Quantitative analysis on order splitting behavior of individual traders and the long memory of the order flow.

Revealing the origin of stylized facts in financial markets is a popular research topic in econophysics. Recently, high-quality data allowed us to understand stylized facts based on microscopic observations. One such successful research was provided by Lillo et al. 2005, proposing the Lillo-Mike-Farmer (LMF) model to describe the dynamics of order-splitting traders (STs). This model explained the origin of the long-range correlation (LRC) in the order flow from the viewpoint of the order-splitting hypothesis. While the plausibility of that scenario was qualitatively verified by Toth et al. 2015, there has been no solid support of the LMF prediction at a quantitative level. In this presentation, we investigate the quantitative prediction by the LMF model through microscopic data analysis. We analyzed a large quote dataset from the Tokyo stock exchange nine years long, including the virtual server account information. We classified traders into STs and random traders and found that the metaorder size distribution submitted by STs has a power-law tail. We finally analyzed the joint distribution of two power-law exponents for the metaorder-size distribution and autocorrelation function to confirm the validity of the LMF prediction.