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Kyle’s model with stochastic liquidity

Author

Listed:
  • Ibrahim Ekren

    (University of Michigan)

  • Brad Mostowski

    (Florida State University)

  • Gordan Žitković

    (The University of Texas at Austin)

Abstract

We construct an equilibrium for the continuous-time Kyle 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 lognormally 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.

Suggested Citation

  • Ibrahim Ekren & Brad Mostowski & Gordan Žitković, 2025. "Kyle’s model with stochastic liquidity," Finance and Stochastics, Springer, vol. 29(4), pages 1195-1231, October.
    • Handle: RePEc:spr:finsto:v:29:y:2025:i:4:d:10.1007_s00780-025-00574-4
    DOI: 10.1007/s00780-025-00574-4
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    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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