Simulation of Limit Order Books

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Most electronic stock exchanges nowadays organize trades via limit order books (LOBs), in order to facilitate trading activity. A limit order book is a centralized record of all outstanding buy (sell) limit orders, which indicate a buyer's (seller's) offer to buy (sell) a specified quantity of a particular stock for a certain price, at a given venue (XETRA, NASDAQ, etc.). These orders remain in the order book until they get either cancelled or executed by a sell (buy) market order.Due to the availability of vasts amounts of historical limit order book data, a lot of research has been devoted in recent years to study empirical aspects of limit order books, investigate how the price is formed within limit order books, how price movements in limit order books may be predicted, as well as methods to simulate limit order books. All those tasks are of complicated nature as many heterogeneous agents with different objectives and different sets of information interact together in limit order books. This turns the limit order book of a stock, future, etc. into a complex, high-dimensional system evolving over time with non-trivial dynamics.The aim of this research project is the development of models to simulate limit order book data which reproduces certain empirical properties observed in real limit order books. These properties regard the resulting price paths, order book shape and order inter-arrival times, as well as non-stationarity patterns. Ultimately, limit order books are responsive systems in which actions affect each other. In essence, if some trader places a limit order, the market (limit order book) reacts to this placement which changes the development of the LOB. Thus, a "useful" model should also be able to simulate the reactions of a limit order book realistically, if an order is placed in the book. Models to simulate LOBs are useful for a variety of things. First of all, they help to better understand financial markets in a variety of scenarios (e.g. during crises). Second, it alleviates issues regarding data sharing. Third, enrichment of data sets from tail events (crises, etc.) can help render financial algorithms more robust, as they can be tested in more critical situations than what is available in historical data.Point processes, multi-agent systems and more have been applied to model limit order books, and are able to reproduce some of the typical characteristics observed in limit order books, but most approaches lack in certain dimensions. Recently, the advent of machine learning and advances in computational power allowed to apply data-driven, non-parametric approaches for the simulation of financial data on a much larger scale than ever before. Despite their lack of analytical tractability, machine learning algorithms tend to be more flexible than conventional models. In particular, generative adversarial networks (GANs) and their extensions have recently been applied to (multivariate) time series generation. The research applying generative adversarial networks to generate limit order book data is yet very limited to. This project aims to develop novel GAN architectures suitable to generate limit order book data, e.g. processes of quantities and prices, with realistic properties which are lacking from the current literature.The project is aligned with the following topics: (1) Artificial intelligence technologies, (2) statistics and applied probability, (3) non-linear systems, (4) operational research.The industrial partner/collaborator is J.P.Morgan.