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Kyle's Model with Stochastic Liquidity and Volatility

Article arXiv papers · Author: Ibrahim Ekren et al.
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Summary

This paper derives a continuous-time equilibrium for Kyle's insider-trading model when noise-trading liquidity is stochastic. It permits a general distribution for the asset's fundamental value and allows stock and volatility dynamics to be correlated. For fundamentals with positive support, the framework is used to examine how changing noise-trading volatility affects asset volatility.

In the log-normal fundamental-value case, the authors find that informed trading makes the log return at maturity Gaussian, despite stochastic volatility in the price process. They also report that both Kyle's Lambda, which measures price impact, and its inverse, market depth, are submartingales in equilibrium. These are theoretical equilibrium results under the model's assumptions; the excerpt provides no empirical validation or guidance on estimating the model from market data.

Key ideas

  • The model extends continuous-time Kyle trading to stochastic liquidity and correlated stock and volatility dynamics.
  • It allows a general distribution for the fundamental price and studies positive-support cases.
  • With log-normal fundamentals, equilibrium log returns at maturity are Gaussian despite stochastic price volatility.
  • Both price impact and market depth are submartingales in the reported equilibrium.
  • The excerpt presents theoretical findings without empirical validation details.

Tags

Market microstructureStatisticsVolatilityEquities
Full text
# Kyle's Model with Stochastic Liquidity


# Kyle's Model with Stochastic Liquidity









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.