Simulating and analyzing order book data: The queue-reactive model
Simulating and analyzing order book data: The queue-reactive model
The paper introduces the queue-reactive model for limit order books (LOB), which splits time into periods where a reference price (e.g., midprice) remains constant. Within these periods, the LOB is modeled as a continuous-time Markov jump process with state-dependent intensities for limit orders, cancellations, and market orders. The authors establish ergodicity conditions and estimate intensities from Euronext data for large-tick stocks like France Telecom. Three model variants are explored: independent queues (Model I), dependent queues with bid-ask symmetry (Model IIa), and cross-dependence between bid and ask sides (Model IIb). The invariant distributions derived from these models accurately match empirical queue size distributions, validating the approach. The model is extended to allow reference price moves via a stochastic mechanism, creating a full queue-reactive model that reproduces both microstructural dynamics and macroscopic volatility. Practical applications include market simulation and transaction cost analysis for complex trading algorithms. The work highlights how order flow intensities depend on LOB state, such as decreasing cancellation rates at best limits and exponential decay of market order intensity with queue size.
Highlights
- 1Introduces the queue-reactive model, splitting time into periods of constant reference price to model LOB dynamics as a Markov queuing system.
- 2Provides ergodicity conditions for the 2K-dimensional Markov jump process under general assumptions.
- 3Estimates order flow intensities from market data, revealing non-trivial dependencies on queue sizes (e.g., decreasing cancellation rates at best limits).
- 4Derives invariant distributions for independent and dependent queue models, matching empirical LOB shapes.
- 5Extends the model to include reference price moves, enabling simulation of price volatility and transaction cost analysis.
Methods
- MMarkov jump process modeling of LOB as a 2K-dimensional queue system with state-dependent intensities.
- MMaximum likelihood estimation of order flow intensities (limit, cancel, market) from high-frequency data.
- MMatrix geometric method for quasi birth-death processes to compute joint stationary distributions.
- MStochastic switching mechanism for reference price changes based on queue depletion or spread insertion.
Results
- RLimit order insertion intensity at best limits is roughly constant except near zero; cancellation intensity is concave increasing then flat.
- RMarket order intensity at best limits decreases exponentially with queue size.
- RInvariant distributions from Model I (independent queues) closely match empirical queue size distributions.
- RModel IIa (dependent queues) shows that limit order insertion at second limit decreases with queue size and is higher when first limit is empty.
- RThe queue-reactive model reproduces both microstructural and macroscopic price properties, with a 'maximal mechanical volatility' below empirical volatility.
Analyze Paper
Generate insights from "Simulating and analyzing order book data: The queue-reactive...".