مدل چرخش میکروسکوپی برای پویایی توزیع بازگشت شاخص بازار سهام کره

In this paper, we studied the dynamics of the log-return distribution of the Korean Composition Stock Price Index (KOSPI) from 1992 to 2004. Based on the microscopic spin model, we found that while the index during the late 1990s showed a power-law distribution, the distribution in the early 2000s was exponential. This change in distribution shape was caused by the duration and velocity, among other parameters, of the information that flowed into the market.

Interdisciplinary research is now routinely carried out, with econophysics being one of the most active interdisciplinary fields [1], [2], [3], [4] and [5]. Many research papers on mature markets have already been published. However, since emerging markets show different characteristics to those of mature markets, they represent an active field for econophysicists. The Korean market, one of the foremost emerging markets, has already been studied by physicists [4] and [5]. We concentrate on the particular properties of the Korean market through the return distribution. It is broadly assumed that the distribution of price changes takes the form of a Gaussian distribution, and that all information is applied to the market immediately by the efficient market hypothesis (EMH) [6]. Using the EMH, the trading profit with arbitrage cannot be obtained from the superiority of information. The price changes in an efficient market cannot be predicted and change randomly. This is suited to classical economics theory. However, experimental proofs reveal that Gaussian distributions of price changes do not exist in real markets [7] and [8]. Mandelbrot determined empirically that the tail part of the distribution is wider and the center of the distribution is sharper and higher than a Gaussian distribution by examining price changes of cotton; this distribution of price changes is termed the Lévy stable distribution [7]. Fama also found a Lévy stable distribution for the New York Stock Exchange (NYSE) [8]. After Mandelbrot's study, the distribution of price changes was identified as non-Gaussian by many researchers [9], [10], [11] and [12]. It was reported that distributions in mature markets have a power-law tail, while those in emerging markets have an exponential tail [13] and [14]. Silva et al. [11] and Vicente et al. [12] reported that the distributions of price changes vary with time lag. Price changes have a power-law distribution for a short time lag, and an exponential distribution when the time lag is long. Moreover, for a very long time lag, the distribution becomes Gaussian. Transition problem of the tail behavior was solved analytically by Dragulescu and Yakovenko [15] using a stochastic model [16]. Financial markets are adaptive evolving systems, so the distributions of price changes are also different for various periods and countries. Especially, the Korean stock market has different properties compared with other countries, and the distribution of price changes is not stable and changes with time. In this paper, we study the characteristics of the Korean stock market using probability distribution functions (PDFs) of the Korean Composition Stock Price Index (KOSPI) and investigate why phenomena different to other countries occur. We also carry out a simulation using the microscopic spin model to explain these differences.

The distribution of the KOSPI log return has recently taken the form of an exponential, while it showed a power-law tail in the 1990s. Moreover, the decay time of the autocorrelation function is continually decreasing. Thus, the duration of information received by agents is also decreasing as the amount of information increases. According to the EMH, the distribution of log return becomes Gaussian when the velocity of information flow is very fast, and all information received immediately affects the opinion of agents in the market. We could identify and confirm a relationship between the distribution of price changes, the velocity of information flow, and the duration of the influence of information for a time series of the Korean stock market. A similar phenomenon occurred in Japan around 1990, as identified from daily data [21], [22] and [23]. However, in mature markets, including the NYSE, the tail index is not increasing or changing in shape. The reason for this is the robustness and maturity of the market. Mature markets are solid enough to endure external shocks, while emerging markets are susceptible to shocks and environmental changes. Modeling of the robustness and maturity of the market is planned as further work in the near future.