Mean-field equilibrium of heterogeneous agents under market impact
How traders with different time horizons shape prices through collective action
When traders act on forecasts over different time periods—some thinking seconds ahead, others days or weeks—their collective buying and selling pushes prices up and down in predictable ways. This paper shows mathematically how an equilibrium emerges: traders anticipate both future signals and the market impact from others' moves, and at balance, the price's predictable component cancels out, leaving only random noise plus the collective footprint of their positions.
Understanding how market impact accumulates across traders with mismatched time horizons helps regulators and traders predict price movements and volatility patterns. The model explains why prices sometimes appear smoother or choppier depending on the mix of fast and slow traders in a market—knowledge that affects how exchanges are designed and how large trades should be executed to minimize disruption.