How Random Order Flow Shapes Price Diffusion and Trading Costs

Summary

The document presents a quantitative model of market trading and price formation in which order arrivals and cancellations are treated as Poisson processes. It uses physics-inspired analysis, dimensional reasoning, simulations, and mean field theory to relate order flow rates to basic market properties.

The model derives scaling relationships for price diffusion, bid-ask spreads, and price impact, linking price risk and transaction costs to the mechanics of supplying liquidity. Its central insight is that even random order flow can produce anomalous price diffusion and temporal structure because orders must be stored to match buyers and sellers. The excerpt offers no empirical data, detailed equations, or specific calibration guidance, so the results should be understood as theoretical predictions whose practical fit would need to be assessed against market data.

Key ideas

• Order arrivals and cancellations are modeled as Poisson processes.
• Order flow rates help determine price diffusion, spreads, and price impact.
• The need to store supply and demand can create price structure even when order flow is random.
• The model combines dimensional analysis, simulation, and mean field theory to derive scaling relations.

Tags

# A quantitative model of trading and price formation in financial markets


# A quantitative model of trading and price formation in financial markets









We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of a market, such as the diffusion rate of prices, which is the standard measure of financial risk, and the spread and price impact functions, which are the main determinants of transaction cost. Guided by dimensional analysis, simulation, and mean field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.

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.