Agent-based approaches to price dynamics of the Korean stock market

Abstract

We study the temporal evolution of the return distribution of the Korean Composite Stock Price Index (KOSPI) for the period from 1995 to 2003. The distribution become narrower to exponential and eventually to Gaussian with elapsing time as well as increasing time horizon (lag) of returns. This behavior shows that the time scale of the Korean stock market have decreased significantly since the Asian financial crisis in 1997. We have applied the Heston model with stochastic volatility to describe the exponential-to-Gaussian crossover. We explore this crossover phenomenon as the anomalous diffusion process. By solving Fokker-Planck equation with piecewise linear and quadratic diffusion coefficients numerically, the crossover phenomena from power-law and exponential tail to Gaussian distribution are reproduced. We also presented some computational experiments performed in an agent-based artificial stock market where a limit order book is employed as price formation mechanism. The effects of informed trader behavior with splitting orders and price limits on daily price movement are explored by this model.