Limit Order Books (LOB) are the fundamental structure of modern markets. By receiving (or canceling) limit orders and market orders, the Bid and Ask queues are formed and trades are executed:
Basic functions for processing Limit and Market orders (including cancelations) can be found as a Python notebook at: https://github.com/MarcosCarreira/LimitOrderBooks.
The minimum interval between prices in the order book is the tick size, and depending of the choice of the relative tick size (tick size divided by the price of the asset), the “shape” and behavior of the LOB will be different.
In Simulating and analyzing order book data: The queue-reactive model, Mathieu and Charles develop a framework where, during the time period where a reference price such as the mid price remains constant, the LOB is modelled as a Markov queuing system, with the intensities of the order flows only depend on the current state of the order book. A stochastic mechanism allows for switches from one period of constant reference price to another. The model reproduces accurately the behavior of market data, and it very useful as a market simulator.
Othmane has worked on modeling the LOB and how best to interact with it from the point of view of a trader:
- Optimal liquidity-based trading tactics
- Optimal inventory management and order book modeling
- Limit Order Strategic Placement with Adverse Selection Risk and the Role of Latency