Optimal Order Placement in Limit Order Markets

Abstract

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 characteristics of the order flows 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 optimal order placement decision depends on the interplay between the state of order books, the fee structure, order flow properties and the aversion to execution risk. In the case of a single exchange, we derive an explicit solution for the optimal split between limit and market orders. For the general case of order placement across multiple exchanges, we propose a stochastic algorithm that computes the optimal routing policy and study the sensitivity of the solution to various parameters. Our algoirthm does not require an explicit statistical model of order flow but exploits data on recent order fills across exchanges in the numerical implementation of the algorithm to acquire this information through a supervised learning procedure.

Multistage Stochastic Programming for VPP Trading in Continuous Intraday Electricity Markets

“…However, the theoretical comparison of IOC and POC models would require the discussion about whether it is profitable for the VPP to submit a market order or a limit order. This topic is well studied in financial market literature [29]. It is an interesting direction for future work in the context of CID electricity markets.…”

Optimal Liquidation and Adverse Selection in Dark Pools

“…Guilbaud and Pham () consider a pro rata market where investors can control their relative usage of market and limit orders, but do not optimize the limit order prices nor sizes. Cont and Kukanov () extend the literature on several fronts, including adverse selection, limit order execution probability being influenced by the observable liquidity in the limit order book, price impact of displayed limit orders (even if unfilled), and simultaneous use of multiple exchanges. They investigate these features in a model with a fixed limit order price but variable limit order size and trading at two discrete time points.…”