A Stochastic Model of the Continuous Double Auction

Summary

This paper develops a microscopic statistical model of the continuous double auction, the order-matching mechanism used by many financial markets. It assumes independent, identically distributed random order flow and analyzes the resulting market behavior through simulation, dimensional analysis, and mean-field approximations. Inputs such as order and cancellation volumes, typical order size, and tick size are directly measurable, so the model requires no free parameters.

The model predicts properties including volatility, order-book depth, bid-ask spread, price impact, and the probability and timing of order fills. It identifies order-size granularity as a more important influence on market behavior than tick size in many cases, and offers an explanation for the concave shape of price impact. These are theoretical predictions grounded in simplified assumptions: random, nonstrategic order flow may not represent actual participants. The work presents zero-intelligence models as useful tools for testing how market structure shapes outcomes, not as complete accounts of market behavior.

Key ideas

• The model represents continuous double auctions with independent random order flow.
• Measured order-flow and order-book quantities determine predictions without free parameters.
• Predictions cover volatility, depth, spread, price impact, and order-fill behavior.
• Order-size granularity often matters more to market behavior than tick size.
• The model explains concave price impact but relies on simplified assumptions about order flow.

Tags

# Statistical theory of the continuous double auction


# Statistical theory of the continuous double auction









Most modern financial markets use a continuous double auction mechanism to store and match orders and facilitate trading. In this paper we develop a microscopic dynamical statistical model for the continuous double auction under the assumption of IID random order flow, and analyze it using simulation, dimensional analysis, and theoretical tools based on mean field approximations. The model makes testable predictions for basic properties of markets, such as price volatility, the depth of stored supply and demand vs. price, the bid-ask spread, the price impact function, and the time and probability of filling orders. These predictions are based on properties of order flow and the limit order book, such as share volume of market and limit orders, cancellations, typical order size, and tick size. Because these quantities can all be measured directly there are no free parameters. We show that the order size, which can be cast as a nondimensional granularity parameter, is in most cases a more significant determinant of market behavior than tick size. We also provide an explanation for the observed highly concave nature of the price impact function. On a broader level, this work suggests how stochastic models based on zero-intelligence agents may be useful to probe the structure of market institutions. Like the model of perfect rationality, a stochastic-zero intelligence model can be used to make strong predictions based on a compact set of assumptions, even if these assumptions are not fully believable.

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