Statistical modeling and simulation of limit order markets

Thesis

This thesis focuses on the statistical modeling of order flow in limit order markets and the development data-driven approaches for the simulation of limit order book dynamics.

In the first part, after introducing various mathematical representations of limit order books (LOB) reflecting different degrees of granularity and information, we investigate the heterogeneity of order flow submitted through brokers using proprietary execution data and unsupervised learning techniques. This results in a statistical description of client order flow as a superposition of four components representing four heterogeneous types of agents – Quantitative, Day VWAP, Signal and Res – which differ through their trade frequency, intraday activity patterns and order sizes.

The second part of the thesis develops data-driven simulation methods for limit order book dynamics. We first present a generative model for transitions of limit order book snapshots using generative adversarial networks (GANs). The model allows efficient simulation of snapshot time series reproducing desired properties and furthermore automatically reflects market impact when interacting with the order book state. Lastly, we propose a hierarchical approach to improve existing LOB simulation methods. In particular, we present a probabilistic model to generate calibrations of order flow models. This preserves theoretical properties of the underlying base model and allows to incorporate realistic features of intraday dynamics such as U-shaped intraday seasonality and trends, volatility dependency and market disruptions into LOB simulations.

Authors: Prenzel, F

• DOI: 10.5287/ora-j5kxoaza1
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: simulation; limit order books; statistical modeling; generative adversarial networks; quantitative finance; market microstructure
• Subjects: Finance--mathematical models