock market. The probability distribution function of the trading volume shows double peaks and follows a power law, P(V/〈V〉)∼(V/〈V〉)−αP(V/〈V〉)∼(V/〈V〉)−α at the tail part of the distribution with α=4.15(4)α=4.15(4) for the KOSPI (Korea composite Stock Price Index) and α=4.22(2)α=4.22(2) for the KOSDAQ (Korea Securities Dealers Automated Quotations), where VV is the trading volume and 〈V〉〈V〉 is the monthly average value of the trading volume. The second peaks originate from the increasing trends of the average volume. The probability distribution function of the volume changes also follows a power law, P(Vr)∼Vr−β, where Vr=V(t)−V(t−T)Vr=V(t)−V(t−T) and TT is a time lag. The exponents ββ depend on the time lag TT. We observe that the exponents ββ for the KOSDAQ are larger than those for the KOSPI.