1,219 research outputs found
Exact solution to a generalised Lillo-Mike-Farmer model with heterogeneous order-splitting strategies
The Lillo-Mike-Farmer (LMF) model is an established econophysics model
describing the order-splitting behaviour of institutional investors in
financial markets. In the original article (LMF, Physical Review E 71, 066122
(2005)), LMF assumed the homogeneity of the traders' order-splitting strategy
and derived a power-law asymptotic solution to the order-sign autocorrelation
function (ACF) based on several heuristic reasonings. This report proposes a
generalised LMF model by incorporating the heterogeneity of traders'
order-splitting behaviour that is exactly solved without heuristics. We find
that the power-law exponent in the order-sign ACF is robust for arbitrary
heterogeneous intensity distributions. On the other hand, the prefactor in the
ACF is very sensitive to heterogeneity in trading strategies and is shown to be
systematically underestimated in the original homogeneous LMF model. Our work
highlights that the ACF prefactor should be more carefully interpreted than the
ACF power-law exponent in data analyses.Comment: 16 pages,4 figure
Can we infer microscopic financial information from the long memory in market-order flow?: a quantitative test of the Lillo-Mike-Farmer model
In financial markets, the market order sign exhibits strong persistence,
widely known as the long-range correlation (LRC) of order flow; specifically,
the sign correlation function displays long memory with power-law exponent
, such that for large time-lag .
One of the most promising microscopic hypotheses is the order-splitting
behaviour at the level of individual traders. Indeed, Lillo, Mike, and Farmer
(LMF) introduced in 2005 a simple microscopic model of order-splitting
behaviour, which predicts that the macroscopic sign correlation is
quantitatively associated with the microscopic distribution of metaorders.
While this hypothesis has been a central issue of debate in econophysics, its
direct quantitative validation has been missing because it requires large
microscopic datasets with high resolution to observe the order-splitting
behaviour of all individual traders. Here we present the first quantitative
validation of this LFM prediction by analysing a large microscopic dataset in
the Tokyo Stock Exchange market for more than nine years. On classifying all
traders as either order-splitting traders or random traders as a statistical
clustering, we directly measured the metaorder-length distributions
as the microscopic parameter of the LMF model and
examined the theoretical prediction on the macroscopic order correlation:
. We discover that the LMF prediction agrees with
the actual data even at the quantitative level. Our work provides the first
solid support of the microscopic model and solves directly a long-standing
problem in the field of econophysics and market microstructure.Comment: 4 pages, 4 figure
Quantitative statistical analysis of order-splitting behaviour of individual trading accounts in the Japanese stock market over nine years
In this research, we focus on the order-splitting behavior. The order
splitting is a trading strategy to execute their large potential metaorder into
small pieces to reduce transaction cost. 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, in 2005,
Lillo, Mike, and Farmer (LMF) introduced a 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 qualitatively investigated by Toth et al. 2015. However, no solid
support has been presented yet on the quantitative prediction by the LMF model
in the lack of large microscopic datasets. In this report, we have provided the
first quantitative statistical analysis of the order-splitting behavior at the
level of each trading account. We analyse a large dataset 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 to identify
the order-splitting traders and the random traders. For most of the stocks, we
find that the metaorder length distribution obeys power laws with exponent
, such that with the metaorder length .
By analysing the sign correlation , we directly
confirmed the LMF prediction . Furthermore, we discuss
how to estimate the total number of the splitting traders only from public data
via the ACF prefactor formula in the LMF model. Our work provides the first
quantitative evidence of the LMF model.Comment: 33 pages, 19 figure
Inferring microscopic financial information from the long memory in market-order flow: A quantitative test of the Lillo-Mike-Farmer model
株式市場での注文流の長期記憶性の起源解明 --18年来の理論的予言をデータ解析で実証--. 京都大学プレスリリース. 2023-11-09.In financial markets, the market-order sign exhibits strong persistence, widely known as the long-range correlation (LRC) of order flow; specifically, the sign autocorrelation function (ACF) displays long memory with power-law exponent γ, such that C(τ)∝τ^−γ for large time-lag τ. One of the most promising microscopic hypotheses is the order-splitting behavior at the level of individual traders. Indeed, Lillo, Mike, and Farmer (LMF) introduced in 2005 a simple microscopic model of order-splitting behavior, which predicts that the macroscopic sign correlation is quantitatively associated with the microscopic distribution of metaorders. While this hypothesis has been a central issue of debate in econophysics, its direct quantitative validation has been missing because it requires large microscopic datasets with high resolution to observe the order-splitting behavior of all individual traders. Here we present the first quantitative validation of this LMF prediction by analyzing a large microscopic dataset in the Tokyo Stock Exchange market for more than nine years. On classifying all traders as either order-splitting traders or random traders as a statistical clustering, we directly measured the metaorder-length distributions P(L)∝L^−α−1 as the microscopic parameter of the LMF model and examined the theoretical prediction on the macroscopic order correlation γ≈α−1. We discover that the LMF prediction agrees with the actual data even at the quantitative level. We also discuss the estimation of the total number of the order-splitting traders from the ACF prefactor, showing that microscopic financial information can be inferred from the LRC in the ACF. Our Letter provides the first solid support of the microscopic model and solves directly a long-standing problem in the field of econophysics and market microstructure
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