Microfounding GARCH Models and Beyond: A Kyle-inspired Model with Adaptive Agents

TL;DR

This paper relaxes the rationality assumption in Kyle's model, introducing adaptive agents to microfound GARCH-like volatility dynamics and explaining phenomena like excess volatility and clustering without relying on fundamental shocks.

Contribution

It develops a stylised Kyle-inspired model with adaptive agents that microfound GARCH behavior and captures complex market phenomena.

Findings

Microfoundation for GARCH models established.

Volatility clustering linked to trader behavior, not fundamental shocks.

Model extends to explain flash crash dynamics.

Abstract

We relax the strong rationality assumption for the agents in the paradigmatic Kyle model of price formation, thereby reconciling the framework of asymmetrically informed traders with the Adaptive Market Hypothesis, where agents use inductive rather than deductive reasoning. Building on these ideas, we propose a stylised model able to account parsimoniously for a rich phenomenology, ranging from excess volatility to volatility clustering. While characterising the excess-volatility dynamics, we provide a microfoundation for GARCH models. Volatility clustering is shown to be related to the self-excited dynamics induced by traders' behaviour, and does not rely on clustered fundamental innovations. Finally, we propose an extension to account for the fragile dynamics exhibited by real markets during flash crashes.