Microscopic Understanding of Cross-Responses between Stocks: a Two-Component Price Impact Model

TL;DR

This paper develops a two-component price impact model to understand how stocks influence each other's prices through short-term liquidity and information flow, supported by empirical data analysis.

Contribution

It introduces a novel impact model incorporating self- and cross-impact functions with parameters fixed by a diffusion measure, enhancing understanding of cross-responses in correlated markets.

Findings

Cross- and self-correlators are linked to cross-responses.

Impact functions compensate for amplification effects due to sign correlators.

Price impacts have temporary and permanent components.

Abstract

We construct a price impact model between stocks in a correlated market. For the price change of a given stock induced by the short-run liquidity of this stock itself and of the information about other stocks, we introduce a self- and a cross-impact function of the time lag. We model the average cross-response functions for individual stocks employing the impact functions of the time lag, the impact functions of traded volumes and the trade-sign correlators. To quantify the self- and cross-impacts, we propose a construction to fix the parameters in the impact functions. These parameters are further corroborated by a diffusion function that measures the correlated motion of prices from different stocks. This construction is mainly ad hoc and alternative ones are not excluded. It turns out that both the sign cross- and self-correlators are connected with the cross-responses. The self- and cross-impact functions are indispensable to compensate amplification effects which are due to the sign correlators integrated over time. We further quantify and interpret the price impacts of time lag in terms of temporary and permanent components. To support our model, we also analyze empirical data, in particular the memory properties of the sign self- and average cross-correlators. The relation between the average cross-responses and the traded volumes which are smaller than their average is of power-law form.