A Stationary Kyle Model for Linear Price Impact and Propagators

Summary

This theoretical market microstructure model derives linear price impact from the equilibrium behavior of rational agents trading with asymmetric information. It generalizes the Kyle setup by removing the terminal date at which fundamental information is revealed, allowing the market to be stationary while retaining informed and noise-driven trading.

For Gaussian noise trades and fundamental information, the authors analyze the stationary equilibrium. They report that the model is consistent with universal price diffusion over short timescales, while longer timescales can exhibit non-universal mean reversion as fluctuations in fundamentals decay. The framework also yields a testable relationship connecting price volatility, the size of fundamental fluctuations, and traded volume. This is a model-based result rather than an empirical trading strategy; the supplied description does not include data tests or specify how the relationship should be estimated in a live market.

Key ideas

• Linear price impact is derived as an equilibrium outcome of rational informed and noise traders.
• Removing the terminal information-revelation date allows the model to describe a stationary market.
• The setup considers Gaussian noise trades and fundamental information.
• It predicts short-timescale diffusion and potentially non-universal mean reversion at longer scales.
• The model links price volatility, fundamental fluctuation size, and trading volume in a testable relationship.

Tags

# A Stationary Kyle Setup: Microfounding propagator models


# A Stationary Kyle Setup: Microfounding propagator models









We provide an economically sound micro-foundation to linear price impact models, by deriving them as the equilibrium of a suitable agent-based system. Our setup generalizes the well-known Kyle model, by dropping the assumption of a terminal time at which fundamental information is revealed so to describe a stationary market, while retaining agents' rationality and asymmetric information. We investigate the stationary equilibrium for arbitrary Gaussian noise trades and fundamental information, and show that the setup is compatible with universal price diffusion at small times, and non-universal mean-reversion at time scales at which fluctuations in fundamentals decay. Our model provides a testable relation between volatility of prices, magnitude of fluctuations in fundamentals and level of volume traded in the market.

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.