Optimizing Limit and Market Order Placement Across Exchanges

Summary

The document presents a framework for deciding how to execute trades in electronic equity markets. A trader may use market orders or limit orders, and may route orders across exchanges. The proposed formulation treats order placement as a convex optimization problem, connecting the decision to order flow, queue sizes in limit order books, exchange fees and rebates, and the trader’s preferences.

For a single exchange, the authors derive an explicit solution for splitting orders between market and limit orders. For multiple exchanges, they propose a stochastic algorithm to compute an optimal policy and use a numerical implementation to examine how the solution responds to parameter changes. This provides a structured way to analyze execution choices, but the description supplies no numerical findings or details of the assumptions, calibration, or real-world validation. The resulting policy’s usefulness will depend on how well its inputs represent the live order books, order flow, and fee schedules faced by a trader.

Key ideas

• Order placement depends on order flow, queue sizes, fees and rebates, and trader preferences.
• The framework formulates execution choices as a convex optimization problem.
• For one exchange, the method derives an explicit split between market and limit orders.
• For multiple exchanges, a stochastic algorithm computes an optimal placement policy.
• Numerical analysis examines sensitivity to model parameters, but the document gives no specific results.

Tags

# Optimal order placement in limit order markets


# Optimal order placement in limit order markets









To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and queue sizes in each limit order book, as well as the structure of transaction fees and rebates across exchanges. We propose a quantitative framework for studying this order placement problem by formulating it as a convex optimization problem. This formulation allows to study how the interplay between the state of order books, the fee structure, order flow properties and preferences of a trader determine the optimal placement decision. In the case of a single exchange, we derive an explicit solution for the optimal split between limit and market orders. For the general problem of order placement across multiple exchanges, we propose a stochastic algorithm for computing the optimal policy and study the sensitivity of the solution to various parameters using a numerical implementation of the algorithm.

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