Quantitative statistical analysis of order-splitting behaviour of individual trading accounts in the Japanese stock market over nine years

概要

Econophysics aims to understand the macroscopic behavior of financial markets from the underlying microscopic decision-making dynamics. In particular, the order splitting of large metaorders is one of the most important trading strategies in this literature: while traders have large potential metaorders, they split the large orders into small pieces (called child orders) to minimize market impact. This strategic behavior is believed to be important because it is a promising candidate for the microscopic origin of the long-range correlation (LRC) in the persistent order flow. Indeed, Lillo, Mike, and Farmer (LMF) [Phys. Rev. E 71, 066122 (2005)] introduced a simple microscopic model of the order-splitting traders to predict the asymptotic behavior of the LRC from the microscopic dynamics, even quantitatively. The plausibility of this scenario has been investigated by Tóth et al. [J. Econ. Dyn. Control 51, 218 (2015)] at a qualitative level. However, no solid support has been presented yet on the quantitative prediction by the LMF model in the lack of large microscopic data sets. In this paper, we have provided a quantitative statistical analysis of the order-splitting behavior at the level of each trading account. We analyze a large data set of the Tokyo stock exchange (TSE) market over nine years, including the account data of traders (called virtual servers). The virtual server is a unit of trading accounts in the TSE market, and we can effectively define the trader IDs by an appropriate preprocessing. We apply a strategy clustering to individual traders in terms of market orders to identify the order-splitting traders and the random traders. The length distribution of metaorders is empirically estimated for each stock every year. For most of the stocks, we find that the metaorder length distribution obeys power laws with exponent α, such that P(L)∝L^−α−1 with the metaorder length L, as theoretically assumed in the LMF model. By analyzing the sign correlation of order flow C(τ)∝τ^−γ, we draw the scatterplot between α and γ, directly confirming the LMF prediction γ≈α−1. Furthermore, we discuss how to estimate the total number of splitting traders only from public data via the autocorrelation function prefactor formula in the LMF model. Our work provides quantitative evidence of the LMF model, strongly supporting the order-splitting hypothesis as the origin of LRC.

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