The Multivariate Kyle model: More is different

TL;DR

This paper extends the Kyle model to multiple correlated securities, establishing a unique impact matrix solution and demonstrating its practical application in calibrating cross-impact matrices in market microstructure.

Contribution

It introduces a unique symmetric impact matrix solution for the multivariate Kyle model and applies it to empirical data, improving calibration methods for cross-impact matrices.

Findings

Unique positive definite impact matrix solution established

Application to US Treasuries data demonstrates practical relevance

Provides a new inference procedure for market microstructure analysis

Abstract

We reconsider the multivariate Kyle model in a risk-neutral setting with a single, perfectly informed rational insider and a rational competitive market maker, setting the price of n correlated securities. We prove the unicity of a symmetric, positive definite solution for the impact matrix and provide insights on its interpretation. We explore its implications from the perspective of empirical market microstructure, and argue that it provides a sensible inference procedure to cure some pathologies encountered in recent attempts to calibrate cross-impact matrices. As an illustration, we determine the empirical cross impact matrix of US. Treasuries, and compare the results with recent alternative calibration methods.