Kyle's Model with Stochastic Liquidity

TL;DR

This paper develops an equilibrium model for Kyle's framework incorporating stochastic liquidity, stochastic volatility, and correlated asset dynamics, revealing how noise trading volatility influences asset return distributions and market depth.

Contribution

It introduces a Kyle's model with stochastic liquidity and volatility, providing new insights into the impact of stochastic volatility on asset return distribution and market depth behavior.

Findings

Log-returns are Gaussian under certain conditions despite stochastic volatility.

Both Kyle's Lambda and market depth are submartingales in equilibrium.

The model captures the effect of stochastic noise trading on asset volatility.

Abstract

We construct an equilibrium for the continuous time Kyle's model with stochastic liquidity, a general distribution of the fundamental price, and correlated stock and volatility dynamics. For distributions with positive support, our equilibrium allows us to study the impact of the stochastic volatility of noise trading on the volatility of the asset. In particular, when the fundamental price is log-normally distributed, informed trading forces the log-return up to maturity to be Gaussian for any choice of noise-trading volatility even though the price process itself comes with stochastic volatility. Surprisingly, we find that in equilibrium both Kyle's Lambda and its inverse (the market depth) are submartingales.