This study generalizes an econophysics model to account for trader heterogeneity, finding robust power-law exponents but sensitive prefactors.
problem The original Lillo-Mike-Farmer model assumed homogeneity in traders' order-splitting strategies, which this study generalizes.
method The study proposes a generalised Lillo-Mike-Farmer model and solves it exactly without heuristic assumptions.
result The power-law exponent in the order-sign ACF is robust for arbitrary heterogeneous intensity distributions, but the prefactor is sensitive to heterogeneity.
Quantitative analysis of order-splitting behavior in Japanese stock market.
problem Understanding and quantifying the order-splitting behavior of traders in the Japanese stock market.
method Analysis of a large dataset of trading accounts over nine years, clustering traders into order-splitting and random traders, and applying statistical methods to analyze metaorder length and sign correlation.
result The metaorder length distribution follows power laws with exponent α, and the sign correlation exponent γ is approximately α-1, supporting the LMF model.
Model identifies order splitting and liquidity replenishment as necessary for the square-root law of market impact.
problem Quantifying the square-root law of market impact and identifying its underlying mechanisms.
method Minimal limit-order-book model with heterogeneous interacting agents calibrated against real data. Counterfactual ablation to isolate mechanisms.
result Order splitting and liquidity replenishment are necessary for the square-root law of market impact.
High order splitting schemes with complex timesteps are applied to Kolmogorov backward equations stemming from stochastic differential equations in Stratonovich form. In the setting of weighted spaces, the necessary analyticity of the split semigroups can be easily proved. A numerical example from interest rate theory,…
Researchers validate LMF order-splitting theory using public JSE data.
problem Lack of reproducibility and cross-market validation of LMF theory due to proprietary data.
method Synthetic metaorder reconstruction using publicly available JSE data.
result LMF theory validated using JSE data for 100 largest stocks.
Study validates Lillo-Mike-Farmer model predicting financial market long-range correlations.
problem Quantifying long-range correlations in financial markets.
method Analyzed nine years of market data to classify traders as order-splitting or random, measured metaorder-length distributions, and compared to LMF model predictions.
result Agreement between LMF model predictions and actual data, validating the model.
Bayesian framework explains price formation with learning and market impact.
problem Understanding how prices form in markets with informed participants.
method Introduces a Bayesian model for updating priors on efficient prices.
result Exponential intensities for aggressive order arrivals are a natural outcome.
Order flow in equity markets is remarkably persistent in the sense that order signs (to buy or sell) are positively autocorrelated out to time lags of tens of thousands of orders, corresponding to many days. Two possible explanations are herding, corresponding to positive correlation in the behavior of different invest…
This paper presents a continuous-time model of intraday trading, pricing, and liquidity with dynamic TWAP and VWAP benchmarks. The model is solved in closed-form for the competitive equilibrium and also for non-price-taking equilibria. The intraday trajectories of TWAP trading targets cause predictable intraday pattern…
This paper investigates the equilibrium interactions between trading targets and private information in a multi-period Kyle (1985) market. There are two investors who each follow dynamic trading strategies: A strategic portfolio rebalancer who engages in order splitting to reach a cumulative trading target and an uncon…
This paper is dedicated to the construction of high-order (in both space and time) finite-difference schemes for both forward and backward PDEs and PIDEs, such that option prices obtained by solving both the forward and backward equations are consistent. This approach is partly inspired by Andreasen & Huge, 2011 who re…
New approach connects stochastic gradient descent to ODE splitting schemes.
problem Improving convergence in stochastic optimization.
method Connection between stochastic gradient descent and ODE splitting schemes.
result Derive a new upper bound on global splitting error.
We present a study of price impact in the over-the-counter credit index market, where no limit order book is used. Contracts are traded via dealers, that compete for the orders of clients. Despite this distinct microstructure, we successfully apply the propagator technique to estimate the price impact of individual tra…
Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. This leads us to adopt the fractional s…
Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [2, 19]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large orders are broken up into pieces and executed incrementally. If the size of such lar…
Minimal Morse functions on Poincaré dodecahedral space are selected via spectral properties.
problem Identifying minimal Morse functions on the Poincaré dodecahedral space.
method Spectral selection property P, obstruction principle, conformal variations, finite dimensional reduction.
result Restoration of minimal Morse selection on the Poincaré dodecahedral space via spectral mechanisms.
Improved decision tree learning guarantees for complex functions.
problem Achieving provable guarantees for decision tree induction with complex target functions.
method Introduces a new splitting criterion that considers correlations between target function and subsets of attributes.
result Proves provable guarantees for all target functions with respect to the uniform distribution, circumventing previous impossibility results.
Hybrid RL method optimizes trading by balancing continuous and discrete actions.
problem Optimal execution in algorithmic trading with continuous-discrete action space.
method Combines continuous and discrete RL agents for better trading decisions.
result Significantly outperforms existing methods in trading efficiency and stability.
A simple learning agent learns to trade in an agent-based market model.
problem Optimal execution of trades in an agent-based financial market model.
method Asynchronous trading through a matching engine, varying initial order sizes and state spaces, calibration of empirical stylized facts and price impact curves.
result Smaller state space agents converge faster in learning and can trade intuitively using spread and volume states.
Large trades in a financial market are usually split into smaller parts and traded incrementally over extended periods of time. We address these large trades as hidden orders. In order to identify and characterize hidden orders we fit hidden Markov models to the time series of the sign of the tick by tick inventory var…