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Kyle's Model with Stochastic Liquidity

Author
Ibrahim Ekren, Brad Mostowski, Gordan Žitković
Date Updated
2022/04/26
Category
q-fin.TR
Date Published
2022/04/23
Date Retrieved
2022/04/26
Description
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.
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URL
https://arxiv.org/abs/2204.11069
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