Preliminary Study on the Fluctuations of Daily Returns in Stock Market Based on Phase Transition Theory

Summary

To examine the state dependence of price fluctuations in a stock market, activity, which is defined as the product of averaged price and total volume of shares, is considered. Changes of daily returns are divided into high and low activity periods, and measure the probability distribution of fluctuations in each activity. It is found that the price fluctuation shows strong dependence on the activity; fluctuation is large in a high-activity state. Time evolution of the fluctuation is also studied An abrupt change in activity induces the steep increase of price fluctuation. Considering the dynamics of fluctuation as a relaxation process after an abrupt disturbance, the relaxation time is estimated from the plot of In σ²versus time. The Fokker-Planck equation is applied to conceive the non-linear effects on the relaxation process.