A quantitative model of trading and price formation in financial markets

TL;DR

This paper develops a physics-inspired quantitative model of financial markets, predicting key properties like price diffusion, spread, and impact functions based on order flow rates, revealing how randomness induces complex market behaviors.

Contribution

It introduces a novel physics-based approach to model market dynamics using Poisson processes, providing testable predictions for price formation and trading costs.

Findings

Price diffusion exhibits anomalous scaling due to order flow.

Market microstructure properties can be derived from order flow rates.

Random order flow can produce complex temporal price structures.

Abstract

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.