Market impact with multi-timescale liquidity

TL;DR

This paper extends a model of latent liquidity in financial markets to include finite memory effects, providing new insights into impact laws, impact decay, and the price diffusivity puzzle.

Contribution

It introduces a multi-timescale liquidity model with finite cancellation and deposition rates, explaining empirical impact laws and addressing the price diffusivity puzzle.

Findings

Finite memory corrections modify the impact law.

Impact decay and permanent impact are characterized.

A spectrum of rates explains empirical impact behavior.

Abstract

We present an extended version of the recently proposed "LLOB" model for the dynamics of latent liquidity in financial markets. By allowing for finite cancellation and deposition rates within a continuous reaction-diffusion setup, we account for finite memory effects on the dynamics of the latent order book. We compute in particular the finite memory corrections to the square root impact law, as well as the impact decay and the permanent impact of a meta-order. The latter is found to be linear in the traded volume and independent of the trading rate, as dictated by no-arbitrage arguments. In addition, we consider the case of a spectrum of cancellation and deposition rates, which allows us to obtain a square root impact law for moderate participation rates, as observed empirically. Our multi-scale framework also provides an alternative solution to the so-called price diffusivity puzzle in the presence of a long-range correlated order flow.