A Multi Agent Model for the Limit Order Book Dynamics

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A Multi Agent Model for the Limit Order Book Dynamics

Marco Bartolozzi
Published on 5/3/2010
Equities
Multi-Agent
High frequency trading

This paper presents a multi-agent model designed to simulate the dynamics of a double auction market at microscopic time scales by faithfully replicating the mechanics of a limit order book (LOB). The agents in the model are 'zero-intelligence' in the sense that they lack utility maximization; instead, their decisions are driven by a stochastic variable called 'market sentiment,' which combines public information (e.g., perceived volatility and liquidity) with private information modeled as Gaussian noise. The model incorporates realistic order submission, cancellation, and matching processes, including the generation of limit and market orders based on a log-normal distribution for price aggressiveness and volume.

Despite its simplicity, the model successfully reproduces several empirical stylized facts of high-frequency financial markets. Key results include negative autocorrelation in returns (bid-ask bounce), leptokurtic return distributions with fat tails, volatility clustering with a Hurst exponent of 0.61, and a nonlinear price impact function that becomes sublinear for large volumes. The average LOB shape exhibits a peak in liquidity near the mid-price, and the spread shows persistence and power-law tails. The model also captures the mean-reverting nature of volume imbalance between buy and sell orders.

The findings suggest that many features of short-term market dynamics can be explained without assuming rational agents, relying instead on simple stochastic decision rules and memory effects from moving averages of public information. The paper concludes that large price movements are more likely caused by temporary liquidity shortages in the LOB rather than by large trade volumes, and it outlines future work to incorporate herding behavior, news, and market-making strategies.

Highlights

  • 1Introduces a multi-agent model that faithfully simulates limit order book mechanics at microscopic time scales.
  • 2Agents use a stochastic 'market sentiment' variable combining public and private information for decision-making.
  • 3Reproduces key empirical features of high-frequency market microstructure, including volatility clustering and non-linear price impact.
  • 4Demonstrates that large price movements are primarily due to temporary liquidity gaps rather than large trade volumes.
  • 5Shows that memory effects from short-term moving averages of public information can generate volatility clustering.

Methods

  • M
    Multi-agent simulation with realistic limit order book mechanics (limit orders, market orders, cancellations).
  • M
    Market sentiment defined as a multiplicative process of public (volatility, liquidity) and private (Gaussian noise) information.
  • M
    Order generation using log-normal distributions for price aggressiveness and volume, with probabilistic mapping to limit or market orders.
  • M
    Detrended fluctuation analysis (DFA) to estimate Hurst exponents for returns, volatility, volume, and spread.

Results

  • R
    Returns exhibit negative autocorrelation (bid-ask bounce) and leptokurtic distribution with fat tails, consistent with empirical data.
  • R
    Volatility and traded volume show clustering with Hurst exponents of 0.61 and 0.70, respectively, matching real market behavior.
  • R
    Price impact function is linear for small volumes but becomes nonlinear for large volumes due to volume barriers in the LOB.
  • R
    Average LOB shape shows a peak in liquidity a few ticks from the mid-price, decaying away, similar to empirical findings.
  • R
    Spread dynamics display persistence (Hurst ~0.56) and a power-law tail distribution, though with weaker persistence than real markets.
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