How to Build a Cross-Impact Model from First Principles: Theoretical Requirements and Empirical Results

24 Pages Posted: 29 Apr 2020 Last revised: 4 Feb 2021

See all articles by Mehdi Tomas

Mehdi Tomas

Ecole Polytechnique

Iacopo Mastromatteo

Capital Fund Management

Michael Benzaquen

Ecole Polytechnique, Palaiseau; Capital Fund Management

Date Written: April 3, 2020

Abstract

Trading a financial instrument induces a price response on itself and on other correlated instruments, a phenomenon known as cross-impact. Unfortunately, empirical measures of cross-impact are affected by a large estimation error due to both the large number of interactions to infer and the strongly fluctuating nature of price returns. In this study we propose a principled approach that leverages simple consistency criteria (symmetries, no-arbitrage conditions, correlation and liquidity limit-case properties) in order to impose ex-ante properties that might be required for practical applications. We validate our approach on empirical data for several asset classes, thus determining which properties are desirable across multiple markets. In particular, our results show that two cross-impact models perform well in all markets studied but only one is suitable for other applications, such as optimal execution.

Suggested Citation

Tomas, Mehdi and Mastromatteo, Iacopo and Benzaquen, Michael, How to Build a Cross-Impact Model from First Principles: Theoretical Requirements and Empirical Results (April 3, 2020). Available at SSRN: https://ssrn.com/abstract=3567815 or http://dx.doi.org/10.2139/ssrn.3567815

Mehdi Tomas

Ecole Polytechnique ( email )

Route de Saclay
Palaiseau, 91128
France

Iacopo Mastromatteo

Capital Fund Management ( email )

France

Michael Benzaquen (Contact Author)

Ecole Polytechnique, Palaiseau ( email )

Route de Saclay
Palaiseau, 91128
France

Capital Fund Management ( email )

23 rue de l'Université
Paris, 75007
France

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
236
Abstract Views
1,018
rank
151,330
PlumX Metrics