A continuous-time Kyle model with price-responsive traders

TL;DR

This paper extends the Kyle model to include price-responsive traders, revealing how feedback effects influence market dynamics, equilibrium properties, and insider profits in a continuous-time setting.

Contribution

It introduces a continuous-time Kyle model with momentum and contrarian traders, deriving a Kalman filter and Riccati system to analyze feedback effects on equilibrium.

Findings

Weak feedback leads to unique, smooth equilibria.

Stronger feedback causes complex dynamics and multiple equilibria.

Explicit comparative statics for insider profits and price informativeness.

Abstract

Classical Kyle-type models of informed trading typically treat noise trader demand as purely exogenous. In reality, many market participants react to price movements and news, generating feedback effects that can significantly alter market dynamics. This paper develops a continuous-time Kyle framework in which two types of price-responsive traders (momentum and contrarian traders) adjust their demand in response to price signals. This extension yields a finite-dimensional Kalman filter for price discovery and leads to a forward-backward Riccati system characterizing equilibrium. We show that when feedback is weak, equilibrium exists and is unique as a smooth perturbation of the classical Kyle solution, allowing us to derive explicit comparative statics for insider profits and price informativeness. For stronger feedback, the model generates rich dynamics, including potential multiplicity of equilibria and amplification effects. Our framework thus bridges the gap between purely exogenous noise and more realistic, behaviorally motivated trading.