# Liquidity Fluctuations and the Latent Dynamics of Price Impact

40 Pages Posted: 14 Aug 2018 Last revised: 22 Dec 2020

See all articles by Luca Mertens

Bloomberg LP

## Alberto Ciacci

Imperial College London - Department of Physics

## Fabrizio Lillo

Università di Bologna

## Giulia Livieri

Scuola Normale Superiore

Date Written: January 20, 2019

### Abstract

Market liquidity is a latent and dynamic variable. We propose a dynamical linear price impact model at high-frequency in which the price impact coefficient is a product of a daily, a diurnal, and an auto-regressive stochastic intraday component. We estimate the model using a Kalman filter on order book data for stocks traded on the NASDAQ in 2016. We show that our price changes estimates conditional on order flow imbalance explain, on average, $82\%$ of real price changes variance. Evidence is also provided on the fact that the conditioning on filtered information improves the estimate of the \text{LOB} liquidity with respect to the one obtained from a static estimation of the price impact. In addition, an out-of-sample analysis shows that our model provides a superior out-of-sample forecast of price impact with respect to historical estimates.

Keywords: market impact, market liquidity, Kalman filter, dynamic linear models, order book depth

JEL Classification: C51, C52, G12

Suggested Citation

Mertens, Luca and Ciacci, Alberto and Lillo, Fabrizio and Livieri, Giulia, Liquidity Fluctuations and the Latent Dynamics of Price Impact (January 20, 2019). Available at SSRN: https://ssrn.com/abstract=3214744 or http://dx.doi.org/10.2139/ssrn.3214744