Reduced form modeling of limit order markets

TL;DR

This paper introduces a simplified stochastic model for limit order markets that incorporates liquidity risk factors, enabling effective analysis and calibration to real market data, capturing key microstructural properties.

Contribution

It presents a new parametric modeling approach that extends classical market models with liquidity factors, facilitating calibration and analysis of market microstructure.

Findings

Model captures liquidity mean reversion

Reproduces crowding out effect on price moves

Effective for analyzing market resiliency

Abstract

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.