A reduced-form model for level-1 limit order books

TL;DR

This paper develops a nonparametric discrete model for level-1 limit order book dynamics, capturing empirical features like drift, correlation, and volatility, and approximates it with a tractable reduced-form diffusion model.

Contribution

It introduces a new nonparametric discrete model for level-1 limit order books that aligns with empirical data and can be approximated by a simplified diffusion model.

Findings

Empirical evidence of drift, correlation, and volatility dependence on order book imbalance.

A nonparametric discrete model fitting empirical correlation and volatility.

Analytical reduced-form approximation of the discrete model.

Abstract

One popular approach to model the limit order books dynamics of the best bid and ask at level-1 is to use the reduced-form diffusion approximations. It is well known that the biggest contributing factor to the price movement is the imbalance of the best bid and ask. We investigate the data of the level-1 limit order books of a basket of stocks and study the numerical evidence of drift, correlation, volatility and their dependence on the imbalance. Based on the numerical discoveries, we develop a nonparametric discrete model for the dynamics of the best bid and ask, which can be approximated by a reduced-form model with analytical tractability that can fit the empirical data of correlation, volatilities and probability of price movement simultaneously.