Reduced-Form Stochastic Models of Limit Order Market Liquidity

Summary

This paper develops parametric stochastic models for limit order markets by extending classical models of perfectly liquid markets with a small set of risk factors describing order-book liquidity. The reduced-form approach is intended to remain tractable: its models can be calibrated and analyzed with standard methods for multivariate stochastic processes. The paper argues that this compact representation can still capture several market properties identified in microstructure research.

A continuous-time model with three factors is calibrated to Copenhagen Stock Exchange data. The calibration exhibits mean reversion in liquidity and a crowding-out effect that influences subsequent mid-price movements. The authors also present the dynamic models as a way to study market resiliency after liquidity shocks. The evidence described is a calibration to one exchange's data; the summary does not provide out-of-sample forecasting results, specific calibration details, or proof that the same behavior holds across markets. The work is a modeling framework for liquidity dynamics rather than a trading strategy.

Key ideas

• Liquidity properties can be represented by adding a small number of risk factors to a classical market model.
• The proposed stochastic models are designed for standard calibration and analysis methods.
• Copenhagen Stock Exchange calibration shows mean-reverting liquidity and a crowding-out effect on later mid-price moves.
• The dynamic framework can be used to analyze resiliency after liquidity shocks.

Tags

# Reduced form modeling of limit order markets


# Reduced form modeling of limit order markets









This paper proposes a parametric approach for stochastic modeling of limit order markets. The models are obtained by augmenting classical perfectly liquid market models by few additional risk factors that describe liquidity properties of the order book. The resulting models are easy to calibrate and to analyze using standard techniques for multivariate stochastic processes. Despite their simplicity, the models are able to capture several properties that have been found in microstructural analysis of limit order markets. Calibration of a continuous-time three-factor model to Copenhagen Stock Exchange data exhibits e.g.\ mean reversion in liquidity as well as the so called crowding out effect which influences subsequent mid-price moves. Our dynamic models are well suited also for analyzing market resiliency after liquidity shocks.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.