Linear models for the impact of order flow on prices I. Propagators: Transient vs. History Dependent Impact

TL;DR

This paper compares two models of market impact, the Transient Impact Model and the History Dependent Impact Model, extending them to include both price-changing and non-price-changing events, leading to improved market impact descriptions especially for large tick stocks.

Contribution

The paper introduces a two-event framework for impact models, enhancing the description of market impact by incorporating both price-changing and non-price-changing events, and demonstrates the superior performance of HDIMs.

Findings

Two-event models significantly improve impact description for large tick stocks.

HDIMs outperform TIMs slightly, despite being theoretically more consistent.

Extended models capture the anti-correlation between past returns and order flow.

Abstract

Market impact is a key concept in the study of financial markets and several models have been proposed in the literature so far. The Transient Impact Model (TIM) posits that the price at high frequency time scales is a linear combination of the signs of the past executed market orders, weighted by a so-called propagator function. An alternative description -- the History Dependent Impact Model (HDIM) -- assumes that the deviation between the realised order sign and its expected level impacts the price linearly and permanently. The two models, however, should be extended since prices are a priori influenced not only by the past order flow, but also by the past realisation of returns themselves. In this paper, we propose a two-event framework, where price-changing and non price-changing events are considered separately. Two-event propagator models provide a remarkable improvement of the description of the market impact, especially for large tick stocks, where the events of price changes are very rare and very informative. Specifically the extended approach captures the excess anti-correlation between past returns and subsequent order flow which is missing in one-event models. Our results document the superior performances of the HDIMs even though only in minor relative terms compared to TIMs. This is somewhat surprising, because HDIMs are well grounded theoretically, while TIMs are, strictly speaking, inconsistent.